On pricing derivatives under GARCH models: a dynamic Gerber-Shiu's approach

摘要: This paper proposes a method for pricing derivatives under the GARCH assumption underlying assets in context of “dynamic” version Gerber-Shiu’s optionpricing model. Instead adopting notion local risk-neutral valuation relationship (LRNVR) introduced by Duan (1995), we employ concept conditional Esscher Transforms Buhlmann et al. (1996) to identify martingale measure incomplete market setting. One advantage our model is that it provides unified and convenient approach deal with different parametric models innovation stock-price process. Under normality stock innovation, result consistent (1995). In line ∗Tak Kuen Siu, Ph.D., Research Fellow Liu Bie Ju Centre Mathematical Sciences, City University Hong Kong, Tat Chee Avenue, Kowloon, e-mail: tksiu@cityu.edu.hk †Howell Tong, Hon. F.I.A., Chair Professor Department Statistics Actuarial Science, The Pokfulam Road, htong@hku.hk. He also Statistics, London School Economics, U.K. ‡Hailiang Yang, A.S.A., an Associate hlyang@hkusua.hku.hk.