A fuzzy approach to option pricing in a Levy process setting

Piotr Nowak · Maciej Romaniuk

31 citations0/0 files storedInternational Journal of Applied Mathematics and Computer Science

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Stochastic processes and financial applications Risk and Portfolio Optimization Fuzzy Systems and Optimization

Abstract

Abstract In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets.We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.

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References

1996Fuzzy sets 1973The Pricing of Options and Corporate Liabilities 1980Fuzzy Sets and Systems - Theory and Applications 1976Option pricing when underlying stock returns are discontinuous 2016“Options, Futures, and Other Derivatives”2003Options, Futures and Other Derivatives 2003Monte Carlo Methods in Financial Engineering 1997Empirical Performance of Alternative Option Pricing Models

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2016Valuing catastrophe bonds involving correlation and CIR interest rate model 2016A geometric Levy model for n -fold compound option pricing in a fuzzy framework

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