Long memory stochastic volatility in option pricing
نویسندگان
چکیده
The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes price and random deviation describing the risk from the random volatility. By using the fact that the option price and random volatility change on different time scales, we find the asymptotic equation for the deviation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.
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