hi everyoneI am modelling LIBOR rate with Vasicek: dr = a(b - r)dt + sigma*dWtI have no clue about typical value for mean-reversion rate a - can anyone help? ( I don t need to match any market price, just need to be realistic)tx in advance for repliese.

have a look at the recent swaption / bermuda swaption thread - some good comments and some "typical" values.though beware that for some instruments the mean reversion value will set the overall price level leaving the vol param as a second order effect, bermudas being a good example.

Realistic is -1% to about 4% ... BUT(!!) after choosing the mean reversion a, and after choosing b(t) to match today's yield curve, one needs to calibrate simga(t) to match some swaption prices ... if one calibrates, then mean reversion becomes a second order effect. Otherwise it's a first order effect.If you can't calibrate to swaptions, and are desperate, calibrate to caplets and assume that the caplet volatility is, say, 20% for all fixing dates t.If you're really desperate, the yield curve is a flat 5%

swaptions have quasi closed form solutions in extended Vasicek ie Hull White. This solution is known as the Jamshidian trick and depends on the model being one factor (and bond prices being monotonic in the rate). Actually, you don't even need to know the long term mean drift term to do this by an appeal to forward measure pricing. You could set up a simple optimization to solve for best fit reversion speed and vol as a function of a collection of swaption prices. actually, it could be done in Excel pretty easily. ah, but I just noticed that you want to do this in the real world measure (I guess). In terms of bond vols, whether you use Vasicek or extended Vasicek is sort of moot, since bond vol in both cases is given by the same expression. I think a market calibration may give you the best estimate of future potential volatility, therefore I would still do the simple calibration I described above.

tx for all answersat the moment I am using:*spot LIBOR = 1.12%*long-run LIBOR = 3%*vol = 0.5%*mean reversion rate = 0.1%On average, the 3% long-run level is hit in 3 years, which is satisfactory for my needs. And with a 5% rate is is hit in less than a year... Is there any formula which helps converting this rate with the expected time of hitting the long-run level?e.

QuoteOriginally posted by: eiriamjhtx for all answersat the moment I am using:*spot LIBOR = 1.12%*long-run LIBOR = 3%*vol = 0.5%*mean reversion rate = 0.1%On average, the 3% long-run level is hit in 3 years, which is satisfactory for my needs. And with a 5% rate is is hit in less than a year... Is there any formula which helps converting this rate with the expected time of hitting the long-run level?e.that reversion speed looks low to me (I would think it should be closer to something like 3%)...so does the vol (of course they offset each other, there is a continuom of pairs of reversions and vols that give the same long term Vol=vol/sqrt(2reversion), but I guess it depends on what you are trying to do.

Gaterek: Considering that muni money market funds are paying 0.50% (but tax free!) before fees, many people are desperate ... they should just learn to be more patient ... due to the miracle of compounding, they will double their money in a mere 132 years. Most people would have said 200, but us quants know about convexity.