Heston-hull-white model for long term exotic option

Abstract

ELS (Equity Linked Security) from investment banks and VA (Variable Annuities) from insurance companies, have become considered by many to become an integral part of their life-long portfolios. The Black-Scholes formula is reasonable to apply when we derive simple European option value with a short-term to maturity. However, by considering stochastic volatility and stochastic interest rate, we can better price the exotic options with long-term maturity since the volatility of the stock varies from time to time as well as the interest rate. I chose the combined Heston stochastic volatility and Hull-White stochastic interest rate model to best determine accurate pricing. In addition, the financial world is now focusing on finding methods for accurate and speedy pricing of exotic and hybrid products. Hybrid model methods are based on combinations from different underlying asset classes. The stochastic volatility model which incorporates the stochastic term structure of interest rate is useful for pricing exotic and hybrid products. Besides, characteristic function, as an essential requirement on all Fourier-based calibrations, can be relatively easily derived through this hybrid model. This also allows the calibration process to have better approximation. For calibration purposes the Fourier cosine expansion will be employed. This novel method, called the COS method, is an alternative to the FFT method. It has been proven to improve the speed of pricing European and some exotic options by Fang & Oosterlee (2009)