This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk. As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. The q-optimal pricing measure is related to the marginal utility indifference price of an agent with constant relative risk aversion. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same. As a concrete example, we specialize to a variant of the Hull-White or Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter q. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying q. Copyright Springer Science + Business Media, Inc. 2005
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机译:本文研究了具有相关性的不完全随机波动率模型中的期权价格。在一般情况下,我们证明了排序结果,该结果表明,具有凸收益的欧洲期权的价格正在波动风险的市场价格中下降。例如,作为我们的主要动机,我们研究了q最优定价方法下的期权定价。 q最优定价度量与具有相对风险规避不变的代理商的边际效用无差异价格有关。利用排序结果,我们证明了在最小,、最小熵和方差最优定价措施下的期权价格之间的比较定理。如果夏普比率是确定的,则比较会崩溃,这是众所周知的结果,即在这三种定价方法下计算出的期权价格是相同的。作为一个具体的例子,我们专注于夏普比的波动率在增加的赫尔-怀特或赫斯顿模型的变体。对于此示例,我们能够推断出期权价格在参数q中正在下降。定价pde的数值解证实了该理论,并显示了由于q的变化而导致的期权价格差异的大小。版权所有Springer Science + Business Media,Inc. 2005
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