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I was of the understanding that risk neutral drift was always the risk free rate. A section from Gregory's book on Credit Value Adjustment seems to say risk neutral drifts are typically estimated from futures. Have I just misunderstood the text (I'm hoping so, because it sounds completely wrong to me)?

If risk neutral drifts can be different than the risk free rate and risk neutral drift can be estimated from futures, how then do we observe real world drifts?

Here is an excerpt of the text:

One area where risk-neutral parameters tend to be used even for risk management simulations is the determination of the drifts of underlying risk factors, which are typically calibrated from forward rates.

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Despite the above problems with drifts, most PFE (potential future exposure) and CVA calculations will calibrate to forward rates in the market. From the CVA point of view, this is justified by hedging. For PFE purposes, this is often done more for convenience’s sake, since it means that simple instruments are by construction priced properly and circumvents the need to attempt to estimate the “real-world” drift of risk factors.

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  • $\begingroup$ I think "drifts of underlying risk factor" is not related to the "risk-neutral drift". Think of the former as the future $\endgroup$ – Thomas Maloney Sep 20 '15 at 22:25
  • $\begingroup$ Posted too soon. Think of the former as the drift of a stock price. $\endgroup$ – Thomas Maloney Sep 20 '15 at 22:26
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The risk neutral drift is the risk free rate for an asset with no dividends, no cost of carry, no repo cost, etc. Otherwise the drift has to be adjusted to take these into account, and the easiest way to do it (when available) is to use forwards (equal to the expected asset value under the forward measure) or futures (equal to the expected asset value under the risk neutral measure).

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  • $\begingroup$ What then would be used to observe real-world drifts ? $\endgroup$ – AfterWorkGuinness Sep 24 '15 at 1:01
  • $\begingroup$ Real world drifts are typically estimated from time series of data, and are used for risk management metrics such as VaR or PFE because here you’re trying to make sure that in the real world you keep the probability of bad things happening low. $\endgroup$ – Antoine Conze Sep 25 '15 at 13:30
  • $\begingroup$ CVA is not a risk management metric, it is the present value of the counterparty credit risk embedded in a transaction or a set of transactions, and represents how much you would need to pay to buy protection against this risk (which you would implement by for instance buying CDS on your counterparty). Hence CVA is the present value of a (complicated) payoff and as such has to be computed under the risk neutral measure. $\endgroup$ – Antoine Conze Sep 25 '15 at 13:30

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