Fuzzy Option Pricing with Data-Driven Volatility using Novel Monte-Carlo Approach

Abstract

Fuzzy numbers play an important part in the advanced theory of computational finance, which is undergoing a revolution aided by the powerful simulation and data-driven models. The volatility parameter is the most important parameter for pricing short-term options and arguably one of the important parameters for all financial time series. Traditional option pricing models determine the option's expected return without taking into account the uncertainty associated with the underlying asset price volatility. Fuzzy set theory can be used to explicitly account for such uncertainty. There has been a growing interest in studying fuzzy option pricing for European options and binary options using hybrid models. However, those fuzzy coefficient hybrid models are not data-driven. This paper uses data-driven volatility forecasts to study fuzzy European option pricing. A simple yet effective fuzzy option pricing model incorporating data-driven exponentially weighted moving average (EWMA) and neuro volatility models is presented to obtain fuzzy volatility forecasts and fuzzy option prices. The dynamics of the underlying assets is complex and hence it is preferable to use the Monte Carlo (MC) simulation, to get rid of the assumptions in the commonly used Black Scholes (BS) models. Using the data-driven fuzzy a-cuts of the annualized volatility, a-cuts of the call and put option prices based on novel MC simulation are obtained using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> or Laplace distributed asset log returns. The driving idea, unlike the existing MC option pricing with normality assumption, is that the proposed novel MC method uses the data-driven <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> or Laplace distribution of asset log returns and nonlinear adaptive fuzzy volatility.