论文标题
在随机波动和跳扩散动力学下，交换选项问题的呼叫转换
A Put-Call Transformation of the Exchange Option Problem under Stochastic Volatility and Jump Diffusion Dynamics
论文作者
论文摘要
我们的价格为欧美交换选择权，其中基础资产价格是使用Merton（1976）的跳跃式建模的，并使用Common Heston（1993）随机波动过程进行了建模。正如Bjerskund and Stensland（1993）所建议的那样，通过将第二个资产收益率工艺设置为数字资产来获得的同等标准措施进行定价。这种数字的选择减少了交换选项的定价问题，即二维问题，以定价以两种资产的收益过程比率（一个一维问题）编写的呼叫选项。然后，通过积分变换从相应的kolmogorov向后方程确定资产收益率过程和瞬时方差过程的关节过渡密度函数。然后，我们确定欧洲交换期权价格的积分表示和早期的溢价，并陈述一个链接的积分方程系统，该系统是美国交换期权价格和相关的早期练习边界的特征。还讨论了早期运动边界的特性。
We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent martingale measure obtained by setting the second asset yield process as the numeraire asset, as suggested by Bjerskund and Stensland (1993). Such a choice for the numeraire reduces the exchange option pricing problem, a two-dimensional problem, to pricing a call option written on the ratio of the yield processes of the two assets, a one-dimensional problem. The joint transition density function of the asset yield ratio process and the instantaneous variance process is then determined from the corresponding Kolmogorov backward equation via integral transforms. We then determine integral representations for the European exchange option price and the early exercise premium and state a linked system of integral equations that characterizes the American exchange option price and the associated early exercise boundary. Properties of the early exercise boundary near maturity are also discussed.
