The paper derives a closed-form option pricing formula accounting for the systematic
risk of the underlying assets. By Black-Scholes option pricing formula, the total risk,
or the volatility of the underlying assets matters in option pricing. As the systematic
risk, the main component of total risk, is claimed to determine the return of assets by
the proponents of the theory of capital asset pricing model (CAPM), the paper tries
to incorporate the systematic risk into the stochastic return process. Additionally, a
GARCH(p,q) process is assumed by the variance of asset returns and the market index
returns, a usual proxy for the systematic risk. The model also extends the GARCH
option pricing formula derived by Heston and Nandi (2000) to include the systematic
risk when the lag of GARCH p and q are greater than one. The numerical study uses
Finance Sector Index in Taiwan Stock Exchange as the price of the underlying asset. The
numerical results show that there exists a beta smile for the implied volatility when the
systematic risk is considered in option pricing, suggesting that the level of the systematic
risk does affect the option price.
Keywords: CAPM, GARCH, risk-neutral density, beta smile.
JEL classification code: G12, G13.
학술대회/행사
학술대회안내
[2008년 제 4차] Systematic Risk in GARCH Option Pricing: A Theoreti
작성자 : 관리자
조회수 : 771
게시일 :
2008-12-11