Paper #1446

Title:

A closed-form option pricing approximation formula for a fractional Heston model

Authors:

Elisa Alòs and Yan Yang

Date:

October 2014

Abstract:

We present a method to develop simple option pricing approximation formulas for a fractional Heston model, where the volatility process is defined by means of a fractional integration of a diffusion process. This model preserves the short-time behaviour of the Heston model, at the same time it explains the slow decrease of the smile amplitude when time to maturity increases. Then, by means of classical It�'s calculus we decompose option prices as the sum of the classical Black-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due to correlation and a term due to the volatility of the volatility. This decomposition procedure does not need the volatility process to be Markovian and allows us to develop easy-to-apply approximation formulas for option prices and implied volatilities, as well as to study their accuracy. Numerical examples are given.

Keywords:

Stochastic volatility, Heston model, Itô's calculus, fractional Brownian motion

JEL codes:

G13; Mathematics Subject Class(2000): 91B28, 91B70

Area of Research:

Statistics, Econometrics and Quantitative Methods

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