Hi Wilmott peopleMany stochastic volatility LIBOR market models have been proposed in the literature. But I didn't find reasons why we have to use it in the paper. I know one reason introducing stochastic vol is to capture the correct smile dynamics, i.e. the smile moves to the right direction as the underlying moves (by Hagan's argument). For some vol dependent option like variance swaps, we also have to use SV model. Can anyone add more reasons please? Thanks.

Well similar to what you've said already is that getting the Black-Scholes skew right means you have a proper or more correct description of the transition density. In other words, the real reason to have a good model of the skew is that you may now have a skew dependent model for other derivatives, not just a standard Black Scholes option.Barriers, et ceteara. HTH?

QuoteOriginally posted by: gcgametHi Wilmott peopleMany stochastic volatility LIBOR market models have been proposed in the literature. But I didn't find reasons why we have to use it in the paper. I know one reason introducing stochastic vol is to capture the correct smile dynamics, i.e. the smile moves to the right direction as the underlying moves (by Hagan's argument). For some vol dependent option like variance swaps, we also have to use SV model. Can anyone add more reasons please? Thanks.To fit the market, dude. This is something you want from all the models without exceptions.

if the sole purpose was to fit the market (as seen today), then LV model does the perfect job. SV is needed to create more realistic vol dynamics...not so much the move in the right direction as in Hagan (...whose argument is somewhat flawed, by the way), but to avoid forward vol smile flattening .Also, as you said, for some products having SV is absolutely a must.

QuoteOriginally posted by: ThinkDifferentif the sole purpose was to fit the market (as seen today), then LV model does the perfect job. SV is needed to create more realistic vol dynamics...not so much the move in the right direction as in Hagan (...whose argument is somewhat flawed, by the way), but to avoid forward vol smile flattening .Also, as you said, for some products having SV is absolutely a must.

QuoteOriginally posted by: ThinkDifferentif the sole purpose was to fit the market (as seen today), then LV model does the perfect job. SV is needed to create more realistic vol dynamics...not so much the move in the right direction as in Hagan (...whose argument is somewhat flawed, by the way), but to avoid forward vol smile flattening .Also, as you said, for some products having SV is absolutely a must.Thanks ThinkDifferent. That's really helpful. Could you explain more about forward vol smile flattening please? Or any reference about the vol dynamics difference between LV and SV model.

QuoteOriginally posted by: OrbitWell similar to what you've said already is that getting the Black-Scholes skew right means you have a proper or more correct description of the transition density. In other words, the real reason to have a good model of the skew is that you may now have a skew dependent model for other derivatives, not just a standard Black Scholes option.Barriers, et ceteara. HTH?Thanks Orbit. I got your idea. Can I ask one more question please? Let's take a particular example. For all I know many people are happy using 1 factor model to price Bermudan swaption. I think it would be better if using SV model to price Bermudans? But is there any strong reason (apart from Hagan's reason) justifying SV model is a must for Bermudans?

since you are interested in the interest rate setting, have a look at Piterbarg's book. Section 8.8 is about smile dynamics. Also see Section 7.1.3, where it is explained when and why LV might imply non-stationary vol smile behaviour.

As for Berms, I'd say about 70% of market participants use low factor models (without SV or LV, e.g. HW), others use single-factor BGM. There are exceptions (cheyette with LV + SV), but those are rare. Also, Berms are relatively liquid and there are regular Totem and broker quotes. You want your model outputs to be in line with those as well.In terms of valuation, using say BGMSV vs BGM should bring the Berm prices slightly lower (the same is true for multi-factor BGM vs single-factor BGM). Now, Totem/broker quotes for Berms are usually lower than those that model gives you, so, from this perspective, it does make sense to use a model with SV. However computational time is key, so people end up using low-factor short rate models with various price adjustments to fit the 'market'.