Risk-indifference Pricing of American-style Contingent Claims

TL;DR

This paper introduces a risk-indifference pricing framework for American-style contingent claims using dynamic convex risk measures, accommodating different information levels and providing a basis for numerical methods via deep learning.

Contribution

It defines continuous-time risk-indifference prices for American options with asymmetric information and characterizes these prices through reflected backward stochastic differential equations.

Findings

Risk-indifference prices are consistent with no-arbitrage principles.

Characterization via reflected BSDEs enables numerical implementation.

Framework applies to stochastic volatility models.

Abstract

This paper studies the pricing of contingent claims of American style, using indifference pricing by fully dynamic convex risk measures. We provide a general definition of risk-indifference prices for buyers and sellers in continuous time, in a setting where buyer and seller have potentially different information, and show that these definitions are consistent with no-arbitrage principles. Specifying to stochastic volatility models, we characterize indifference prices via solutions of Backward Stochastic Differential Equations reflected at Backward Stochastic Differential Equations and show that this characterization provides a basis for the implementation of numerical methods using deep learning.