A proof for French's empirical formula on option pricing.
The French formula for option pricing of the title is a variation of the standard Black-Scholes formula where the discounts consider calendar time while the volatility ingredients use trading time. Trading time is calendar time with the weekends and holidays removed. This variation of the standard Black-Scholes formula is obtained by applying the Black-Scholes theory with deterministic interest rate and volatility; the volatility to be used is a fixed value for weekdays and zero for weekends. In this note the authors use fractional Brownian motion to model the evolution of the market and derive this variation of the Black-Scholes formula.
scientific article; zbMATH DE number 1755344