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雷达卡
英文标题：
《Utility indifference valuation for non-smooth payoffs with an
application to power derivatives》
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作者：
Giuseppe Benedetti and Luciano Campi
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最新提交年份：
2013
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英文摘要：
We consider the problem of exponential utility indifference valuation under the simplified framework where traded and nontraded assets are uncorrelated but where the claim to be priced possibly depends on both. Traded asset prices follow a multivariate Black and Scholes model, while nontraded asset prices evolve as generalized Ornstein-Uhlenbeck processes. We provide a BSDE characterization of the utility indifference price (UIP) for a large class of non-smooth, possibly unbounded, payoffs depending simultaneously on both classes of assets. Focusing then on European claims and using the Gaussian structure of the model allows us to employ some BSDE techniques (in particular, a Malliavin-type representation theorem due to Ma (2002)) to prove the regularity of Z and to characterize the UIP for possibly discontinuous European payoffs as a viscosity solution of a suitable PDE with continuous space derivatives. The optimal hedging strategy is also identified essentially as the delta hedging strategy corresponding to the UIP. Since there are no closed-form formulas in general, we also obtain asymptotic expansions for prices and hedging strategies when the risk aversion parameter is small. Finally, our results are applied to pricing and hedging power derivatives in various structural models for energy markets.
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中文摘要：
我们考虑了在简化框架下的指数效用无差异估值问题，其中交易资产和非交易资产是不相关的，但定价要求可能取决于两者。交易资产价格遵循多元Black and Scholes模型，而非交易资产价格则按照广义的Ornstein-Uhlenbeck过程演化。对于同时依赖于两类资产的一大类非光滑、可能无界的收益，我们提供了效用无差异价格（UIP）的BSDE特征。然后，关注欧洲索赔并使用模型的高斯结构，允许我们使用一些BSDE技术（特别是Malliavin型表示定理，根据Ma（2002））来证明Z的正则性，并将可能不连续的欧洲支付的UIP描述为具有连续空间导数的适当偏微分方程的粘性解。最优套期保值策略本质上也被确定为与UIP对应的增量套期保值策略。由于一般不存在闭式公式，当风险规避参数很小时，我们还得到了价格和套期保值策略的渐近展开式。最后，我们的结果被应用于能源市场各种结构模型中的电力衍生品定价和套期保值。
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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