Abstract
This paper proposes a fuzzy jump-diffusion option pricing model based on Merton's normal jump-diffusion price dynamics. The logarithm of the stock price is assumed to be a Gaussian fuzzy number and the diffusion and jump parameters of the Merton model are assumed to be triangular fuzzy numbers to model the impreciseness which occur due to the variation in financial markets. Using these assumptions, a fuzzy formula for a European call option has been proposed. Given any value of the option price, its belief degree is obtained by using the bisection search algorithm. The fuzzy call option prices have been defuzzified and it has been found that the fuzzy jump-diffusion model outperforms Wu's fuzzy Black- Scholes model. This is one of the first studies where the impreciseness of the stock price and input parameters has been modelled taking into account occasional large jumps in stock price trajectory and thereby proposing a fuzzy option pricing model.
The Option Pricing Model Based on Time Values: An Application of the Universal Approximation Theory on Unbounded Domains
