Polynomial chaos for simulating random volatilities

Roland Pulch and Cathrin van Emmerich

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 2, 245-255

Abstract: In financial mathematics, the fair price of options can be achieved by solutions of parabolic differential equations. The volatility usually enters the model as a constant parameter. However, since this constant has to be estimated with respect to the underlying market, it makes sense to replace the volatility by an according random variable. Consequently, a differential equation with stochastic input occurs, whose solution determines the fair price in the refined model. Corresponding expected values and variances can be computed approximately via a Monte Carlo method. Alternatively, the generalised polynomial chaos yields an efficient approach for calculating the required data. Based on a parabolic equation modelling the fair price of Asian options, the technique is developed and corresponding numerical simulations are presented.

Keywords: Polynomial chaos; Parabolic equation; Method of lines; Volatility; Option price (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:2:p:245-255

DOI: 10.1016/j.matcom.2009.05.008

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