The paper presents a valuation model of futures options trading at exchanges with initial margin requirements and daily price limit, and this result gives an academic guidance to design trading rules at exchanges. Unl...The paper presents a valuation model of futures options trading at exchanges with initial margin requirements and daily price limit, and this result gives an academic guidance to design trading rules at exchanges. Unlike the leading work of Black, certain trading rules are considered so as to be more fit for practical futures markets. The paper prices futures options with initial margin requirements and daily price limit by duplicating them with the help of the theory of backward stochastic differential equations （BSDEs, for short）. Furthermore, an explicit expression of the price Of the call （or the put） futures option is given and also is shown to be the unique solution of the associated nonlinear partial differential equation.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
基金Supported by National Natural Science Foundation of China (Grant Nos. 10701050, 10426022)Shandong Province (Grant No. Q2007A04), Postdoctoral Science Foundation of Shanghai (Grant No. 06R214121) National Basic Research Program of China (973 Program) (Grant No. 2007CB814904)
文摘The paper presents a valuation model of futures options trading at exchanges with initial margin requirements and daily price limit, and this result gives an academic guidance to design trading rules at exchanges. Unlike the leading work of Black, certain trading rules are considered so as to be more fit for practical futures markets. The paper prices futures options with initial margin requirements and daily price limit by duplicating them with the help of the theory of backward stochastic differential equations （BSDEs, for short）. Furthermore, an explicit expression of the price Of the call （or the put） futures option is given and also is shown to be the unique solution of the associated nonlinear partial differential equation.
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.
