Journal of Data Science

Abstract: In this article, we consider a model of time-varying volatility which generalizes the classical Black-Scholes model to include regime-switching properties. Specifically, the unobservable state variables for stock fluctuations are modeled by a Markov process, and the drift and volatility parameters take different values depending on the state of this hidden Markov process. We provide a closed-form formula for the arbitrage-free price of the European call option, when the hidden Markov process has finite number of states. Two simulation methods, the discrete diffusion method and the Markovian tree method, for computing the European call option price are presented for comparison.

Abstract: Polya tree, by embedding parametric families as a special case, provides natural suit to test goodness of fit of a parametric null with non parametric alternatives. For this purpose, we present a new construction on Polya tree for random probability measure, which aims to perform an easy multiple χ 2 test for goodness of fit. Examples of data analyses are provided in simulation studies to highlight the performance of the proposed methods.