2004/03/31 by Sergei Fedotov, Fedotov, Sergei, Abby Tan +1
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Physical sciences #Financial Risk and Volatility Modeling #Other Condensed Matter (cond-mat.other) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #cond-mat.other #q-fin.PR
paper · pdf · doi:10.48550/arxiv.cond-mat/0403761
openalex publication_date 2004/03/31 · arxiv created 2004/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to present a simple 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 the option price and random volatility change on different time scales, we find the asymptotic equation for the derivation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.