12.8 Conclusion


12.8 Conclusion

The implications of the modelling approach presented by BGM are twofold. Firstly, we see that, in order to justify the market convention of pricing caplets by means of the Black formula, one needs to consider forward rates under a forward measure [ 9 ]. No forward rates are lognormal under the spot measure, but rather under an appropriate forward measure, which depends on the settlement date of the forward rate.

Secondly, the modelling framework presented here is somewhat different to that used by previously studied models. Other models, specifically the HJM model (see Chapter 11), model unobservable market parameters. Instantaneous forward rates, as modelled by HJM, are not observable and so implementation requires a suitable discretisation. BGM have developed a continuous time model of discrete forward rates which are market observable quantities .

One of the most difficult tasks faced by users of the traditional models is that of ensuring the recovery of market- observed values and volatilities [ 45 ]. Within the BGM framework the modelled variables are in fact the market-observed quantities, and hence one is spared the difficult task of transforming unobservable model parameters into values of traded quantities.

Another more subtle advantage is that the BGM model may be used to directly express views about future values and volatilities of market observables. Via the BGM model, these predictions are directly translated into option prices and the resulting option strategy will be a direct reflection of the view taken on traded quantities.




Interest Rate Modelling
Interest Rate Modelling (Finance and Capital Markets Series)
ISBN: 1403934703
EAN: 2147483647
Year: 2004
Pages: 132

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