In John C. Hull’s book “Options, Futures, and Other Derivatives,” the author discusses several key formulas and equations that are used in the pricing and analysis of derivatives. Some of the most important option pricing formulas include:
- Black-Scholes formula: This formula is used to calculate the theoretical price of European put and call options.
- Black 76 formula: This formula is an extension of the Black-Scholes formula, and is used to calculate the theoretical price of American put and call options.
- Binomial model: This model is used to calculate the theoretical price of American put and call options using a lattice approach.
- Monte Carlo simulation: This method is used to calculate the theoretical price of options using random sampling.
- Implied volatility: This is the volatility that is implied by the market price of an option. It is calculated by solving for the volatility that makes the theoretical price of an option equal to its market price.
- Greeks: The Greeks are a set of sensitivity measures that are used to calculate the sensitivity of an option’s theoretical price to changes in various underlying factors, such as the underlying asset price, volatility, time to expiration, and interest rates.
- Forward price: This is the expected future price of the underlying asset, and is used to calculate the theoretical price of forward and futures contracts.
- Forward implied volatility: This is the volatility that is implied by the market price of a forward or futures contract. It is calculated by solving for the volatility that makes the theoretical price of a forward or futures contract equal to its market price.
Terms:
Delta: This is the rate of change of an option’s theoretical price with respect to the underlying asset price. It is used to calculate the theoretical value of an option’s hedge ratio.
Gamma: This is the rate of change of an option’s delta with respect to the underlying asset price. It is used to calculate the rate at which the hedge ratio of an option changes as the underlying asset price moves.
Vega: This is the rate of change of an option’s theoretical price with respect to the underlying asset’s volatility. It is used to calculate the theoretical value of an option’s vega risk.
Theta: This is the rate of change of an option’s theoretical price with respect to the amount of time until expiration. It is used to calculate the theoretical value of an option’s theta decay.
Rho: This is the rate of change of an option’s theoretical price with respect to the interest rate. It is used to calculate the theoretical value of an option’s rho risk.
Call option: This is a type of option that gives the holder the right, but not the obligation, to buy the underlying asset at a predetermined price on or before the expiration date.
Put option: This is a type of option that gives the holder the right, but not the obligation, to sell the underlying asset at a predetermined price on or before the expiration date.
Exercise price: This is the price at which the underlying asset can be bought or sold if the option is exercised. It is also known as the strike price.
Expiration date: This is the date on which the option expires and can no longer be exercised.
Intrinsic value: This is the difference between the underlying asset price and the exercise price of an option, if the option is in the money.
Time value: This is the difference between the theoretical price of an option and its intrinsic value, if the option has any intrinsic value. It represents the value of the option that is due to the remaining time until expiration.
In the money: This refers to a situation where an option has intrinsic value. A call option is in the money if the underlying asset price is above the exercise price, and a put option is in the money if the underlying asset price is below the exercise price.
Out of the money: This refers to a situation where an option does not have intrinsic value. A call option is out of the money if the underlying asset price is below the exercise price, and a put option is out of the money if the underlying asset price is above the exercise price.
At the money: This refers to a situation where the underlying asset price is equal to the exercise price of an option. An at the money option has no intrinsic value, but still has time value.
Moneyness: This refers to the relationship between the underlying asset price and the exercise price of an option, and is used to determine whether an option is in the money, out of the money, or at the money.