American Options with Asymmetric Information and Reflected BSDE

TL;DR

This paper models American options in a market with asymmetric information using reflected backward stochastic differential equations, providing a way to quantify the value of extra information for the buyer.

Contribution

It introduces a novel representation of American option value with asymmetric information through solutions of reflected BSDEs, accounting for the buyer's additional knowledge.

Findings

Representation of American option value with asymmetric information using RBSDEs

Quantification of the value of extra information for the buyer

Application of initial enlargement of filtration in pricing models

Abstract

We consider an American contingent claim on a financial market where the buyer has additional information. Both agents (seller and buyer) observe the same prices, while the information available to them may differ due to some extra exogenous knowledge the buyer has. The buyer's information flow is modeled by an initial enlargement of the reference filtration. It seems natural to investigate the value of the American contingent claim with asymmetric information. We provide a representation for the cost of the additional information relying on some results on reflected backward stochastic differential equations (RBSDE). This is done by using an interpretation of prices of American contingent claims with extra information for the buyer by solutions of appropriate RBSDE.