Historical or implied?

To calculate counterparty exposure, we need to know the volatility of our risk factors (interest rates, stock prices, etc.) in the future.

How can we forecast the future volatilities? We can either

  • use the volatility implied by options (caps, floors and swaptions for interest rate, FX options for exchange rate)

or

  • use historical volatility of the risk factors.

Which one will better predict the volatility in the future? The analysis by De Jong et al. suggests that the volatility implied by the options is a poor predictor, because it consistently overestimates realised volatility. That means, we have to use historical volatility in exposure calculations. Their results, however, are based on fairly old data; it would be interesting to repeat their experiments with recent time series.

On the other hand, when we calculate CVA, we must use implied volatilities, by definition of CVA.

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