Pricing Derivatives with Counterparty Risk and Collateralization: A Fixed Point Approach by Dr. Tim Leung

Event Date: 

Wednesday, February 5, 2014 -
3:30pm to 5:00pm

Event Date Details: 

Refreshments served at 3:15 PM

Event Location: 

  • South Hall 5607F

Dr. Tim Leung (Columbia University)

Title: Pricing Derivatives with Counterparty Risk and Collateralization: A Fixed Point Approach

Abstract: We study a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. A fixed point approach is proposed to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fixed point via contraction mapping. This leads us to develop an accurate iterative numerical scheme for valuation. Specifically, we solve a sequence of linear inhomogeneous PDEs, whose solutions converge to the fixed point price function. We apply our methodology to compute the bid and ask prices for both defaultable equity and fixed-income derivatives, and illustrate the non-trivial effects of counterparty risk, collateralization ratio and liquidation convention on the bid-ask spreads. (joint work with Jinbeom Kim (Barclays))