在标的资产价格遵循跳跃扩散过程条件下,怎样定价重设型卖权是十分重要的.本文的目标就是计算出跳跃扩散重设型卖权的定价公式。按照Merton的思想,利用几何Brown运动描述只有系统风险的资产价格运动,用 Poisson随机过程描述产生非系统...在标的资产价格遵循跳跃扩散过程条件下,怎样定价重设型卖权是十分重要的.本文的目标就是计算出跳跃扩散重设型卖权的定价公式。按照Merton的思想,利用几何Brown运动描述只有系统风险的资产价格运动,用 Poisson随机过程描述产生非系统风险的偶然的资产价格的跳跃,并且假设跳跃幅度服从正态分布.通过求解 Ito skorohod随机方程,对冲系统风险运用风险中性定价方法,进而用一维与二维的正态分布函数计算各个部分的条件期望,得到无穷级数形式的跳跃扩散重设型卖权的定价公式.展开更多
We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asse...We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two- stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.展开更多
文摘在标的资产价格遵循跳跃扩散过程条件下,怎样定价重设型卖权是十分重要的.本文的目标就是计算出跳跃扩散重设型卖权的定价公式。按照Merton的思想,利用几何Brown运动描述只有系统风险的资产价格运动,用 Poisson随机过程描述产生非系统风险的偶然的资产价格的跳跃,并且假设跳跃幅度服从正态分布.通过求解 Ito skorohod随机方程,对冲系统风险运用风险中性定价方法,进而用一维与二维的正态分布函数计算各个部分的条件期望,得到无穷级数形式的跳跃扩散重设型卖权的定价公式.
基金the Research Grants Councilof the Hong Kong Special Administrative Region,China(Project No.HKU 754008H)
文摘We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two- stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.
