Abstract
One of the key components of counterparty credit risk (CCR) measurement is generating scenarios for the evolution of the underlying risk factors, such as interest and exchange rates, equity and commodity prices, and credit spreads. Geometric Brownian Motion (GBM) is a widely used method for modeling the evolution of exchange rates. An important limitation of GBM is that, due to the assumption of constant drift and volatility, stylized facts of financial time-series, such as volatility clustering and heavy-tailedness in the returns distribution, cannot be captured. We propose a model where volatility and drift are able to switch between regimes; more specifically, they are governed by an unobservable Markov chain. Hence, we model exchange rates with a hidden Markov model (HMM) and generate scenarios for counterparty exposure using this approach. A numerical study is carried out and backtesting results for a number of exchange rates are presented. The impact of using a regime-switching model on counterparty exposure is found to be profound for derivatives with non-linear payoffs.
Highlights
One of the main factors that amplified the financial crisis of 2007–2008 was the failure to capture major risks associated with over-the-counter (OTC) derivative-related exposures (Basel Committee on Banking Supervision 2010a)
In the rest of this section, we introduce the theory of hidden Markov models (HMMs), following Rabiner (1990)
In order to study the impact of using a two-state HMM, instead of a Geometric Brownian Motion (GBM), on regulatory and economic capital, we consider the case of foreign exhange (FX) call options on the RUB/EUR rate
Summary
One of the main factors that amplified the financial crisis of 2007–2008 was the failure to capture major risks associated with over-the-counter (OTC) derivative-related exposures (Basel Committee on Banking Supervision 2010a). Banks are required to hold regulatory capital against their current and future exposures to all counterparties in OTC derivative transactions. Risk Factor Evolution (RFE) models are, arguably, the most important part of counterparty exposure modeling, since small changes in the underlying risk factors may have a profound impact on the exposure and, as a result, on the regulatory and economic capital buffers. It is, crucial for financial institutions to put significant effort in the design and calibration of RFE models and, in addition, have a sound framework in place in order to assess the forecasting capability of the model
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