Plain Vanilla Options

In this article, Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) presents plain vanilla options.

Introduction

An option contract is a financial derivative that gives its holder the right (but not the obligation) to trade an underlying asset at a price and a date set in advance.

In finance, plain vanilla refers to the most basic version of any financial instrument with standard features. Thus, a plain vanilla option simply refers to a contract that provides the option to buy or sell an underlying stock (or any financial asset) at a fixed price (known as the exercise/strike price) at an expiration date in the future. The expiration date (or maturity) of the option is the date when the holder can exercise her option if she wants.

In the US, options were first traded on an exchange on 26th April 1973. The Chicago Board Options Exchange (CBOE) was the first to create standardized, listed options. Today, there are over 50 exchanges worldwide that trade options.

When an option is bought, its holder pays a fixed amount to the option writer as the cost for the flexibility of trading that the option provides. This cost, which is essentially the value of an option (and the margin taken by the issuer), is known as the premium. The premium depends on the characteristics of the option like the strike price and the maturity, and on market data like the price of the underlying asset and especially its volatility. Many different underlying assets can be traded through options including stocks, bonds, commodities, foreign currencies.

Types of options

Vanilla options are of two types: call and put.

Call options

The holder of a call option has the right to buy a particular asset at a strike price K at maturity T. If the asset price at maturity denoted by S_T is higher than K, then it is beneficial for the call option holder to exercise his option at time T as the price set in the call option contract K is lower than the market price S_T. If the asset price at maturity S_T is lower than K, then it is not beneficial for the call option holder to exercise his option at time T as the price set in the call option contract K is higher than the market price S_T; he is then better off to buy the asset on the market at price S_T than at price K.

For example, consider a call option on BNP Paribas stock with a strike price of €50 and a maturity date March 31^st. The holder of this call option thus has the right but not the obligation to buy one BNP Paribas stock for €50 at maturity. He will exercise his option on March 31^st if and only if the stock price is higher than €50.

The equation below gives the pay-off function of a call option that is the value of the call option at maturity T denoted by C_T as a function of the price of the underlying asset S_T.

Figure 1 gives a graphical representation of the pay-off function of a call option that is the value of the call option at maturity T as a function of the price of the underlying asset at maturity T, S_T, for a given strike price (equal to €50 in the figure).

Figure 1. Pay-off function of a call option

Put options

Similarly, the holder of a put option has the right to sell a particular asset at a strike price K at maturity T. If the asset price at maturity denoted by S_T is higher than K, then it is beneficial for the put option holder not to exercise his option at time T as the price set in the put option contract K is lower than the market price S_T; he is then better off to sell the asset on the market at price S_T than at price K. If the asset price at maturity S_T is lower than K, then it is beneficial for the put option holder to exercise his option at time T as the price set in the put option contract K is higher than the market price S_T.

For example, consider a put option on BNP Paribas stock with a strike price of €50 and a maturity date March 31^st. The holder of this put option thus has the right but not the obligation to sell one BNP Paribas stock for €50 at maturity. He will exercise his put option on March 31^st if and only if the stock price is lower than €50.

The equation below gives the pay-off function of a put option that is the value of the put option at maturity T denoted by P_T as a function of the price of the underlying asset S_T.

Figure 2 gives a graphical representation of the pay-off function of a put option that is the value of the put option at maturity T as a function of the price of the underlying asset S_T for a given strike price (equal to €50 in the figure).

Figure 2. Pay-off function of a put option

Types of exercise

Options can be categorized based on their exercise restrictions.

American options

American options have the most flexible arrangement allowing holders to exercise their options at any time prior to the expiration date. They are widely traded over listed exchanges.

European options

European options provide less flexibility and allow holders to exercise options on only one specific date, which is the expiration date. They thus have a lower value compared to American options and are generally traded OTC.

Bermudan options

There are also Bermudan options that allow exercise of options on a set of specific dates before the expiration and thus provide holders a level of flexibility midway between American and European Options.

Moneyness

Options can also be characterized by their “moneyness” which compares the current price of the underlying asset to the option strike.

In-the-money options

An option with a positive intrinsic value is said to be ‘in the money’. This is the case for a call option if the current market price of the asset is higher than the strike price, and similarly for a put option if the current market price of the asset is lower than the strike price.

Out-of-the-money options

An option with a zero intrinsic value is said to be ‘out of the money’. This is the case for a call option if the current market price of the asset is lower than the strike price, and similarly for a put option if the current market price of the asset is higher than the strike price.

At-the-money options

An option with a strike price close or equal to the current market price is said to be ‘at the money’.

Option writers

The above discussion mainly revolves around option purchasers. However, there is also someone who is liable to sell (for a call) or buy (for a put) the underlying security whenever any holder exercises an option. The writer of an option is the person who is obligated to buy/sell the underlying in case of a call/put exercise. As a counterpart, the writer also receives the option premium from the holder.

The best-case scenario for a writer would be that the option is not exercised by its holder as the option remains out of the money (the writer earning the premium without being obliged to pay the cash flow at maturity). However, option writers are exposed to downside risks especially if the options they write are not covered i.e., holding a long or short position already in the underlying security depending on the option written.

Benefits

For traders with strong market views looking to leverage benefits from small to medium-term fluctuations in market price, buying options is an efficient means to offset their risk exposure. The buyer only risks a small amount of investment, and the downside is only limited to the initial premium whereas the upside is a high payoff if the speculation is in her/his favor. The traders can also take up multiple positions in different assets through options and leverage trade opportunities with profitable positions covering more than the hedging costs.

Option Trading

Most vanilla options are traded through exchanges that make it convenient to match buyers with sellers and vice versa. Trading of standardized contracts also promotes liquidity of the instruments in the market. Vanilla options generally come in series of standardized strike prices and expiration dates. For instance, for an option contract on an Apple Inc. stock (AAPL) expiring on 20^th August 2021, the offered strike prices are $115, $120, $125, $130 and so on. Similarly, the expiration dates for listed stock options is generally the third Friday of the month in which the contract expires. If the Friday falls on a holiday, the expiration date becomes Thursday immediately before the third Friday.

Option pricing

The value an option is known at maturity as it is given by the contract. But what is the value of an option at the time of its issuance or at a time before maturity? Many mathematical models have been developed to answer this question. The most famous model is the Black-Scholes-Merton option pricing model. It uses a Brownian motion to model the behavior of stock market prices.

Use of options

Hedging

Options are commonly used in hedging. For instance, you can purchase an option on a stock to limit your losses to say 15% of your position, should the stock decline more than that during the option period.

Speculation

If one has a strong view about the potential market direction of an underlying security, one can make great returns on exploiting options, provided the view was right. This is essentially speculation in option trading. For instance, if you have a bullish opinion regarding a stock, you can purchase a call option on it that will allow you to purchase the stock at the strike price that will be lower than the future price (hopefully!). Thus, if you are right, you could exercise the option and your payoff would be the price difference between the stock price and the strike price. If you are wrong, you lose out on the premium you paid for the option.

Volatility

The volatility of the underlying asset affects positively option prices: stocks with higher volatility have more expensive option contracts that those with low volatility. In fact, the implied volatility (IV) of an option is that value of the volatility of the underlying instrument for which an option pricing model (such as the Black-Scholes-Merton model) will return a theoretical value equal to the current market price of that option. Hence, when the implied volatility increases, the price of options increases as well, assuming all other factors remain constant. When the implied volatility increases after a trade has been placed, it is good news for the option owner and, conversely bad news for the seller. Inversely, when the implied volatility decreases after a trade has been placed, it is bad news for the option owner and, conversely good news for the seller.

Note that the implied volatility tends to depend on the strike price and maturity date of the options for a given underlying asset. Once the implied volatility for the at-the-money contracts is determined in any given expiration month, market makers use pricing models and volatility skews to calculate implied volatility at other strike prices that are less heavily traded. So, every option has an associated volatility and risk profiles can vary drastically among options. Traders may at times balance out the risk of volatility by hedging one option with another.

Thus, it is essential to interpret and analyze risks before venturing into option trading. There are also many strategies that can be applied to vanilla options in order to benefit better and limit risk such as long and short calls/puts, bull and bear spreads, straddles and strangles, butterflies, condors among many.

Related posts on the SimTrade blog

   ▶ All posts about Options

   ▶ Jayati WALIA Derivatives Market

   ▶ Jayati WALIA Black-Scholes-Merton option pricing model

   ▶ Jayati WALIA Brownian Motion in Finance

Useful Resources

Nasdaq Historical data for Apple stock

AVATRADE What are vanilla options

TheStreet Options Trading

About the author

The article was written in August 2021 by Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022).