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I have a problem and I hope someone could help me.

I calibrated the Hull-White model to Caps and Floors from t=0 so the bond prices are equivalent to todays term structure. See: Hull-White zero-coupon bond price does not depend on the volatility?

For Caps it prices them correctly using the OIS curve as the term structure. But I get huge mispricings for Floors.

The mispricing mostly appears for the first 2-5 Caplets and later it disappears.

Do you have an idea what the problem could be, or do I have a fundamental mistake?

I am just calibrating the HW model to Cap and Floor prices.

Thanks in advance Chris

Christian M
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  • Try to calibrate the model using cap and floor implied Black (1976) volatilies rather than prices. Also use the sum of squared relative errors as objective function rather than the sum of squared errors. Caps and floors are related by the cap floor parity which is model independent and only requires correctly priced bonds. So, if you get a good fit with the implied cap volatilies, you should also be able to price floors accurately. – Kevin Nov 13 '19 at 21:07
  • Thanks for the answer, I already use Caplet volatilities. I will try to calibrate to the sum of squared relative errors. – Christian M Nov 13 '19 at 21:18
  • The longer the maturity, the higher the cap prices (the long maturity caplets will dominate the price) and a plain SSE approach will try to fit the long maturity caplets very well and will sacrifice the fitting of the (cheap) shorter caplets. So, using relative errors, your overall SSE fit will worsen but you fit all caplets equally well. Are you using implied caplet volatilies or implied cap volatilities? – Kevin Nov 13 '19 at 21:26
  • strangely, the Caplets are not a problem. I fit the Caplets exact to the Black Caplet values. It's just the Floorlets that make serious problem. – Christian M Nov 13 '19 at 21:28
  • Just for curiosity, do you use market implied cap Black volatilities or caplet Black volatilities? – Kevin Nov 13 '19 at 22:14
  • I produced the caplet volatilities via a bootstrapper. I use a market data software (form specific) that allows to bootstrap the caplet volas. – Christian M Nov 13 '19 at 22:20
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    Hi, I just want to tell you that i achived an exact calibration for Floors now. I bootstrapped the zero curve from 6 month instruments. With this initial Zero curve I am able to price Floors exact and correctly. – Christian M Nov 14 '19 at 17:39
  • I'm glad that you solved it, you surely learnt a lot during the process. You can answer your question here on SE. Briefly describe where the precise error was and how you solved it. Your answer may help future students and practitioners (: – Kevin Nov 14 '19 at 19:52

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I solved the problem by just simply using the Zero curve derived from 6 month instruments instead of the OIS.

Christian M
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