General Properties of Solutions to Inhomogeneous Black-Scholes Equations with Discontinuous Maturity Payoffs and Application

Abstract

We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results are applied in pricing defaultable discrete coupon bonds.

26 pages, 4 figures. In Version 2 the section 5 is revised

References in corpus (2)

• Higher Order Binaries with Time Dependent Coefficients and Two Factors - Model for Defaultable Bond with Discrete Default Information
• The Pricing of Multiple-Expiry Exotics

Cited by in corpus (2)

• Pricing Formulae of Power Binary and Normal Distribution Standard Options and Applications
• Analysis on the Pricing model for a Discrete Coupon Bond with Early redemption provision by the Structural Approach