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Paper #1446

A closed-form option pricing approximation formula for a fractional Heston model
Elisa Al˛s i Yan Yang
Octubre 2014
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.
Paraules clau:
Stochastic volatility, Heston model, It˘'s calculus, fractional Brownian motion
Codis JEL:
G13; Mathematics Subject Class(2000): 91B28, 91B70
Àrea de Recerca:
Estadística, Econometria i Mètodes Quantitatius

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