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.
