Quantifying and hedging wrong-way risk in interest rate swaps using copulas

Quantifying and hedging wrong-way risk in interest rate swaps using copulas

Draijer, M.J. (TU Delft Electrical Engineering, Mathematics and Computer Science)

Cirillo, P. (mentor)
Oosterlee, C.W. (graduation committee)
Arendshorst, Bart (mentor)

Delft University of Technology

Applied Mathematics

2020-07-17

Wrong-way risk (WWR), which is the dependence between the probability of default (PD) and the exposure at default of a counterparty, is an aspect of credit risk that can lead to high losses. This thesis aims firstly to quantify WWR in interest rate swaps (IRSs) using a copula model, where a copula is used to couple the PD implied by credit default swap (CDS) spreads and the 10 year swap rates. Specific attention is given to choosing and fitting a copula. For datasets obtained from periods of regular economic conditions and periods of financial crisis, the t copula is found to be the best fit. In general, negative dependence between the log-returns of the implied PDs and the log-returns of the swap rates is observed, especially in the tails of high PD log-returns and low swap rate log-returns during regular periods. This means that the general demand for loans is lower during a worsening economy. During crisis periods however, the dependence is weaker than in regular periods; implying that loans are in higher demand in these times, e.g. because companies need loans to survive.
The second purpose of this thesis is the introduction of a novel product aimed at hedging WWR in IRSs. This product, named an IRS partial insurance contract (IPI), introduces an upper bound to the credit losses on an IRS. If this bound is exceeded, the amount by which the losses exceed the bound is paid out by the IPI seller to the IPI buyer. An analytical expression for the no-arbitrage price of an IPI is obtained, using a copula model for WWR. This expression shows that an IPI can be replicated by a portfolio of swaptions and CDSs.

Wrong-way risk
Copulas
Interest rate swaps
Derivatives

http://resolver.tudelft.nl/uuid:dbd8cfc4-df7e-4847-b41f-0381eb08d651

Student theses

master thesis

© 2020 M.J. Draijer