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
The pricing theories of capital assets are the principal part in the modern financial theories. Presently, the capital asset pricing model and the arbitrage pricing theory, including their evolutional forms, all don＇...The pricing theories of capital assets are the principal part in the modern financial theories. Presently, the capital asset pricing model and the arbitrage pricing theory, including their evolutional forms, all don＇t embody the premium of non-system risks and non-factor risks. This paper analyses the risk reward of traditional capital assets pricing models, revises the traditional capital assets pricing models, and advances the revised models of capital assets pricing theories basing on full-risk reward.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.
文摘The pricing theories of capital assets are the principal part in the modern financial theories. Presently, the capital asset pricing model and the arbitrage pricing theory, including their evolutional forms, all don＇t embody the premium of non-system risks and non-factor risks. This paper analyses the risk reward of traditional capital assets pricing models, revises the traditional capital assets pricing models, and advances the revised models of capital assets pricing theories basing on full-risk reward.
