Abstract
In this paper, we consider the pricing problem of options with counterparty default risks. We study the asymptotic behavior of vulnerable option prices in the worst case scenario under an uncertain volatility model which contains both corporate assets and underlying assets. We propose a method to estimate the price of vulnerable options when the volatility of the underlying assets is within a small interval. By imposing additional conditions on the boundary condition and cutting the obtained Black–Scholes–Barenblatt equation into two Black–Scholes-like equations, we obtain an approximate method for solving the fully nonlinear partial differential equation satisfied by the price of vulnerable options under the uncertain volatility model.
Highlights
With the continuous opening and development of China’s financial market in recent years, the domestic option market has made a major breakthrough in practical terms
2 Pricing vulnerable options under uncertain volatility model we introduce the vulnerable options under uncertain volatility model
5 Conclusion In this paper, we analyze the behavior of vulnerable option prices in the worst case scenario
Summary
With the continuous opening and development of China’s financial market in recent years, the domestic option market has made a major breakthrough in practical terms. The option pricing under uncertain volatility model by nonlinear partial differential equation (PDE for short) has been studied in their papers. 2, the vulnerable options under the uncertain volatility model are briefly introduced, and the BSB equations of the option prices are given. Through the analysis of the error term, the expected form of the error term is obtained and decomposed into three parts These three parts of control are given by the stochastic control theory and the character of the worst-case vulnerable option price process. We get the vulnerable option prices in the worst case scenario at time t < T as follows: F(t, Xt, Yt) = e–r(T–t) esssup E φ(XT , YT )|Ft , σ ∈A[σ ,σ ]. We decide to solve this problem by simplifying it to two Black–Scholes-like PDEs
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