5.77 option_lookback

Function File: [value] = option_lookback (CallPutFlag, lookback_type, S, X1, X2, T, r, sigma, divrate)

Compute the prices of European Lookback call or put options of type floating strike or fixed strike.

Floating Strike options:
A floating strike lookback call / put gives you the right to buy / sell the the underlying security at the lowest / highest price observed during options lifetime. Pricing according to Goldman, Sosin and Gatto (1979) ("Path dependent options: Buy at the Low Sell at the High", Journal of Finance, 34(5), 1111- 1127) valuation formulas.

Fixed Strike options:
A fixed strike lookback call / put pays out the maximum of the difference between the highed observed price and the strike and 0 (call option) or the maximum of the difference between strike and lowest observed price and 0 (put option). Pricing according to Conze and Viswanathan (1991) ("Path dependent options: The Case of Lookback Options", Journal of Finance, 36, 1893 - 1907) formulas.

All formulas are taken from Haug, Complete Guide to Option Pricing Formulas, 2nd edition, page 141ff.

Variables:

• CallPutFlag: Call: ’1’, Put: ’0’
• lookback_type: can be ’floating_strike’,’fixed_strike’
• S: stock price at time 0
• X1: strike price (or S_min or S_max for fixed strike)
• X2: payoff strike of fixed strike option
• T: time to maturity in days
• r: annual risk-free interest rate (continuously compounded, act/365)
• sigma: implied volatility of the stock price measured as annual standard deviation
• divrate: dividend rate p.a., continously compounded

See also: option_binary, option_bs.