论文标题
在随机波动性跳跃扩散动力下的交换期权价格的代表
Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamics
论文作者
论文摘要
在本文中，我们根据Merton（1976），Heston（1993）和Bates（1996）的模型提供了在随机波动跳跃（SVJD）动态下的欧美交换期权价格的代表。还引入了ra子 - 尼克比衍生物过程，以促进从客观市场衡量标准转移到其他等效概率措施（包括等效的玛格尔措施）的转变。在同等标准的措施下，我们得出了以交换期权价格来表征的全部派对微分方程。我们还使用Geman等人提出的数字变更技术来得出欧洲交换期权价格的代表。 （1995）和Caldana和Fusai（2013）得出的傅立叶反演公式，并表明这两种表示是可比的。最后，我们表明，美国的交换期权价格可以分解为欧洲交换期权的价格和早期的溢价。
In this article, we provide representations of European and American exchange option prices under stochastic volatility jump-diffusion (SVJD) dynamics following models by Merton (1976), Heston (1993), and Bates (1996). A Radon-Nikodym derivative process is also introduced to facilitate the shift from the objective market measure to other equivalent probability measures, including the equivalent martingale measure. Under the equivalent martingale measure, we derive the integro-partial differential equation that characterizes the exchange option prices. We also derive representations of the European exchange option price using the change-of-numeraire technique proposed by Geman et al. (1995) and the Fourier inversion formula derived by Caldana and Fusai (2013), and show that these two representations are comparable. Lastly, we show that the American exchange option price can be decomposed into the price of the European exchange option and an early exercise premium.
