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Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model
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. 1 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 to a higher price of the option. This appears in clear contrast
to the presence of memory in the price itself which makes the price of the
option cheaper.Comment: 9 pages, 4 figures, APFA5 Torin
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