Extreme Spread

The time to maturity of an extreme spread option is divided into two periods: one period starting at time zero and ending at some arbitrary date, and another starting at that arbitrary date and ending at the expiration date. A payoff at maturity of an extreme spread call (put) option equals the positive part of the difference between the maximum (minimum) value of the underlying asset of the second (first) period and the maximum (minimum) value of the underlying asset of the first (second) period.[1] The payoff at expiration of a reverse extreme spread call (put) option equals the positive part of the difference between the minimum (maximum) of the underlying asset of the second (first) period and the minimum (maximum) value of the underlying asset of the first (second) period. Extreme spread options can be priced analytically using a model introduced by Bermin (1996).

The FinOptions function ExtremeSpread can be used to evaluate European extreme spread options.

Floating Strike Lookback

The Lookback call (put) option gives the holder the right to buy (sell) an asset at its lowest (highest) price observed during the life of the option. This observed price is applied as the strike price. The payout for a call option is essentially the asset price minus the minimum spot price observed during the life of the option. The payout for a put option is essentially the maximum spot price observed during the life of the option minus the asset price. Therefore, a floating strike Lookback option is always in the money and should always be exercised. Floating strike options can be priced analytically using a model introduced by Goldman, Sosin, and Gatto (1979). Monte Carlo simulation is used for the numerical calculation of a European style floating strike options.

FinOptions has two functions to evaluate European floating strike Lookback options: Lookback and LookbackMC. The latter using Monte Carlo simulation to evaluate the theoretical value.

Fixed Strike Lookback

For a fixed strike Lookback option, the strike price is known in advance. The call option payoff is given by the difference between the maximum observed price of the underlying asset during the life of the option and the fixed strike price. The put option payoff is given by the difference between the fixed strike price and the minimum observed price of the underlying asset during the life of the option. A fixed strike Lookback call (put) option payoff is equal to that of a standard plain call (put) option when the final asset price is the maximum (minimum) observed value during the options life. Fixed strike Lookback options can be priced analytically using a model introduced by Conze and Viswanathan (1991).

The FinOptions function LookbackFixed can be used to evaluate European fixed strike Lookback options.

Partial-time Fixed Strike

For a partial-time fixed strike Lookback option, the Lookback period starts at a predetermined date after the initialization date of the option. The partial-time fixed strike Lookback call option payoff is given by the difference between the maximum observed price of the underlying asset during the Lookback period and the fixed strike price. The partial-time fixed strike Lookback put option payoff is given by the difference between the fixed strike price and the minimum observed price of the underlying asset during the Lookback period. The partial-time fixed strike Lookback option is cheaper than a similar standard fixed strike Lookback option. Partial-time fixed strike Lookback options can be priced analytically using a model introduced by Heynen and Kat (1994).

The FinOptions function LookbackPFixed can be used to evaluate European partial-time floating strike Lookback options.

Partial-time Floating Strike

For a partial-time floating strike Lookback option, the Lookback period starts at time zero and ends at an arbitrary date before expiration. Except for the partial Lookback period, the option is similar to a floating strike Lookback option. The partial-time floating strike Lookback option is cheaper than a similar standard floating strike Lookback option. Partial-time floating strike Lookback options can be priced analytically using a model introduced by Heynen and Kat (1994).

The FinOptions function LookbackPFloat can be used to evaluate European partial-time floating strike Lookback options.