Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging
研究了用流动性资产S和流动性期权Y作为代理，对流动性差的资产Z的欧式期权进行最优定价和对冲，通过效用无差异方法推导出HJB方程并给出解析解。
This work addresses the problem of optimal pricing and hedging of a European option on an illiquid asset Z using two proxies: a liquid asset S and a liquid European option on another liquid asset Y. We assume that the S-hedge is dynamic while the Y-hedge is static. Using the indifference pricing approach, we derive a Hamilton--Jacobi--Bellman equation for the value function. We solve this equation analytically (in quadrature) using an asymptotic expansion around the limit of perfect correlation between assets Y and Z. While in this paper we apply our framework to an incomplete market version of Merton's credit-equity 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.