Markov Financial Model Using Hidden Markov Model

Abstract

Black-Scholes model is a very famous model using to estimate option prices in stock market. The model is based on Brownian motion and Normal distribution as an evolutionary process of the underlying asset. However, the evolutionary process of the underlying asset is always in a changing environment that changing from "good" to "bad", "bad" to "normal", and so on. Therefore, the option values can be affected by this environment. Janssen (Janssen, Manca and E.Volpe, 2009) proposed a new model for Black-Scholes formula by assuming the environment as a Markov chain with the state space including "good", "normal", "bad", etc. (sometime called Markov Black-Scholes model in this paper). The most importance of this model is to estimate the parameters of the Markov chain which is the best appropriate to the environment that the underlying asset in. This issue still not be addressed reasonably up to now. On the other hand, Zucchini and Macdonald 2009 introduced Hidden Markov models for time series using R programming. Thus, we applied the Hidden Markov model using Normal distribution to the historical data of VN-Index to find out the Markov model that fits best the data. It is clear that Hidden Markov model can be used to estimate the parameters for the Markov Black-Scholes model. In this article, we present in detail how to use Hidden Markov model in Markov Black-Scholes model and illustrate the acquired results for daily VN-Index historical data from 2009 to 2011. This combination makes the parameters in the model have more significance for the reality.