WISHART STOCHASTIC VOLATILITY MODELS WITH APPLICATIONS TO EMERGING FINANCIAL MARKETS DATA

Abstract

Financial markets are known to be far from deterministic but stochastic and hence random models tend to perfectly model the markets. The most recent development in stochastic models is the Wishart Stochastic Volatility Model which is a n dimensional model. The study aimed at modelling returns volatility in emerging financial market using Wishart Stochastic Volatility Model. Pricing in one dimension and two dimension was explored. A suitable Wishart Stochastic Volatility Model for an emerging financial market was constructed basing on the characteristics of an emerging financial market. Foreign Exchange derivative pricing was done under constant and stochastic correlation using finite difference method called the Crank Nicolson method. The study compared the modified Model (with stochastic correlation) to the Black scholes model (with constant correlation) using real data from emerging financial markets that is the exchange rates data for Kenya as the domestic currency and South Africa as the foreign currency. The modified model provide better volatility smiles compared to the Black scholes model and outperformed the Black scholes model as observed from the smallest AIC and BIC values.