- adnanmirza
**Posts:**16**Joined:**

Hi,We are trying to implement the PFE / CVA model. The system model requires an input for USD mean reversion.Can anybody give an idea of the ballpark number that I should use for USD mean reversion?I have a model from my coleague that is generating mean reversion of USD short term rates of approx 20%. Does that sound okay?Regards,Adnan

The ballpark figures should be somewhere between 0.75% to 5%, with the caveat that this analysis was done in 2008.I believe Bloomberg also computes a mean reversion input for their HW 1F model, which also falls within the band stated above.What model are you using? How do you calibrate the mean reversion from it?karfey

- adnanmirza
**Posts:**16**Joined:**

Thank you for the reply.We are using HW 1F. Can you help me with the bloomberg page that has teh mean reversion?Thanks, Adnan

If you analyze the behavior of USD interest rates, either on a historical basis or by looking at swaption implied vols, you are forced to conclude that the mean reversion parameter in a 1-factor Gaussian model is negative, unless you put a tremendous weight on the slope of the forward rate vols between 10 and 30 years. USD vol curves (as well as those of other major currencies I have looked at) are almost always hump-shaped, with the short end being tied down by central bank policy and the (very) long end being anchored by theoretical and common sense arguments. I sympathize with the desire to keep the rate model component of a complex modeling framework like CVA simple, but you are paying a price for it.

- adnanmirza
**Posts:**16**Joined:**

Thankyou for the replies. This was helpful

QuoteOriginally posted by: bearishIf you analyze the behavior of USD interest rates, either on a historical basis or by looking at swaption implied vols, you are forced to conclude that the mean reversion parameter in a 1-factor Gaussian model is negative, unless you put a tremendous weight on the slope of the forward rate vols between 10 and 30 years. USD vol curves (as well as those of other major currencies I have looked at) are almost always hump-shaped, with the short end being tied down by central bank policy and the (very) long end being anchored by theoretical and common sense arguments. I sympathize with the desire to keep the rate model component of a complex modeling framework like CVA simple, but you are paying a price for it.Hi bearish, if you say mean reversion is negative, are you also saying the forward rates are highly correlated across all maturities?My basis is that mean reversion introduces auto-decorrelation to the system, so a very low, even negative mean reversion that is implied from the system, can only mean that there is very little decorrelation in the system.

QuoteOriginally posted by: karfeyQuoteOriginally posted by: bearishIf you analyze the behavior of USD interest rates, either on a historical basis or by looking at swaption implied vols, you are forced to conclude that the mean reversion parameter in a 1-factor Gaussian model is negative, unless you put a tremendous weight on the slope of the forward rate vols between 10 and 30 years. USD vol curves (as well as those of other major currencies I have looked at) are almost always hump-shaped, with the short end being tied down by central bank policy and the (very) long end being anchored by theoretical and common sense arguments. I sympathize with the desire to keep the rate model component of a complex modeling framework like CVA simple, but you are paying a price for it.Hi bearish, if you say mean reversion is negative, are you also saying the forward rates are highly correlated across all maturities?My basis is that mean reversion introduces auto-decorrelation to the system, so a very low, even negative mean reversion that is implied from the system, can only mean that there is very little decorrelation in the system.You will note that I specified the context to be a 1-factor Gaussian model, in which case the forward rates are perfectly correlated across all maturities, at least instantaneously. You can get much more realistic behavior with a 2-factor model, Gaussian or not. I think it is realistic to have one factor that has very high persistence (i.e. very low, but positive mean reversion) coupled with a negatively correlated second factor with a higher speed of mean reversion. This combination is one (but certainly not the only) way to generate the humped vol curve we tend to observe.

My apologies for the confusion. I was trying to describe the auto-correlation between the short rates at different points in time, which is actually what mean reversion is all about.A positive mean reversion says that short rates which are higher (than a theta value...) in this instant has a tendency to be lower in the next instant, hence they are negatively auto-correlated. It has nothing to do with the terminal correlation, which, in the 1-factor world, all rates are perfectly correlated, at the same point in time. Therefore, I am still trying to figure out how:-historical time series-looking at swaption volsWe can infer that mean reversion is negative.and also, if we add a upward slope to the 10Y-30Y forward rate vols, mean reversion will be positive.appreciate your time and patience.

When we construct and estimate short rate models, we are almost never particularly interested in the behavior of the short rate per se. The short rate is a modeling device and usually an idealized notion, and to the extent that it has a real world manifestation (the standard swap curve built off futures and swaps that references 3M Libor would be an example of a curve that has no observable short rate associated with it) it is likely to be subject to all sorts of technical effects that only people on the money market desk get excited about. Thus, the nature of the short rate process is mostly of interest to the extent that we can (usually laboriously and painfully) deduce from it various properties of the dynamics of the whole yield curve. In particular, short rate mean reversion under Q, i.e. after filtering out risk premium effects, maps into exponential decay of the volatility of instantaneous forward rates as a function of their maturity. The forward rate volatilities can be integrated up to give you a spot rate volatility structure, from which you can derive the sorts of things you are likely to actually be interested in, like the volatility of swap rates or bond prices. So from this perspective, short rate mean reversion is all about volatility.

to be honest,mean reversion does not make any sense in the current rates environment !global interest rates are impacted by deterministic process that overshadow their stochastic nature. i.e central banks liquidity injections , ZIRP, market complacency and subdued volatility are all factors to takeinto account ,and they all impact future mean reversion levels .keep in mind that all processes have a built in assumption that they areMarkovian,so that the future only depends on the now,he best guess for mean reversion will depend on your stress scenarios.SAAB-RIYAD-Hello

- DominicConnor
**Posts:**11684**Joined:**

Some parts of the evolution of exchange rates are indeed best treated as deterministic, but they are based upon political processes which are really non-deterministics, the fact that we don't have an obvious distribution to apply to political processes, doesn't mean they are not random.

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