discretely & continuously compounded rates

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pwyborn
Posts: 25
Joined: Sat Oct 29, 2011 12:42 pm

Re: discretely & continuously compounded rates

Postby pwyborn » Sat Aug 04, 2012 11:02 am

Hi Raymond,

Its great to have other forum users to engage in a discussion of the questions I posted.

Just to clarify, there are NO two sets of forward rates, one set being what we observe in the market and the other being that which derived from the spot curve. There is ONLY one set, which is that we derive from the spot curve.

Indeed, forward rates are forced into being by arbitrage coercison. However, I dont see the link between this and the conclusion you draw which is that it leads to a better forecast. From what Carol is saying, forward rate is simply one of the forecasts of the actual future spot rate. Whether it is a better forecast is open to debate, in Carol`s words, its an empirical decision. Certainly, interest rate model builders wouldn`t think so, otherwise they wouldnt spend the time and efforts in model building. In other words, IF forward rate is a better forecast indeed, then ALL the interest rate models should go out the window!

Cheers, Pete
l

chiyui1212
Posts: 2
Joined: Sat Aug 04, 2012 10:03 am

Re: discretely & continuously compounded rates

Postby chiyui1212 » Sat Aug 04, 2012 2:03 pm

Hi Pete,

Thank you for your correction. It seems that I'm not really familiar with this kind of thinking >_<

Raymond

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: discretely & continuously compounded rates

Postby coalexander » Sat Aug 04, 2012 6:58 pm

Hi Raymond,

You raise a good point about models. A interest rate model is used for pricing and hedging interest rate options and swaptions, especially those with path dependent features because vanilla options like caps, floors and European swaptions are so liquid that we don't need a model to price them. In fact, their market prices are used to calibrate the parameters of the model so that there is no arbitrage between the model's vanilla option prices and their market prices.

Having calibrated a model, you could use it to forecast the underlying, after all that's all the model does (then you put some option-like pay-off on top of the futures distributions of the underlying etc etc). So, if it is a spot rate model,** then you get forecasts of the future spot rate from the model. A forecast is a distribution. Usually we represent it by a single point (the mean). Maybe the modeller believes his model gives a "better" mean of the model's spot rate forecast than the current forward rate. Then he'll trade his model against the market. But this is just a question of belief. The modeller needs to test the accuracy of his forecasts compared with the accuracy of the forward rates...that is an empirical question.

Cheers, Carol

** The standard model for forward rates is the LIBOR model (explained in volume 3) which is for forward rates anayway.


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