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)
Heston-Hull-White모델은 확률 변동성 모델인 Heston 모델과 확률 이자율 모델인 Hull-White 모델을 결합한 하이브리드 모델이다. 본 연구에서 주식파생상품 ELS (Equity Linked Security)와 변액연금 GMWB (Guaranteed Minimum Withdrawal Benefits) 의 가격을 프라이싱하기 위해 위의 모델을 이용한다. 이 모델을 이용한 프라이싱을 통해, 장기 파생상품의 경우, 변동성과 이자율을 고정상수가 아닌 확률적 term structure을 적용하는 방법의 중요성을 분석한다. 그리하여 국내 시장에 하이브리드 모델을 적용하여 프라이싱을 해 본 결과, 확률적 변동성과 확률적 이자율의 중요도를 비교한다. 뿐만 아니라, 칼리브레이션을 위해, 기존 연구인 Fourier Transform이 아닌 Cosine Expansion Series를 적용하여 효율성을 높여보았다.
