 EdisonCruise
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Posts: 117
Joined: September 15th, 2012, 4:22 am

### How to hedge exotic interest rate derivative under BGM model?

In M.S. Joshi ?s book ?The concepts of mathematical finance?, it talks a lot on pricing exotic interest rate derivative under BGM model. I think it is mainly based on the Monte Carlo method by simulating the forward rate. However, I am not clear on how to hedge the exotic interest rate derivative in practice, like delta-hedging of stock option? What kind of instrument should be use to hedge and how to calculate its "delta"?
Last edited by EdisonCruise on September 7th, 2015, 10:00 pm, edited 1 time in total. list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### How to hedge exotic interest rate derivative under BGM model?

It will be reasonable to specify the underlying and the derivative contracts. bearish
Posts: 5691
Joined: February 3rd, 2011, 2:19 pm

### How to hedge exotic interest rate derivative under BGM model?

Usually, the starting point for your model is a set of hedge instruments (futures, swaps, and related options) and their market quotes. At least conceptually, having valued your product based on a model that has been fit to those market quotes, you can perturb each of them and record the resulting change in value for your product, thus producing the sensitivities that will form the basis for your hedges. This is not an easy problem. You may want to consult the three volume expose by Andersen and Piterbarg for details. EdisonCruise
Topic Author
Posts: 117
Joined: September 15th, 2012, 4:22 am

### How to hedge exotic interest rate derivative under BGM model?

Thank you so much for your replies.I refer to Sami ATTAOUI?s paper ?Hedging Performance of the Libor Market Model: The Cap Market case?. The author indeed did as what bearish said. He constructed the hedging portfolio for a cap as below:?Given this 3-factor model, a delta-based hedge portfolio is composed of three hedge instruments that are common to all caplets. The natural hedge instruments used here are the zero-coupon bonds. The first hedge instrument is a short-maturity bond (3 months). The second instrument is a spread of bonds consisting of short position of short-maturity bond and a long position of long-maturity bond (10 years). Finally, a butterfly composed of long positions of short- and long-maturity bonds and a short position of intermediate-maturity bond (5.5 years) is used to hedge against the curvature risk. We applied the same hedging strategy to both models standard LMM and CEV LMM. The Delta ratio is computed in both cases through Monte-Carlo simulation.?Then I have some further questions. The author only uses a 3-factor model rather than a higher one. From the practical point of view, is it because more factor models need more hedging instruments and the poor liquidity of long-maturity bond makes them fail to be the hedging instruments? So in practice, a 3-factor model balances the availability of hedging instruments and the hedging performance?  