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Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition by Jon Gregory

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16.3 Exposure Hedges

The next sections will examine the above CVA components in more detail and from a practical perspective. The following assumptions will be used unless otherwise stated:

Trade: 5-year payer interest rate swap
Interest rates: Increasing term structure corresponding to 1- to 5-year interest rates of 4.0%, 4.25%, 4.5%, 4.75% and 5.0%, respectively
Volatility: The interest rate volatility is assumed to be 25%11
Credit quality: We assume the counterparty has an initial CDS premium of 500 bps and recovery rate of 40%
Notional: 100m (most of the results are given as percentages so this is not relevant)

For all quantitative examples, we will tend to assume a complete liquidity of hedging instruments but also comment on the practicality of the strategies due to the availability of the hedging instruments in today's market.

We first consider the hedging of the CVA component arising from the exposure that can be divided into the impact of spot/forward rates and volatilities. Correlation (which is typically not hedgeable) is discussed later.

16.3.1 Spot/Forward Rates

The hedging of underlying CVA spot rates for CVA usually mirrors hedges corresponding to the risk-free instrument. In Figure 16.4 we show both the risk-free and CVA interest rate sensitivities for the interest rate swap in question.

Figure 16.4 Sensitivity of the risk-free swap value and the CVA of the swap to a 1 bp move in the underlying interest rates assuming the counterparty CDS premium is ...

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