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Nonlinear Regression for an Asymptotic Option Price

Song, Seong-Joo;Song, Jong-Woo

  • Published : 2008.10.31

Abstract

This paper approaches the problem of option pricing in an incomplete market, where the underlying asset price process follows a compound Poisson model. We assume that the price process follows a compound Poisson model under an equivalent martingale measure and it converges weakly to the Black-Scholes model. First, we express the option price as the expectation of the discounted payoff and expand it at the Black-Scholes price to obtain a pricing formula with three unknown parameters. Then we estimate those parameters using the market option data. This method can use the option data on the same stock with different expiration dates and different strike prices.

Keywords

Option pricing;compound Poisson;asymptotic expansion;nonlinear regression

References

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Cited by

  1. Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression vol.40, pp.2, 2011, https://doi.org/10.1016/j.jkss.2010.10.001