摘要翻译：
本文研究了非流动性资产$Z$上的欧式期权的最优定价和套期保值问题，使用了一组代理：流动性资产$S$和$N$流动性欧式期权$P_i$,每个代理都写在流动性资产$Y_i上，i=1,N$。我们假设$s$-hedge是动态的，而多名称$y$-hedge是静态的。利用指数效用的无差异定价方法，导出了价值函数的HJB方程，并建立了一个有效的数值算法。后者基于变量的多次变化、分裂格式和一组快速高斯变换(FGT),它比有限差分法在复杂度和局部空间误差方面更有效。虽然在本文中，我们将我们的框架应用于信贷-股票默顿模型的不完全市场版本，但同样的方法也可以用于其他资产类别（股票、商品、外汇等），例如对具有非流动性罢工或非流动性奇异期权的期权定价和对冲。
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英文标题：
《Pricing Illiquid Options with $N+1$ Liquid Proxies Using Mixed
  Dynamic-Static Hedging》
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作者：
I. Halperin and A. Itkin
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最新提交年份：
2012
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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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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  We study the problem of optimal pricing and hedging of a European option written on an illiquid asset $Z$ using a set of proxies: a liquid asset $S$, and $N$ liquid European options $P_i$, each written on a liquid asset $Y_i, i=1,N$. We assume that the $S$-hedge is dynamic while the multi-name $Y$-hedge is static. Using the indifference pricing approach with an exponential utility, we derive a HJB equation for the value function, and build an efficient numerical algorithm. The latter is based on several changes of variables, a splitting scheme, and a set of Fast Gauss Transforms (FGT), which turns out to be more efficient in terms of complexity and lower local space error than a finite-difference method. While in this paper we apply our framework to an incomplete market version of the credit-equity Merton's model, the same approach can be used for other asset classes (equity, commodity, FX, etc.), e.g. for pricing and hedging options with illiquid strikes or illiquid exotic options.
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PDF链接：
https://arxiv.org/pdf/1209.3503