带跳模型中期权价格的性质
Properties of option prices in models with jumps
摘要：
利用期权价格满足抛物型积分微分方程这一事实，研究了带跳模型中期权价格的凸性和单调性。给出了保凸性成立的条件，即在所选的鞅测度下，具有凸合约函数的期权的价值作为标的股票价格的函数是凸的。保凸性被用来推导出期权价值相对于模型中不同参数的单调性，如波动率、跳跃大小和跳跃强度。
英文摘要：
We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro-differential equations. Conditions are provided under which preservation of convexity holds, i.e. under which the value, calculated under a chosen martingale measure, of an option with a convex contract function is convex as a function of the underlying stock price. The preservation of convexity is then used to derive monotonicity properties of the option value with respect to the different parameters of the model, such as the volatility, the jump size and the jump intensity.
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