SIMULATION STUDY OF PARAMETERS’ INFLUENCE OF HESTON’S STOCHASTIC-JUMP MODEL ON VOLATILITY SMILE

Abstract

Abstract
This paper aims at presenting Heston’s Stochastic-Jump model, then study the parameters influence of the model on volatility smile. Complete derivation of the Heston’s Stochastic-Jump model was presented. Simulation studies were conducted and results show that Heston’s Stochastic-Jump model addresses the shortcomings of the Black-Scholes because the way the volatility is modelled is more realistic from financial market’s point of view compared to the constant volatility assumption since it takes into consideration what is observed in financial markets. Hence, combining jumps and stochastic volatility therefore
produces models which are more flexible and that can accurately fit observable market data.

Keywords: Heston’s Stochastic Model, Heston’s Stochastic-Jump Model, Black-Scholes’ Model, Volatility Smile