Exotic options, or “path-dependent” options are options whose payoff depends on the behavior of the price of the underlying between 0 and the maturity, rather than merely on the final price of the underlying, such a...Exotic options, or “path-dependent” options are options whose payoff depends on the behavior of the price of the underlying between 0 and the maturity, rather than merely on the final price of the underlying, such as compound options, reset options and so on. In this paper, a generalization of the Geske formula for compound call options is obtained in the case of time-dependent volatility and time-dependent interest rate by applying martingale methods and the change of numeraire or the change of probability measure. An analytic formula for the reset call options with predetermined dates is also derived in the case by using the same approach. In contrast to partial differential equation (PDE) approach, our approach is simpler.展开更多
This paper studies incomplete stock market that includes discontinuous price processes. The discontinuity is modeled by very general point processes admitting only stochastic intensities. Prices are driven by jump-dif...This paper studies incomplete stock market that includes discontinuous price processes. The discontinuity is modeled by very general point processes admitting only stochastic intensities. Prices are driven by jump-diffusion uncertainty and have random but predictable jumps. The space of risk-neutral measures that are associated with the market is identified and related to fictitious completions. The construction of replicating portfolios is discussed, and convex duality methods are used to prove existence of optimal consumption and investment policies for a problem of utility maximization.展开更多
In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in th...In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in the period 31 May 2011 to 30 March 2018 obtained from Ethiopia commodity exchange(ECX)market to analyse the price fluctuation.The nature of log-returns of the price is asymmetric(negatively skewed)and exhibits high kurtosis.We used jump diffusion models for modeling and option pricing the coffee price.The method of maximum likelihood is applied to estimate the parameters of the models.We used the root mean square error(RMSE)to test the validation of the models.The values of RMSE for Merton’s and double exponential jump diffusion models are 0.1093 and 0.0783,respectively.These results indicate that the models fit the data very well.We used analytical and Monte Carlo technique to find the call option pricing of WSDA3 price.Based on the empirical results,we concluded that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of this coffee price.展开更多
基金Project (No. Y604137) supported by the Natural Science Foundationof Zhejiang Province, China
文摘Exotic options, or “path-dependent” options are options whose payoff depends on the behavior of the price of the underlying between 0 and the maturity, rather than merely on the final price of the underlying, such as compound options, reset options and so on. In this paper, a generalization of the Geske formula for compound call options is obtained in the case of time-dependent volatility and time-dependent interest rate by applying martingale methods and the change of numeraire or the change of probability measure. An analytic formula for the reset call options with predetermined dates is also derived in the case by using the same approach. In contrast to partial differential equation (PDE) approach, our approach is simpler.
基金This research is partially supported by NSF under DMI-9908294 and DMI-0196084.
文摘This paper studies incomplete stock market that includes discontinuous price processes. The discontinuity is modeled by very general point processes admitting only stochastic intensities. Prices are driven by jump-diffusion uncertainty and have random but predictable jumps. The space of risk-neutral measures that are associated with the market is identified and related to fictitious completions. The construction of replicating portfolios is discussed, and convex duality methods are used to prove existence of optimal consumption and investment policies for a problem of utility maximization.
文摘In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in the period 31 May 2011 to 30 March 2018 obtained from Ethiopia commodity exchange(ECX)market to analyse the price fluctuation.The nature of log-returns of the price is asymmetric(negatively skewed)and exhibits high kurtosis.We used jump diffusion models for modeling and option pricing the coffee price.The method of maximum likelihood is applied to estimate the parameters of the models.We used the root mean square error(RMSE)to test the validation of the models.The values of RMSE for Merton’s and double exponential jump diffusion models are 0.1093 and 0.0783,respectively.These results indicate that the models fit the data very well.We used analytical and Monte Carlo technique to find the call option pricing of WSDA3 price.Based on the empirical results,we concluded that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of this coffee price.