# Seminar on Counterparty Risk and Funding

## Dr Alessandro Gnoatto

**Abstract**

The 2007 – 2009 financial crisis has had major implications on the formulation of several well-established concepts from financial mathematics. The classical problem of pricing and hedging of contingent claims needs to be analyzed under new conditions. Taking the perspective of a derivative desk, the price of a derivative should take into account the possibility that the counterparty might default. Moreover, the trading desk may finance its activity by means of different sources of funding simultaneously. The funding strategy of the desk will be influenced by the legal agreements that are in place with the counterparty, which are summarized by the credit support annex (CSA).

While practitioners have proposed several extensions of the classical Black-Scholes PDE hedging argument, academics have employed tools such as backward stochastic differential equations (BSDEs) to address these problems. In this seminar we will mainly base our analysis on BSDEs techniques while using PDEs as an informal tool to build intuition.

**Time/Date**: Tuesday 8-10 a.m.

**Target Participants**: Master students of Business Mathematics or Mathematics. Interested participants are asked to apply by email: *alessandro@alessandrognoatto.com*.

**Pre-requisites**: Finanzmathematik 2. Given the importance of interest rate related examples Finanzmathematik 3 is also desireable.

**References**

- Bielecki, T.R., Rutkowski, M.: Valuation and Hedging of Contracts with Funding Costs and Collateralization. SIAM J. Finan. Math., 6(1), 594–655. (2015)
- Brigo, D., Masetti, M.: A Formula for Interest Rate Swaps Valuation under Counterparty Risk in presence of Netting Agreements. (2005) https://papers.ssrn.com/sol3/papers2.cfm?abstract_id=717344
- Brigo, D. Buescu, C. Pallavicini, A., Liu, Q.: A note on the self-financing condition for funding, collateral and discounting Int. J. Theor. Appl. Finan. 18, 1550011 (2015)
- Burgard, C., Kjaer, M.: Partial differential equation representations of derivatives with counterparty risk and funding costs. J. Credit Risk 7(3), 1–19 (2011)
- Crépey,S.: Bilateral counterparty risk under funding constraints Part I: Pricing. Math. Financ. 25(1), 1–22 (2012a)
- Crépey, S.: Bilateral counterparty risk under funding constraints Part II: CVA. Math. Financ. 25(1), 23–50 (2012b)
- Crépey, S., Bielecki, T., Brigo, D.: Counterparty Risk and Funding: A Tale of Two Puzzles. Taylor & Francis, Abingdon (2014)
- Piterbarg,V.:Funding beyond discounting: collateral agreements and derivatives pricing. Risk Mag. 2, 97–102 (2010)