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danchikas
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Joined: January 9th, 2002, 12:33 pm

term structure/brainfood/question combo

September 3rd, 2002, 2:41 pm

Hallo out there,Though a lot has been posted on the wonderful topic of term structure estimation/modelling/calibrating etc etc, I'll dare to start a new thread.So imagine you want to build a model of say LIBOR term structure and apart established models (bdt/hw) you want to build something of your own, say more "market-savvy" (maybe just to show your boss who's a big fan of market-savviness) model that incorporates the fact that in the past a lot of the movement in the LIBOR market occured on the "economic" days (like FOMC meetings, check 2001 ). Now the way to go I guess is a MC simulation that incorporates the fact in some of the ways, e.g.:a) you could play the role of a sage and try to forecast the likely movement or use some combo of available forecasts/adjusted implied forward rates to build a likely distribution of rates on that day to draw a point from there and then use brownian bridge on the points;b) or you could just say that on those days jumps are more likely and feed the fact into some sort of jump-diffusion process;c) there have to be other ways i'm sure!So far I was leaning to the path (a). Of course when you try to play a sage for too long of a period, you're busted, but what about the short-term forecasts? Don't you think with the rates where they are some likely scenarios in which the story will unfold could be incorporated? And doesn't it come from the same opera as "stock pinning", discussed somewhere on the forum?Actually, that wasn't the question; I must admit I didn't do a very good job paperdigging through the problem, so I thought maybe you know some sources on the (similar) issue?Ufff, I'm certainly over my typical words quota here, looking forward to hear your opinions and suggestions.Daniel
 
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Johnny
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Joined: October 18th, 2001, 3:26 pm

term structure/brainfood/question combo

September 3rd, 2002, 3:24 pm

By a bizarre coincidence I was wondering about this kind of thing a few weeks ago. I never go as far as doing anything about it, but I'll share my thoughts with you ... but please accept that these are just ruminations, nothing more.1. A one-factor model, like Vasicek, assumes that all yield curve movements are attributable to stochastic short rate. In a similar way, you could have a model in which all yield curve movements are attributable to changes of monetary policy on FOMC meeting days. To do this you could have a model of short rates which only has a jump on the dates of FOMC meetings and nothing on other dates. The most simple version of this would have a fixed jump size of 25 bps, but you could do more complex things. However, the more complex you got, the further you would be from the spirit of your "market savvy" model.2. I'm pretty sure that a one-factor model of this sort would not be arbitrage free. So you'd need to incorporate some other factor. I can't think of anything to stop you doing this in the same way as other multi-factor models, but retaining the jump-only FOMC/short rate process. But please accept that I haven't thought this through ...
Last edited by Johnny on September 2nd, 2002, 10:00 pm, edited 1 time in total.
 
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danchikas
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Joined: January 9th, 2002, 12:33 pm

term structure/brainfood/question combo

September 4th, 2002, 3:17 pm

Hello again,Thanks for the reply, Johny.Basically I am forgetting for a second about the term structure modelling, looking just at the real data for LIBOR, and here are my "additional" thoughts:- if we start off with a combination of expectations & liquidity theory, then the "normal" shape for the yield curve should be upward-sloping; it doesn't mean the rates will go up (although if we do a simple excercise of building an implied forward yield curve + interpolate for the longer maturities it will imply rising rates forever, or am i wrong? isn't it also a drawback for some of the models?), however when the spread between maturites shrinks below the liquidity premium, or the curve reverses, it signals that the markets expect the rates to go down; now this all is trivial, but don't you think these reshapings tend to occur after the "jumps"? (haven't done a thorough statistic analysis on that, but historical data seems to support the idea). Otherwise there are lengthy periods of combined relatively low-volatility-parallel-movement type of dynamics.- all said above would imply a kind of multi-factor (or a self-modifying single factor) model which would not only allow for the jumps on economic days, but also for increased probability for changes in the subsequent shape of the whole interest rate curve. - one of the implementations allowing for such "feed-back", could actually incorporate jumps through the mean term and do e.g. the following: if the current shape of the curve implies increase in the rates, then the probability of an upward jump (say fixed of +25BP or +50BP, depending on the spread) is greater and if such occurs, then the curve reshapes into a "normal" position; if the jump doesn't occur, then the original shape is maintained. That of course, along other things, assumes that the CB doesn't like to surprise the market (which is of course not always true but you could leave some back-door for such possibilities as well), but could be a starting point for implementing the model.Ok, such model is cumbersome enough already to be useless (), but don't you think such feed-back relationship between jumps and the subsequent shape is quite realistic?Eager to hear your opinions.Daniel
 
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Aaron
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Joined: July 23rd, 2001, 3:46 pm

term structure/brainfood/question combo

September 5th, 2002, 1:30 pm

I suggest looking into market segmentation models. These are built to match the market, they explicitly allow arbitrage between (but not within) segments. They are the only models I know of that accurately predict the medium and long term effects of short-term shocks such as Fed actions.Looking at days when jumps are likely is tricky. The Fed does not always act on schedule, and there are other types of shocks. My inclination would be to use implied volatility of short-term interest rates as a model parameter. You can measure it, and it should capture the increased volatility on certain days. That should be okay for short-term forcasts, say out a week, but not for longer term. However, I'm not sure there's much value in knowing today that, say, next March 10 is likely to have a bigger interest rate move than March 9 or March 11.