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Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model

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  • Perelló, Josep

Abstract

The expOU stochastic volatility model is capable of reproducing fairly well most important statistical properties of financial markets daily data. Among them, the presence of multiple time scales in the volatility autocorrelation is perhaps the most relevant which makes appear fat tails in the return distributions. This paper wants to go further on with the expOU model we have studied in Ref. [J. Masoliver, J. Perelló, Quant. Finance 6 (2006) 423] by exploring an aspect of practical interest. Having as a benchmark the parameters estimated from the Dow Jones daily data, we want to compute the price for the European option. This is actually done by Monte Carlo, running a large number of simulations. Our main interest is to “see” the effects of a long-range market memory from our expOU model in its subsequent European call option. We pay attention to the effects of the existence of a broad range of time scales in the volatility. We find that a richer set of time scales brings the price of the option higher. This appears in clear contrast to the presence of memory in the price itself which makes the price of the option cheaper.

Suggested Citation

  • Perelló, Josep, 2007. "Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 213-218.
    • Handle: RePEc:eee:phsmap:v:382:y:2007:i:1:p:213-218
    DOI: 10.1016/j.physa.2007.02.050
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    References listed on IDEAS

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    1. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169.
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    Cited by:

    1. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.

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