Modelling Credit Risk & Funding

Specialeforsvar ved Jakob Banning Iversen

 Titel: Modelling Credit Risk & Funding

Abstract: This thesis covers the topics of adjusting financial contracts for the cost of counterparty credit risk (CVA) and funding costs (FVA). A secondary topic is tackling the lack of a risk-free rate for discounting. Recent evolution in finance has shown that the value of a derivative is impacted by real world frictions. These frictions are specific to each party, and so are the valuation adjustments (xVA). Quantifying the impact on the contract value, auxiliary models for, among others, counterparty default and funding spreads are needed. Building, merging and running these auxiliary models are the responsibility of xVA desks, which have been allocated increasing resources in recent years. The main purpose of this thesis is to establish a unifying framework for calculating CVA and FVA. The central example throughout this paper is pricing of an interest rate swap (IRS) against ISS Global A/S (ISS), and quantifying counterparty credit risk and funding cost. Advancing from theoretically pricing the IRS, we calibrate a short rate Hull-White (HW) model to the swap market, develop and calibrate a Cox-Ingersoll-Ross (CIR) model for default simulation and finally establish a Piterbarg-like setup for stochastic funding. Ultimately all models are merged in a fully stochastic framework, to estimate the impact of counterparty credit risk and funding. Throughout, we treat issues such as; finding the appropriate proxy for a risk-free rate, pricing in the presence of multiple curves, calibration of models, effects of collateralization, portfolio CVA and FVA aggregation, wrong- and right-way risk and computational issues relating to xVA’s. All models are implemented in MATLAB and the intuitive understanding of every theoretical result is emphasized. Throughout the paper we support complex discussions, structures and results by visual representations. In a setup with a repo market, funding and collateral, we are able to estimate contract prices by a Feynman-Kac expression. This expression is compared to the value without funding costs to estimate funding effects. The main finding in this paper is that even in times of relatively low funding spreads (10-30bps), FVA may be considerable and of comparable size to CVA. On the notional €100, 20 year swap, CVA is estimated to −€1.3493 and FVA to −€0.81001. In addition to producing numerical estimates, we also show that we can unify all stochastic models in a single framework giving results consistent with the theoretical foundation. We discuss the problematic consequences of adjusting for funding and finish with a review of the opposition. Finally, we debate what some of the structural issues of xVA calculations are and where the development is headed in the coming years.

Vejledere:  Rolf Poulsen, William Cooper, SEB
Censor:      Christoffer Kanstrup, Danske Bank