Exposure modelling under change of measure

Master Thesis


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University of Cape Town

The credit risk of a portfolio is often managed via measures of counter-party exposure, such as potential future exposure (PFE) and expected exposure (EE), with these measures playing an important role in setting economic and regulatory capital levels. For the sake of risk measurement and risk management these exposure measures should be computed under the real-world probability measure. However, due to the similarity of these exposure calculations to those used in calculating credit valuation adjustments, some have begun to compute them under the risk-neutral measure instead. This is problematic, as the magnitudes of PFEs and EEs differ under different equivalent martingale measures and their associated numéraires. Working with the Hull-White (HW) model of the short rate, the effect of a change of measure on the PFE and EE profiles of vanilla interest rate swaps and European swaptions is shown under three common measures: the money-market account measure, the T-forward measure and the Linear Gaussian Markovian (LGM) measure. A modified Least Squares Monte Carlo (LSM) algorithm, which allows for substantial computational savings, is then introduced in order to approximate contract level exposures under each of the aforementioned probability measures. Finally, a change of measure is implemented within the modified LSM algorithm in order to approximate exposure profiles under the real-world measure. The modified LSM algorithm is particularly useful for computing exposure profiles of contracts without closed-form valuation formulae, which would otherwise take significantly longer to compute via a standard Monte Carlo approach.