离散抽样方差互换定价研究

Pricing discretely-sampled variance swaps under a class of SVJ models

文章在一类随机波动跳跃(SVJ)模型下给出离散抽样远期起始方差互换公平敲定价解析解存在的充分条件和具体计算方法.文中所定义的这一类SVJ模型包含了很多现有文献中广泛使用的SVJ模型.先前关于离散抽样方差互换公平敲定价解析解的研究都局限在仿射型随机波动模型下,而文章中的方法不仅适用于仿射模型,对许多非仿射模型同样适用.文章在Heston模型和Hull&White模型下给出解析解表达式和数值计算结果.Heston模型为仿射结构,现有文献已有解析解;而Hull&White模型为非仿射结构,现有文献中只提供了数值解.通过比较可以发现,文章中的结果与现有文献中的解析解和数值解非常接近,从而佐证了结论的正确性.

We derive analytic formulas for fair strike prices of discretely-sampled( forward-start) variance swaps under a class of stochastic volatility jump( SVJ) models. This class covers a couple of stochastic volatility and jump models which have been studied widely in literature including both affine and non-affine models.We demonstrate a general methodology to find analytic formulas for the class while we obtain explicit solutions for several special cases. Numerical examples show that our solutions give close results to Monte Carlo simulations. Obviously,our explicit solutions beat the latter in speed.