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prodiptag
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Posts: 124
Joined: September 12th, 2008, 4:41 pm

pricing options on momentum strategy

March 21st, 2009, 3:12 pm

HiGreat if someone can help me on this ....Suppose you are following a strict rule based trading strategy, where you go long or short on ~10y g-secs based on some momentum rule based on moving averages of price. Is it possible to price an option on this strategy using any common model (common model - short rate model (hw, cir etc) or fwd rate model (hjm etc) ). I am trying to use monte carlo to simulate the rates and price. But I have doubts whether I am able to capture the convexity in the trading rule.
 
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Aaron
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Joined: July 23rd, 2001, 3:46 pm

pricing options on momentum strategy

March 21st, 2009, 9:22 pm

I'm not sure what you mean.Any dynamic interest rate model will allow you to price this by simulation. Since you're making constant maturity investments, you could even use vanilla Black-Scholes assumptions.If you're asking whether any common interest rate model will give you an analytic price for this option, the answer is no.If you're asking whether any common interest rate model, calibrated to liquid vanilla instruments like government bonds, eurodollar swaptions and longer-term caps and floors, will give you an accurate price for this option, the answer depends on the term of your moving averages. I wouldn't even consider using a common model for terms under 30 days. If you are doing 30 day ma versus 180 day ma, one might work, but I wouldn't guess which one, I'd just backtest each one. But if you're doing a 3 day versus 15 day, or intraday trading, I'd use a different approach.For shorter-term, and maybe for all terms, you need a model that captures sort term volatility variation and trending. Jumps will dominate your results. There is a lot of work on this kind of model for equity and FX, which you can use because you're got a one-dimensional underlying. Interest rate models are not designed for this kind of work, they are designed for yield curves, a multidimensional underlying.
 
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prodiptag
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Posts: 124
Joined: September 12th, 2008, 4:41 pm

pricing options on momentum strategy

March 22nd, 2009, 3:04 pm

Thanks!Firstly I do not even hope for analytical price!My pricing problem is more like the 30day vs 180 day ma. The model i am using is a short rate model with jumps and captures short term volatility variations well. Now what I am not sure about is the trending part. Since trending is a significant risk in this options, do I need to model it explicitly - so to speak the autocorrelations of rate? Could you give any reference (even other asset classes, as you sad, mine is a 1D problem) please? thanks
 
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Aaron
Posts: 6433
Joined: July 23rd, 2001, 3:46 pm

pricing options on momentum strategy

March 22nd, 2009, 11:07 pm

You should not have to model trends explicitly, this should fall out when you do your market calibration.I wouldn't worry too much about theory, just test it and see if it works. The models are not designed for this problem, but they might work.If the models don't work, you will learn how actual market price movements differ from assumptions. Perhaps you will find trends or some other behavior. Then you can try to model it. You can also try to construct arbitrage portfolios that take advantage of what you've noticed.
 
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prodiptag
Topic Author
Posts: 124
Joined: September 12th, 2008, 4:41 pm

pricing options on momentum strategy

March 28th, 2009, 6:52 pm

Thanks for your guidance. I tried to estimate the option price - using a jump-diffusion model, and it does not seem to be totally off. but I was wondering how to check if this model is okay. I can compare the implied vols I am getting from my model to realized vol and check for any trends/differences etc. but any difference cannot establish that my model is wrong. I can also run the greeks and check for historical hedge effectiveness of the options based on the model, but then again I dont have any benchmark. Is there any standard tests for this situations. thanks v.m.
 
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Aaron
Posts: 6433
Joined: July 23rd, 2001, 3:46 pm

pricing options on momentum strategy

March 29th, 2009, 4:24 am

But how did you calibrate your jump-diffusion model?If I understand it now, you have the basic problem faced by all exotic pricing model. You have a model calibrated to liquid derivative instruments. You know it does not match market price movements perfectly, but you still want to use it to price an exotic. Theory cannot help you, unless you know the true underlying process, which doesn't happen in finance. The problem is the liquid derivative instruments do not contain enough information to price the exotic.All you can do is what you have done, test the exotic prices to see if one side or the other consistently makes money, and test the hedge to see how much it reduces variance.The benchmark depends on your application. If you're trading these exotics, you need to build in enough profit to cover the statistical error your pricing test reveals, and the volatility that remains after hedging. You also have to think about economic fundamentals, to get some idea of the risk you are taking.
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