Options

An option is a derivative instrument which derives its value from another underlying asset. An option holder or buyer has a right to buy or sell the underlying asset from or to, respectively, an option writer or option seller at a pre-determined price. The event when such a transaction happens is called exercising the option. Depending on the type, an option can be exercised during or at the end of its exercise period or life. One key aspect of an option is that it’s a “right” and not an “obligation”, which means the option holder can decide to exercise the option or let it expire worthless at his will. On the other hand, it is an obligation for the option writer to sell or buy the asset at the pre-determined price when the option holder chooses to buy or sell, respectively.

 Option Characteristics: An option is usually described by the following characteristics:            

  • Exercise Price/Strike Price: The pre-determined price at which an option can be exercised is called its exercise price or strike price. Generally, it is the market price of the underlying asset at the time of writing the option.
  • Life/Exercise Period: The period during or at the end of which (depending on option type, American or European) the option can be exercised is called its exercise period or life. It is generally denoted by a number of months for publicly traded stock or index options. It can run into a number of years for Employee Stock Option Plans (ESOPs).
  • Implied Volatility (IV): It is derived using option valuation methodologies, and is a measure of how the market is valuing a particular option. Higher IV means higher time value of the option.
  • In the Money (ITM): An option is ITM when the option holder will gain from exercising the option.
  • Out of the Money (OTM): An option is OTM when the option holder will not gain from exercising the option.
  • At the Money (ATM): An option is ATM when the option holder neither gains nor loses from exercising the option. An option is generally ATM when the underlying price is equal to the strike price of the option.

Option Types: Options can be broadly classified based on the time of exercise and the right (buying or selling) of the holder.

  • American Option: An American Option can be exercised at any time during the life of the option. If an American option is written on 1st of January and has a life of three months, then the option holder or buyer can exercise it during any of the days between 1st January to 31st
  • European Option: A European Option can only be exercised at the end of its life. If the option written in the previous example was of European nature, it could be exercised only on 31st
  • Call Option: A call option gives the holder a right to buy the underlying asset at the strike price. If the holder chooses to exercise, the option writer will have an obligation to sell the asset to the option holder at the strike price. If a call option is written for a stock with a strike price of 100, then if the market price of a stock rises to 110, the option holder can exercise the option and pocket his gain of 10. This gain is called option pay-off and is calculate as:

                                                      Payoff of Call Option = Max (S-K,0)

                                     where S is the market price of spot price and K is the strike price.

  • Put Option: A put option gives the holder a right to sell the underlying asset at the strike price. If the holder chooses to exercise, the option writer will have an obligation to buy the asset from the option holder at the strike price. If a put option is written for a stock with a strike price of 100, then if the market price of the stock falls to 90, the option holder can exercise the option and pocket the payoff of 10.

                                                   Payoff of Put Option = Max (K-S,0)

                                   where S and K have the same meaning as in call option.

Option Valuation: Option valuation is a complex process. Two methods are generally used to value options. One is called the Binomial Method and the other is called Black-Scholes Model. There are many MS Excel based utilities available online that can be used to value options. You will need to know the following six parameters to value an option using these models:

  • Strike Price
  • Current Market Price
  • Volatility in the price of the underlying asset
  • Risk-free rate
  • Dividend yield
  • Time to expiry or remaining life of the option

References:

Book:

Options, Futures and Other Derivatives by John C Hull

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