2012/05/15 by Igor Halperin, Andrey Itkin, Halperin, Igor +1 · 1 citation
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #Credit Risk and Financial Regulations #FOS: Economics and business #Financial Risk and Volatility Modeling #General Finance (q-fin.GN) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1205.3507
openalex publication_date 2012/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work addresses the problem of optimal pricing and hedging of a European\noption on an illiquid asset Z using two proxies: a liquid asset S and a liquid\nEuropean option on another liquid asset Y. We assume that the S-hedge is\ndynamic while the Y-hedge is static. Using the indifference pricing approach we\nderive a HJB equation for the value function, and solve it analytically (in\nquadratures) using an asymptotic expansion around the limit of the perfect\ncorrelation between assets Y and Z. While in this paper we apply our framework\nto an incomplete market version of the credit-equity Merton's model, the same\napproach can be used for other asset classes (equity, commodity, FX, etc.),≠.g. for pricing and hedging options with illiquid strikes or illiquid exotic\noptions.\n