I was working on the UVUR model proposed by mercurio.The model proposes that the volatilities at each point in the implied volatility curve is resultant of two simultaneous brownian motions in the underlying. I have a small doubt on the issue though. In calibration of the volatility and interest rate for both the distributions, i realized that i was getting interest rate in one of the brownian motion negative. Is this ok to have? i thought it was not possible to model negative interest rates....can somebody throw light at this?

Simply speaking negative interest rates are logically impossible. So the model is inconsistent

Why do you say that they are logically impossible?Imagne a worlsd where robbery is rife ,and where there is deflation, and a stagnant economy. Banks do not want people's money, and people do not want to keep it themselves, for fear of being robed, so banks charge you to look after it. This is a negative interest rate.

inconsistent? try to google for "negative interest rate" + Japan, besides data you will find http://www.boj.or.jp/en/type/press/koen/ko0611b.pdf

Negative (nominal) interest rates did occur in Switzerland in the late seventies. Foreigners were buying neg. int. rate bonds because the Swiss franc was very strong; it's like they were willing to pay for the advantage of holding the currency.

interest rates can't be negative as they are a claim(of a higher quality than equity and of lesser return potential).if data doesn't match the theory, change the data. modeling and empiricism are quite different things.

Interest rates can be negative e.g. if there is only electronic money...

QuoteOriginally posted by: amit7ulinterest rates can't be negative as they are a claim(of a higher quality than equity and of lesser return potential).if data doesn't match the theory, change the data. modeling and empiricism are quite different things.What on earth are you talking about? You may have a model that says that they cannot go negative, but your model is not the real world.Conditions for negative rates are not very frequent, but they do exist.I suggest that you read "the getaway", for a good example of negative rates in 'El rey''s kingdom...

I definitely remember frequently trading negative interest rates in Japan via the FX Forward markets before the end of Quantative Easing - as recently as 18months ago.

i agree with LordR, cpulman and NorthernJohn, Avt, Miretta and all who say -ve int. rates are possible.modeling and reality are quite different things, thats what i said.coming to the original question by vikram, UVUR is some sort of mixture model, it works on the assumption that inputs(of BSM pricing function) implied vol and interest rates have a distribution too. so each possibility is a perfect BSM world thus each rate should be +ve.

Interest rates may indeed become negative. For example : real interest rates. In such cases, usinga model that excludes negative interest rates (e.g. - CIR) is simply inadequate. The Vasicek model, and its extended version (aka Hull-White) for example, allow negative interest rates. (Negative rates are excludedin the Hull white only through their trinomial tree methodology; the analytic solution to the SDE might indeed become negative) The CIR does not. Which is better?There is no clear answer -- it depends of course on the application -- in modeling nominal interest ratesa model should preferably only allow positive non-negative interest rates; in modeling inflation however,i.e -- real interest rates -- it is actually desirable to have the flexibility of going negative.