What are options and who needs them? Educational program for geeks, part 6 / Sudo Null IT News

My name is Mikhail Andreev, I am a developer in our FX Derivatives Desk division (in industry slang the position is called Quant Developer). In this post I will tell you about options and everything connected with them. These instruments are not as close to the common man as, for example, a bank deposit, but they are important for modern financial markets. And they are discussed periodically in the non-specialized media, and I think it is useful to have a general understanding of options and how financial companies work with them.

In addition, this topic is related to interesting mathematics, computational methods and the development of software systems - everything we love. This post is an extended version of my video lecture “Options. Basic parameters and examples of use" as part of the Finmath for Fintech course.

So let's start with a few simple definitions. Like everywhere else, there is a “bird language” here, which we will get to know a little.

What is an option?

Options are a class of derivative financial instruments.
The term “derivative” means that the payout under such a contract depends on the price of some underlying asset (underlying). The name seems to hint that such a tool provides some kind of optionality, that is, the ability to choose. But since there are two participants in the transaction, one of them receives the opportunity, and the other, on the contrary, undertakes the obligation that he will provide such an opportunity to choose.

Vanilla flavor

There are quite a large number of different options contracts.
There are simpler ones, there are more complex ones, with bells and whistles, and there are even more complex ones. In English, simple options are called plain vanilla option. According to the Internet, this is because the simplest and cheapest ice cream in an American stall was vanilla.

And the most vanilla option is the European option.

European option

A European option is a contract under which the buyer of the contract receives the right, but not the obligation, to buy or sell an underlying asset at a pre-agreed price at a time specified in the contract in the future.
The underlying asset can be a stock or a foreign exchange rate. An option on the exchange rate is called an FX option; it gives the right to exchange one currency for another at a pre-fixed rate. The market rate for the underlying asset is called spot and is denoted in formulas as St.

An option that gives the right to buy the underlying asset is called a call option. The right to sell is a put option. The price at which an option gives the right to enter into a transaction in the future is called a strike, denoted by .

The time specified in advance in the contract at which the option can be exercised is the option expiration date (expiry date).

Option

The concept of options is more often associated with the foreign exchange market, but it has a broader meaning. Legally, this is an agreement that presupposes the right to buy/sell an option, but does not obligate it to do so. We are talking about a pre-agreed price at a certain point in time or during a specific period of time.

What are options in simple words

The term “option” comes from the Latin. Optio, which translated means “choice, discretion, desire.” Futures are a similar financial instrument, but they have a number of fundamental differences. Options have been used for several centuries; until the 19th century, they helped develop the trade in tulip bulbs. They made it possible to agree on a future transaction even if the potential buyer did not have funds.

Options are a popular trading instrument.

Subsequently, the first share options were introduced on the London Stock Exchange. This happened in 1820. The initiative was taken up by US financiers, and already in 1860 the first assets in American stocks appeared on the Chicago Board Options Exchange (CBOE), and by the 1990s a full list of assets was formed to suit any needs.

In Russia, the main options trading platform is the Moscow Exchange Derivatives Market. Regardless of the selected asset, contracts to sell (Put Option), buy (Call Option) or bilateral (Double Option) are placed on the exchange. Since the 90s of the 20th century, attempts have been made to find a mathematical approach to trade and to form pricing models.

Exchange and over-the-counter options

Financial options are free transactions and therefore can be concluded not only within the framework of the exchange. The latter seek to transfer trading within the framework of special exchanges, but this does not guarantee the complete exclusion of those who wish to negotiate on their own.

All financial transactions on the stock exchange are aimed at making a profit.

As a result, there are two directions of trade:

OTC. They are concluded on free terms, the sellers here are usually large investment companies, and the buyers are companies that need to hedge risks on open positions and portfolios.
Exchange. Transactions are concluded through an intermediary, a clearing house. The functions of the clearing company include accounting of contracts. It acts as the “second party” to each trade and charges the appropriate “margin fee.”

The market continues to develop. This is how varieties appeared on the Forex and FLEX markets with free conditions for setting the expiration date and strike price. Legislative regulation changes following current trends in the financial market.

One of the obstacles to transferring transactions to an exchange basis is the “option premium,” which implies payment for the right to conclude contracts. The amount of payments depends either on the result of equalization of supply and demand in the market among buyers and sellers, or on the basis of a mathematical model that allows one to calculate the premium based on the current price of the underlying asset.

Options pricing models

At the first stages of the formation of market options, pricing was carried out in a random order, but since 1973, various models for the formation of asset prices began to form. Risky transactions were settled first. There was no other application for the CAMP model; the system turned out to be too highly specialized.

Option pricing models in the future are designed to reduce trading risks.

The most well-known pricing models are:

Black-Scholes model. It is considered the most common option. This system is also applicable for the company’s equity capital and derivative securities such as warrants. The main factor in pricing is the future volatility of the basis. The price rises and falls in proportion to the value of the asset.
Binomial model. Allows you to evaluate an option at any time before its exercise. The method is used on the American stock exchange, where it is possible to close a transaction at any time at the request of the seller/buyer.
Monte Carlo model. An estimate of the mathematical expectation of payment over the entire history of the underlying asset is used. The essence of the technique is similar to a dice - during the calculation process, the investor generates as many iterations as possible and calculates the average value from them.
Heston model. Applicable only on the European market. Works on the hypothesis of an asset price distribution that differs from lognormal, taking into account a random volatility value.

The last two pricing options are the most complex; specialized programs are usually used for calculations. Manual calculation requires a lot of time and specialized knowledge. Against this background, the Black-Scholes model is especially popular.

Types and styles of options

Existing financial instruments are divided into conditional categories. Thanks to this approach, it is easier to assess the risks and profitability of various assets and choose from the options presented by the exchange. There is also a division by type - American and European.

The division into categories makes it easier to choose the optimal type of asset.

Depending on the underlying asset, there are four main groups:

Commodity. Physical goods and futures for the supply of goods are involved.
Currency. Cash currency and currency futures are traded.
Stock. Options on shares (issuers), index futures.
Interest. Trading involves interest rate futures, agreements on future interest rates.

European/American options mainly differ in terms of maturity. The first ones can be repaid exclusively on the specified date. The second - on any day during the option period. In fact, American assets are determined only by the deadline for their placement on the stock exchange, while European ones work according to the classical scheme.

Binary options

When considering the question of what options are, most often we are talking about their binary variety. The key idea of this type of asset is to make a profit if specified conditions are met at a specified time, or no profit if the conditions are not met at the specified time. In practice, the latter means losses, since exchange commissions are inevitable.

An experienced trader is able to make a profit from falling and rising rates.

By analogy with other types of options, binary options are divided into the following types:

Call/Put. Implies a forecast of the direction of movement of value relative to the moment of acquisition of the asset.
One Touch/No Touch. The trader predicts the achievement of a certain price level (the first indicator) or the impossibility of this before the expiration point.
In/Out. The forecast is made either for price movement within the corridor or for its breakdown (until expiration).

The simplicity and accessibility of trading strategies in the binary options market is one of the components of the success of this asset. There are many examples of application: buying an option to exceed a certain price level, buying an increase to a specified price, and selling an option when the specified value is exceeded.

Legal aspects

The topic of options, including binary ones, from the point of view of legislative regulation has the status of a little-studied problem. Despite the long existence of this trading instrument on the world market, in Russia the issue of the legal status of options has not yet been resolved. On the one hand, there is an analogy with the Forex market, which is subject to a number of restrictive laws.

On the other hand, binary options are too similar to gambling, because the presence or absence of profit depends solely on whether the trader has guessed the price corridor and the price level in the future. A similar situation is developing in Israel, where organizations providing access to the options market were closed in a short time.

In most cases, traders can only rely on international practice and rely only on the integrity of brokers. An attempt to resolve the issue was the emergence of TsROFR, a controlling organization covering the binary options market. If the broker has received a certificate from this authority, you can count on guarantees of fair trading and protection of the interests of traders.

Why is this necessary?

Option as insurance

Essentially similar to an option and a familiar contract to everyone, it is insurance. Anyone who buys insurance receives the right, under certain conditions, to receive an insurance premium, and the insurance company undertakes to pay this premium. And here are a couple of examples.

Business Koli

Kolya is the owner of a jig production business.
Everyone needs a good jig, so Kolya is doing well. He entered the international market and sells jigs abroad. For example, production is located in a country where the currency XXX, widely known in academic literature, is used, and jigs are sold abroad to a country where another well-known currency, YYY, is used. Planning and managing the highly competitive jig business takes Kolya a lot of time and effort. And then there’s a new problem - the changing exchange rate of the YYY currency for the XXX currency. This exchange rate is designated XXXYYY.

Kolya knows the business well and can quite accurately say that in six months he will have a profit of 1 to 3 million YYY. They will need to be converted into XXX currency in order to pay salaries, rent, taxes and invest something in business development. What to do if during this time the XXXYYY rate goes up? Kolya is confident enough that he will definitely need to convert one million, so he can enter into a forward contract for one million XXXYYY. But there are another two million that he is not so sure about. Therefore, Kolya buys a call option on the XXXYYY currency pair.

Kolya bought a call option and will receive a payment at expiration:

If at the time of option expiration the market exchange rate ST was less than the strike, i.e. ST < K, then it is not profitable to use the Kolya option; it is cheaper to simply exchange the currency at the current rate. The option does not impose any obligations on Kolya in this case. By analogy with insurance, the “insured event” did not occur.

But if the exchange rate goes up, then Kolya will definitely want to exchange the currency at a rate equal to the option strike, which in this case will be more profitable than the market one.

Petit speculator strategy

Options are also used in various stock trading strategies.
Petya is a stock speculator and he has a super-ML-AI-crystal-ball-algorithm that predicts that in a month the shares of some company XYZ will plummet in price. Therefore, Petya buys a put option on XYZ stock. Those. the right to sell a share at the rate (option strike).

If the stock price at the time of expiration of the option (ST) really turned out to be below the strike, then Petya can buy the share on the market cheaper and sell this share, taking advantage of the right that the option gives him. Thus, Petya will make a profit: .

But if the stock price nevertheless goes in the other direction and turns out to be greater than the option strike, then the Petit option gives nothing, and the option payout is zero.

Petya bought a put option and at the time the option is exercised he will receive a payment: .

These examples do not mean that a put option is only for speculators, and a call option is for hedging risks. If Petit’s model predicted an increase in the exchange rate, then he would need a call option, and if Kolya’s business had developed in such a way that he needed to plan a currency exchange in the other direction, then the choice would be a put option.

It can be seen that the practical use of options in speculative strategies on the exchange rate of the underlying asset only requires correctly guessing which inequalities will be true for prices in the future. It's not that difficult (just kidding). The same applies to the use of combinations of vanilla options, which will be discussed below.

What is the power of options, why are they dangerous and how to calculate everything correctly

Almost all startups experience periods of limited resources, especially financial ones. The factor of a full-fledged team becomes critical when it comes time to raise the first investment round. The investor wants to see a project that has the core competencies necessary for success. Many people use options to attract and retain valuable employees. Essentially, this is an opportunity to hire employees for promises of participation in co-ownership of the company. We tell you how to use them correctly.

The essence of the option

An option is an agreement under which an employee receives the right to buy back shares of the company at a pre-agreed price within a certain period of time. It is assumed that under such conditions the employee will make every effort to increase the value of the company, because at the same time the value of his option increases.

Options are used by most non-public companies in the Silicon Valley technology sector. All the early employees of Google, Facebook and other mega-successful companies made millions from their stock options. In Silicon Valley, you'll hear plenty of stories (sometimes urban legends) about owners of dry cleaners, pizzerias, sandwich shops, and even hair salons who provided their services to young Apple, Sun, Cisco, Yahoo, AirBnB and other future unicorns for stock options and made millions of dollars from these companies. .

In some ways, receiving options is an honor, so the opportunity to receive an option is given to employees who have proven their worth. Options are also standard practice when hiring executives and other key team members.

In-the-money option and out-of-the-money option

When the price of the underlying asset at expiration is such that the option payout is zero, the option is said to have ended out-of-the-money (OTM) .
For a call option this means ST < K, for a put option - ST > K. If the rate is on the other side of the strike, then they say that the option turned out to be in-the-money (ITM) . The case of equality ST = K is called at-the-money (ATM) .

At the time the option contract is concluded, no one knows what the price of the underlying asset will be at the time the option is exercised. But the current price of the asset is known to everyone. If we apply discount rules to the current price, we can calculate the fair price of a forward contract for this underlying asset with a delivery time equal to the option expiration time. This is called at-the-money forward (ATMF) . Knowing this price, you can divide options that have not yet expired into ITM and OTM, depending on the option strike.

For strikes less than the ATMF, call options will be in-the-money and put options will be out-of-the-money. For strikes larger than ATMF, the opposite will happen.

Formally, you can define both call and put options for any strike, but in practice at-the-money-forward and out-of-the-money options will be liquid. After all, if the option strike is deep in the in-the-money zone, then the probability that the option will be exercised is estimated by the market to be close to one, and the price of such a contract is determined more by discounting than by the optionality specified by the option strike. Sometimes you can trade ITM options, but only if their strike is close enough to the ATMF level.

What is an option contract

This concept and its features are regulated by Art. 429.3 of the Civil Code: the conclusion of an option agreement implies the obligation of one party to perform in favor of the other party upon first request the action established by the document, for example, to deliver goods or perform work.

In essence, this document is any civil transaction with a deferred execution “until demand”.

Fantastic options and where they live

So where can you buy an option?
The answer, as often happens, begins with the words “it depends...”. First of all, it depends on what underlying asset you want to buy an option on. Stock markets, exchange rates, interest rates, commodity exchanges (commodity) differ from each other. Naturally, trading options on different underlying assets has its own characteristics.

Exchange

Let's start with stock options.
Shares are usually bought and sold on an exchange. For an option contract, this is convenient because there is a good source of the stock price, incl. It is easy to determine the value of the option at the time of expiration. This rate, from the option point of view, is the spot rate. You can even use some popular stock price index, such as the S&P500, as a spot rate for an option. Trading securities through an exchange is such a successful idea that stock options are also traded on an exchange. For example, on the Chicago Board Options Exchange. In order to organize options trading on the stock exchange, it is necessary to standardize the parameters of options. For a vanilla option, these are: the underlying asset, the strike, and the expiry.

Moreover, in order for trading an option with given parameters on the stock exchange to make sense, it is necessary that this option option be sufficiently liquid, i.e. for him there would be a sufficient number of people willing to buy and sell.

Non-exchange

Not everyone and not always have enough of the options that can be bought on the stock exchange.
What to do? Buy or sell not on the stock exchange! Such transactions are called over-the-counter (OTC). In principle, this can be a transaction between any market participants. But where OTC markets arise, there is someone who specializes in providing quotes (and therefore the ability to buy/sell): market makers. With the development of computers and digital communication channels, OTC markets have changed greatly. Previously, for such a transaction it was necessary to call the market maker or intermediary by phone. Now everything can be done through specialized programs. There are software interfaces for receiving quotes and making trades for use in trading robots. In active markets, there are aggregators that will automatically find the best buy and sell offer for a given contract automatically by asking different market makers. In many ways, at least from the point of view of liquidity, availability of current quotes and ease of entering into a transaction, this is no longer much different from trading on the stock exchange. An example of a successful OTC market is the foreign exchange market and the FX market. And options on it are also actively traded.

The advantage of the OTC market is that there is no need to introduce standards for the contracts that can be traded. Therefore, the market maker can provide clients with the opportunity to request a price for any contract for which the market maker is able to calculate the price.

For vanilla options, this means arbitrary strike and expiration values. But this is just the beginning. There are many different variants of options besides vanilla options. Anything that is not a vanilla option is called an exotic option, or exotic for short.

I will tell you about some exotics below. Now it is important to note that each type of exotic options also has other parameters that vanilla options do not have, and the problem of standardizing contracts for exchange trading becomes even more acute. After all, exchange trading makes sense only for fairly liquid contracts; on the exchange you can only buy what someone else wants to sell. So exotic options are traded only on the OTC market.

Derivatives on derivatives

Not only spot transactions, but also all sorts of derivative instruments are actively traded on financial markets.
Futures, swaps, etc. And yes, there are options on them too. For example, exchange rates for oil and other commodities are futures rates. Accordingly, an option on oil is an option on futures.

Options on currency futures are also traded on exchanges, for example on the Chicago Mercantile Exchange (CME)

If you have already asked the question: “Do options on options exist?”, then the answer is: yes, they do exist. If there is potential demand for an option and the market maker has the capacity to undertake such obligations, i.e. understanding how to calculate the price and how to then manage risks (hedge) such a contract, then the market will sooner or later respond to such demand with supply.

The more different products a market maker can offer, the more different customers it can attract. You also need to understand that in the options market, like in any other financial product market, there are purchase prices and sale prices, the difference between them is called the spread, and this is the main source of income for the market maker. Naturally, the spread is narrower for more liquid products, and wider for less liquid products.

But let's go back to vanilla options and look at examples of products made up of them.

Options history

Trading with options has been known for several centuries. During the tulip mania boom of the 1630s, options on tulip bulbs were common. Options provided the opportunity to purchase bulbs for those who did not have the money to buy even one bulb. By the time the option expired, they had resold their right at a profit or loss.

In the 1820s, stock options began to be traded on the London Stock Exchange. In the 60s of the 20th century, the over-the-counter market for options on commodities and stocks was widely developed in the United States of America. The creation of the Chicago Board Options Exchange (CBOE) in 1973 marked the beginning of options trading on the exchange. By the 90s of the 20th century, a wide range of options had formed on all leading exchanges and the over-the-counter market.

In Russia, options are traded on the Derivatives section of the Moscow Exchange.

Vanilla strategies

We know what the payout schedule for call and put options looks like, but there are a couple more obvious things to mention.
First, options can be either bought or sold. In financial market jargon, we say that we are long option if we bought an option, and that we are short option if we sold the option. The payoff for a short position in an option is equal to the payout for a long position with the opposite sign. Secondly, in order to buy an option (take a long position), you need to pay a premium, and the party that assumes obligations under the option (short position) receives a premium for this. Incl. It makes sense to consider not only the option payment, but also the total profit taking into account the premium.

We get four options. The dotted lines show graphs of the payout functions (without taking into account the premium), and the solid lines show the profit/loss function taking into account the premium:

The next simple idea is that options can be bought and sold not individually, but in combinations. Some combinations are so popular and important to the market that they have established names.

Balance Combination: Straddle

The first combination on our list is straddle. It turns out if you add up call and put options with the same strike. ATM straddle is especially popular, i.e. both options have a strike equal to the at-the-money forward.

In this picture, the dotted line shows the profit on individual options (taking into account the premium). And the solid line is their sum, i.e. profit for the entire structure, naturally also taking into account the bonus.

If you look at straddle as a speculative strategy on the price of the underlying asset, then if you buy straddle, you will make a profit if the price level of the underlying asset goes far enough from the at-the-money level, and it does not matter in which direction.

If you have already heard something about options and know what an option delta is, then you can clarify that for some underlying assets they prefer to use not an ATMF straddle, but a deltoneutral (DN) straddle. Those. The strike is chosen so that the delta of the put and call options adds up to zero.

Association game: Strangle

Look at this picture. What associations do you have?

The common name for a combination of vanilla options with this payout is strangle.

The English dictionary says that strangle is “to kill someone by pressing their throat so that they cannot breathe.” Those. we are talking about strangulation. Why such a brutal name arose for such a payout function, I don’t know. Apparently, this is how Wall Street options traders' associations worked in the early 20th century. On the other hand, it could have been worse. You could call it "chainsaw massacre", for example.

From the point of view of option strategies, strangle is a put + call, with different strikes. Similar to straddle, but due to the fact that in this combination the option strikes are in the OTM zone, these options are cheaper than ATMF options. Consequently, the whole combination will be cheaper than ATMF straddle.

For a speculator, strangle has approximately the same meaning as straddle, with the difference that strangle is cheaper, but to make a profit, the rate needs to move further away from the ATM level.

Options pricing models

All mathematical models for calculating option prices are based on the idea of an efficient market. It is assumed that the “fair” premium of an option corresponds to its value at which neither the buyer nor the seller of the option, on average, makes a profit.

To calculate the premium, the properties of a stochastic process are postulated to model the behavior of the price of the underlying asset underlying the option contract. The parameters of such a model are estimated based on historical data. One of the most important statistical parameters influencing the amount of the premium is the volatility of the price of the underlying asset. The larger it is, the greater the uncertainty in predicting the future price, and, therefore, the greater the premium (risk) that the option seller must receive. The second important parameter, also directly related to uncertainty, is the time until the option expires. The further before this date, the higher the premium (at the same delivery price of the underlying asset specified in the option contract).

The most popular option models:

Black-Scholes model
Binomial model
Heston model
Monte Carlo model
Bjerksund-Stensland model
Cox-Rubinstein model
Yates model

Risk Reversal

The next combination is risk reversal.
We buy an OTM call option and sell an OTM put option. From the point of view of a speculative strategy, this is a fairly aggressive bet that the price of the underlying asset will go up. Because We sell a put option and receive a premium for it, then the cost of such a bet will be lower, but if the rate goes down, our problems will be greater.

Butterfly

To construct a payout according to a structure called “butterfly”, two options are no longer enough.
In the figure below, this combination is replicated using call options as follows: we buy options with strikes 28 and 32 with a par of 1 and sell an option with a strike of 30 with a par of 2. The same payoff can be constructed if we buy strangle and sell straddle. And this is usually what they do in practice.

Replicating this payoff only through call options, as in the figure, is interesting in the following ways. Let's denote the central strike in the structure as , and the difference between this strike and the other two as . Then the price of such a structure will be equal to . In this form, it is similar to a difference scheme for calculating the second derivative. Of course, for this you need to tend to zero, and such data cannot be obtained directly from market quotes, but in some cases, using the quotes that are available, you can get a good approximation. Or at least a meaningful numerical estimate of the convexity of a function.

Sometimes this property is convenient for theoretical analysis. In books you can see discussions where infinitely small “butterflies” are considered. Those. butterfly structure, in which the difference between strikes tends to zero.

On this site you can experiment with the parameters for these and some other vanilla option combinations.

Awards

The seller pays a premium to purchase the contract. When selling, the seller receives a reward.

On the one hand, premiums are a payment for potential chances for the buyer, on the other hand, a reward for risks for the seller. The amount of the incentive depends on how profitable the purchase of this agreement is at that moment in time.

In a growing market, there is interest in buying calls, and accordingly its value also increases. As the value of the asset decreases, the value of the call decreases.

When rates fall, the buyer's risks are limited only by the amount of the incentive.

The seller's risk is practically unlimited, since he must fulfill the contract if the buyer demands it, the profit is limited only by premium payments.

As a counterbalance, purchase of puts. Having bought it for 100 shares at a price of $70, the holder receives the right to sell securities at this price and is interested in its reduction before the end of the contract. The reward in this transaction will increase as the price of the securities falls.

Barriers to Expair

Let's return to the payoff function of one option.
For example, take the ATMF call option. For the person who purchased it, this contract seems to fix the future rate of the asset at the time the option is exercised, if the rate turns out to be higher than the ATMF level. The ATMF level is some current estimate of the “fair” rate at the time of expiration, but, of course, the real value of this rate in the future is a random variable. Nobody knows exactly what will happen to the exchange rate. But it can still be said that one course level is more likely than another. And we can say that the probability of exchange rate values far from ATMF is less than those close to them. But a regular call option works for all possible exchange rates greater than the strike. And this, by the way, is included in his bonus. Is it possible not to pay for this if we estimate the probability of exceeding a certain level as zero?

If such a thought comes to mind, then it would be a good idea to find out how much such a play-off will cost (the graph shows the payment without taking into account the bonus):

Or this:

If the market maker's clients are interested in such products, then the market maker must be able to calculate prices for them.

The first payoff function can be easily replicated using two call options. One option needs to be bought, the other one must be sold.

The second playoff is called a barrier option. In this case, the barrier acts only on expairs; a barrier with this rule is sometimes called a European barrier. And the effect of the barrier in this case is that when the spot crosses the barrier, the option seems to “knock out”. This is called a "knockout barrier".

There may also be a knockin barrier. The owner of such an option will receive a payment only if the asset price at expiration has moved far enough from the strike:

In this example, the option strike is 100 and the KI barrier is 115.

How to make money on options

Earnings on options can be made by changing the price of an asset. A trader who correctly predicts the rise or fall of their value makes a profit. To generate income, you need to register on one of the specialized broker websites, create a deposit, choose a competent trading strategy, conduct constant market analysis and make transactions.

You should first undergo theoretical and practical training in trading methods and understand financial mechanisms and analytical principles.

Binary options

In order to replicate the payout with European barriers, simple vanilla options are not enough.
We need options with the same escape rules as European options, but the payout function for which looks like a step. Such options are called binary options in Russian. There are two names in English: binary option and digital option.

Binary options themselves are a purely speculative instrument, like a lottery ticket. If the rate is below the strike, the owner of the binary call option receives a fixed payment; if not, then he receives nothing. But if they are part of an EKI or EKO play-off, they can help choose the parameters (and therefore the price) of insurance against unfavorable movements in the underlying asset that are more suitable for a particular case.

Contract Specification

An option is an agreement between two counterparties, concluded in accordance with the conditions specified in the option specification. Options contracts can be quite complex, but typically contain the following characteristics:

Type of option (Put or Call option);
The amount of the underlying asset in one contract;
The exercise price (strike price) of the option at which physical delivery of the underlying asset will occur;
Option expiration date;
Settlement or delivery option (whether the seller must deliver the physical underlying asset or pay an equivalent amount of money to the option buyer).

Vanilla is different from vanilla

In addition to European options, there are also American options .
The difference is that a European option can only be exercised at expiration. And the American option is also available at any time before.

Such geographical names are apparently connected with the fact that at some point one type of options was popular in European markets, and another in American markets. But today these are just established terms.

American options are often traded on stock exchanges. And in general, they are quite common. And they can also be classified as vanilla options rather than exotic.

Option name encoding

Since all options traded on FORTS are standardized, you can obtain basic information about the contract by their name. How to decipher the code correctly?

1. Code of the underlying asset . Shows what is being traded. On the Moscow Exchange website you can find a table indicating all the codes. The most popular are the following:

RI – RTS index;
MX – Moscow Exchange index;
GD – gold bullion;
BR – Brent oil;
Si – dollar to ruble exchange rate;
ED – euro to dollar exchange rate;
SR – Sberbank shares;
GZ – Gazprom shares;
LK – Lukoil shares;
NM – Norilsk Nickel shares

2. Strike. Contract price, i.e. the value of the asset fixed by the option.

3. Type of calculations . A is an option with payment of a premium, B is a margined option. On FORTS the second type of calculations is always used, so the value of this classifier is always B.

4. Month and type of option exercise . For call options, the first part of the Latin alphabet is used, from A to L; for put options, the second part is used, from M to X. It is easier to navigate using the table.

5. Year of execution . FORTS uses the designation of the last digit of the year. For example, 9 means 2022, 0 means 2020, and 1 means 2022.

Sometimes there is a letter at the end of the option - A, B, C or D. Then you have a weekly option. A means the option will be exercised on the first Thursday of the month, B on the second, C on the third, and D on the last.

The full option code is much easier to decipher, especially when you know the decoding of the short code.

Continuous barriers

The most real exotic options are barrier options.
In such options there is a barrier, but unlike European barriers, which apply only to expiration, here we mean a barrier that is valid throughout the life of the option. Such barriers are called either continuous or American. If they talk about a barrier without specifying anything, they usually mean just such barriers. A continuous barrier can also be placed in the OTM range of the underlying asset rate relative to the option strike, which does not make sense for a European barrier. And in general, here the number of possible options increases. You can define a barrier option with two barriers (upper and lower). You can make one barrier of the knockout type, and another of the knockin type... There are many options, some more popular, some rare. Such exotic goods are traded, of course, on the OTC market.

What is important about this type of exotic is that its final payment depends not only on the price of the asset at expiration, but also on the entire path that the random process of the underlying asset’s rate has taken from the moment the contract was concluded to the expiration.

Historical reference

At first, these mechanisms were used as a method of protection, hedging and insurance. These types of arrangements were required by farmers and buyers of agricultural products to prevent losses from adverse changes in value.

This option effectively differs from other trading methods because it allows its owner to not execute the procedure if the conditions become unfavorable to him.

The benefits and full potential of these agreements were appreciated by trading participants.

For this tool, the main factors for constructing all strategies are the fixed value and time.

Over time, option transactions for other commodities appeared - oil, metals, stocks.

These instruments have been traded on the exchange since 1973 after the opening of the Chicago Specialized Exchange. Different types of options allow traders to maneuver in the market.

Asian options

Another typical example of an option, the price of which depends not only on the value that the spot reached on the escape route, but also on the entire path, or at least on the prices realized at some predetermined points along this path.
The Asian option uses averaging of such intermediate values. For example, this can be done this way: to determine the payout according to the call option rule, it is not the spot value at expiration that is taken, but the average value. And the payment will be equal. Such an option is less sensitive to short-term deviations in the price of the underlying asset, which may occur accidentally at the time the option is exercised.

Options that depend on the realized spot path, such as Asian and continuous barrier options, typically require the use of more complex models and more expensive computational methods.

Exchange and over-the-counter options

Exchange traded options are standardized derivatives. Their treatment is similar to futures contracts. During trading, only the option premium changes; the remaining parameters of the transaction are specified in the option specification.

Options with different Strike prices (strike prices) and exercise dates are considered different options. The clearing house of the exchange acts as an intermediary between the seller and buyer of the option. All positions of trading participants are recorded by the clearing house. If a trader makes an opposite trade on an option with the same strike price and expiration date, his position is closed. When concluding a transaction, the seller of the option is obliged to provide the exchange with a security deposit, which is retained by the exchange until the option expires.

OTC options are not traded on an exchange and do not require standardization. In this way they are similar to forward contracts. The option parameters are set by the participants in the transaction. They are also responsible for exercising the option. OTC options trading is most often used by large financial institutions to hedge their trades.

A little about modeling

So, now it is generally clear what contracts participants in the options market have to deal with. Now we can say a few words about what tasks, for example, a market maker needs to solve in order for his activities in the market to be successful.

Pricing

On an exchange or OTC market, you can get prices for liquid call and put options at different expirations and different strikes.
This will be a certain number of points with parameters. But you need to be able to work not only with these options, but also with other strikes, other expirations and exotic options. For this purpose, models are built based on the results of non-school probability theory (stochastic differential equations, martingale measure, etc.). If you look at what these models do from a bird's eye view, they answer questions like "how to calculate the price for a vanilla option for which there is no quota in the market, based on the prices that are there?" or “how, having this data on the prices of liquid vanilla options, calculate the prices of more complex contracts - binary, or with continuous barriers, or any other exotic?”

Here it turns out to be convenient, or at least generally accepted, to talk about some characteristic that is associated with the probabilities of realizing different possible values of the exchange rate of the underlying asset and is a function of the parameters. This characteristic is called “implied volatility”. Because This is a function of two parameters, then we talk about the volatility surface. If the expiration is fixed, then it is a function of one variable, and then they talk about the “smile” of volatility.

From an options traders' perspective, options trading is volatility trading. And speculative strategies using one or more vanilla options can be aimed specifically at volatility speculation.

“Trading abstract volatility in a vacuum”

Usually, for the calculations that need to be made, there is no solution in analytical form and it is necessary to use computational methods. Typical computational methods that are used are numerical solution of partial differential equations and the Monte Carlo method.

Position Management: Dynamic Hedging

Mathematical models and computational methods help to calculate the prices of different options in accordance with other prices of more liquid instruments.
But this is only one side of the problem. Prices reflect current market expectations. These expectations change, and no one knows what will be realized in the future. Clients come to the market maker and want to make a deal with him: some in order to get insurance, others in order to implement some kind of speculative strategy. The client chooses which transactions will be requested and when. The market maker must be willing to assume the appropriate obligations for the option. To do this, he needs some kind of algorithm of actions on how to fulfill these obligations. Some kind of technology that would help him replicate the option payout, regardless of what happens in the market. Sounds too good to be true? This is partly true, but, nevertheless, there is technology that comes surprisingly close to this.

The technology is called dynamic hedging. The bottom line is that we calculate certain risk indicators for our position and periodically buy some instruments on the market that compensate for these risks. A typical example of such risk is delta, the partial derivative of the price of a derivative with respect to the exchange rate of the underlying asset. In order to compensate for the delta, you simply need to buy the underlying asset in an amount equal to the delta, and with the opposite sign. What does short selling mean? A strategy based on delta hedging is called (surprise!) delta hedging .

Using mathematical models that typically make assumptions that are not usually met in practice, it can be shown that delta hedging can mathematically exactly replicate the payoff of an option. In this case, you just need, in addition to all the simplifications and assumptions included in the model, to direct the period between portfolio rebalancing to zero. This is how option replication works using delta hedging in the famous Black-Scholes model.

Despite the fact that rigorous mathematical proof requires neglecting many things that are important in practice, the very idea of dynamic hedging turns out to be surprisingly resistant to the fact that many of these assumptions do not hold in practice. This is what allows the market maker to engage in his activities, significantly reducing the risk he takes on.

Here it doesn’t hurt for a market maker to have a large client base with diverse interests. Of course, how a market maker finds the buy and sell quote for volatility is conceptually similar to how a market maker finds that quote in the spot market. The difference is that for each asset you need to find not two prices, but purchase and sale quotas for implied volatility for those strike and expiration values that are considered reasonable in the market. This usually means that at a minimum you need to have these buy and sell quotas for several reference points and calibrate the model parameters so that the model matches them.

The points to which the model needs to be calibrated can be specified in different ways. In the FX options market, the reference points are quotes on straddle, risk reversal and butterfly.

Options markets

The entire history of options markets can be divided into two periods - exchange and non-exchange.

The first mention of options dates back to the second millennium BC. The first known hedging type investment was a call option trade and appears to have taken place approximately 2,500 years ago. Aristotle related the story of the poor philosopher Thales, who demonstrated to skeptics that he had invented a “universal financial mechanism” and profited by contracting with the owners of olive presses for the exclusive right to use their equipment to process the upcoming harvest. The press owners were happy to pass on the risk of future olive prices to him and receive an advance payment as a hedge against a poor harvest. It turned out that Thales correctly predicted a rich harvest, and the demand for the services of olive presses increased. He sold his rights to use the presses and made a profit. In the call option, Thales only risked his down payment. Although he did not invest in the fields, the workers, or the olive presses, he was actively involved in olive production, taking on risks that olive farmers and press owners could not or would not take—and allowed them to focus on the production and processing of olives. They received income from their work, and he received income from his.

Another fairly well-known reference to options is the tulip boom in Holland. Tulip traders who wanted to hedge their ability to build up inventories when prices rose bought call options, which gave them the right, but not the obligation, to buy the product within a certain period at an agreed price. Flower growers, seeking protection against falling prices, bought put options, giving them the right to deliver or sell tulips to another party at a pre-agreed price. The other party to these options, the sellers, assumed the risk in exchange for premiums paid by the option buyers. Sellers of call options were compensated by premiums for the risk of rising prices, and sellers of put options were compensated for the risk of falling prices. After this incident, as well as after a series of collapses of financial pyramids in Britain that occurred at the beginning of the 18th century, the “Bubble Act” was passed in 1720, according to which the status of “limited liability” could be obtained only on the basis of a special act of parliament. Around the same time, a recognized futures market existed in Japan, where landowners who received rent in kind (a share of the rice harvest) used options to insure themselves against crop failure.

In the US, options have been used for a long time. Put and call options began trading on the stock exchange in the 1790s, shortly after the famous Sycamore Agreement (1792), which launched the New York Stock Exchange. During the American Civil War, the Confederate government used a financial product consisting of a bond and a cotton option for the bondholder to finance military purchases abroad. At the same time, it ensured the formation of a foreign clientele interested in the survival of the Confederacy. The risk of depreciation of the Confederate dollar was covered by the right to receive British or French currency for the bonds. The opportunity to receive cotton as a debt against inflation was tempting because cotton was offered for 6 pence when European prices were about 24 pence. In addition, the bonds were convertible into cotton "at any time." This opportunity protected from the vicissitudes of war those creditors who, having shown efficiency, managed to acquire their cotton before the final defeat of the Confederates.

In 1848, the world's largest futures exchange, CBOT (Chicago Board of Trade), was founded in Chicago. At that time, mainly grain was traded on this exchange, then forward contracts for grain and options appeared in circulation. Options appeared there by the 60s of the 19th century, and at the beginning of the 20th century the Association of Brokers and Options Dealers (Put and Call Brokers and Dealers Association) appeared.

However, the real beginning of the history of modern derivative instruments is considered to be the 1970s, when forward contracts for foreign currency began to be traded on CBOT. After trading in futures and stock options on CBOT was banned in 1972, the CBOE (Chicago Board Options Exchange) was created in 1973, which was a real revolution in the world of options. The fact is that the emergence of SVOE actually meant the entry of futures contracts to a new level - the level of a standardized exchange-traded financial product.

Before the introduction of exchange trading, call and put options were traded "over the counter" in the over-the-counter market. In this form of market, there were several options dealers. They found the buyer and seller of the contract, helped them come to an agreement on the terms of the contract, and carried out the transaction. Dealers typically took a commission from the transaction price. Options of this type typically had an exercise price equal to the current stock price; thus, if at the time the contract was entered into, the stock was selling at 46 3/8, then this price was the strike price of the option. This led to inconvenient calculations. In addition, these over-the-counter options had expirations in fixed time periods tied to the time the contract was entered into, with a choice of time periods of 6 months plus 10 days, 95 days, 65 or 35 days.

Another unusual condition: until the moment of exercise, the call holder receives dividends, that is, the strike must actually be adjusted by the amount of dividends paid over the life of the option. In addition to the rather difficult task of finding counterparties, a major obstacle to the development of the options market in an over-the-counter environment was the almost complete absence of a secondary market.

And so, on April 26, 1973, the Chicago Board Options Exchange opened its doors. Trading volume on the first day amounted to 911 option contracts for 16 shares. In addition to standardizing the terms of options contracts, the exchange introduced a system of market makers for listed equity markets, and was also responsible for the Options Clearing Corporation (OCC), the guarantor of all options transactions. Both the first and second are very important to ensure the viability of the new exchange in terms of market breadth, ensuring liquidity and reliability of the execution process.

After that, the options market grew at a pace that defies description: the American Stock Exchange (AMEX) included options in its listing in January 1975, and the Philadelphia Exchange in June. Moreover, the success of the exchange-traded options market ultimately accelerated the development of options as we see them today. The continued introduction of new products - such as index options - and the subsequent growth and revitalization of the respective exchanges is directly related to the success of the Chicago Board Options Exchange. The old over-the-counter market has shrunk significantly, except for options on unlisted stocks.

The next important innovation is the emergence of index trading. The Chicago Board Options Exchange introduced the first options on the OEX index on March 11, 1983. Today OEX is better known as the S&P 100 index, but still has the ticker symbol "OEX". It is by far the most successful index and stock options product in the history of stock options.

Meanwhile, the Chicago Mercantile Exchange (CME) began trading S&P 500 index futures, whose success and influence spread far beyond the futures and options trading arena, and which eventually became the "king of index trading" and subsequently the tool which was blamed for the 1987 stock market crash and many other tumultuous periods in the stock market (MacMillan link).

The reason index contracts were popular is that first, an investor could monitor the market as a whole and act directly on that view. Before the advent of index products, an investor had to realize his vision of the market by purchasing quite a large number of individual shares. As you know, you can be right about the market as a whole and wrong about a specific security. The ability to trade indices and index options solves this problem.

The first futures options began to be traded in 1972 - these were options on currency futures and they were traded on the CME. The first exchange-traded options on interest rate futures appeared in 1975. This was followed by Treasury futures in 1976. However, the most popular contracts - 30-year US government bonds and Eurodollar futures - were listed only in 1977 and 1981, respectively. Options on these products appeared only a few years later (in 1982 - on bonds, in 1986 - on Eurodollars). The first agricultural options, on soybeans, were listed in 1984.

Today, there is also a huge volume of trading in options contracts, unaccounted for in exchange statistics, since today there is again a powerful over-the-counter derivatives market. And although the modern over-the-counter market is much more sophisticated than its predecessor, both markets have certain similarities. Key similarity: The contracts traded in these markets are not standardized. Today's large financial institutions that use options tend to tailor them to their portfolios and the positions they need to hedge. Moreover, they may require expiration dates other than the standard ones. A very big difference between the modern over-the-counter market and the over-the-counter market of past years is that today contracts are issued mainly by large investment companies. These companies hire options strategists to hedge their overall portfolio, a very little reminiscent of trading of yesteryear when a brokerage firm simply found a buyer and a seller and then brought them together to execute the trade. However, exchanges are making attempts to shift over-the-counter trading into the exchange market space. SVOE has already introduced so-called FLEX options, the terms of which allow for varying expiration dates and strike prices, as an initial step in introducing new products to this market.

Main dates of the exchange period:

before 1973 - over-the-counter stock options
since 1973 - stock options on shares
since 1981 - interest rate options (on bonds, mortgages, treasury bills)
since 1982 - currency options, options on bond futures contracts
since 1983 - options on stock indices, options on futures contracts on stock indices

The founder of stock options trading is the Chicago Board of Trade (Exchange) - CBOT, which by the beginning of 1973 created a specialized branch - the Chicago Board Options Exchange (CBOE). The initial assets of exchange-traded options were shares of American companies that are in greatest demand on the stock market.

Where and how to buy options?

Exchange options are traded exclusively on the FORTS section of the Moscow Exchange. To buy (or sell) them, you need to open an account with any Russian broker.

Please note that not all brokers automatically provide access to the derivatives market. Sometimes you need to fill out a separate application for admission.

For the purchase/sale of an option, a commission is charged at broker rates.

Position	Share
CEO	5–10%
COO	2–5%
Lead Engineer	0,5–1%
Engineer with 5+ years of experience	0,33–0,66%
Manager or junior engineer	0,2–0,33%