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Sep 6

Term Structure Lattice to Price Bermudan swaption

Posted by abiao at 10:58 | Code » VBA/Excel | Comments(1) | Reads(12028)
The modelling philosophy for term-structure models is somewhat different to the modelling philosophy for equity models. In the latter case, stock price dynamics are usually specified under the physical probability measure, P, before their dynamics under an EMM, Q, are determined. For example, in the binomial Black-Scholes framework a unique Q is easily determined after the P-dynamics of the stock-price are given. Moreover, it is easy to check that the model does not allow any arbitrage: we just need d < R < u.

In contrast, with term-structure models we often assume that zero-coupon bonds of every maturity exists and it is not always easy to directly specify their P-dynamics in an arbitrage-free manner that it is economically satisfactory. For example, in a T-period binomial model there are O(T) zero-coupon bond prices that we need to specify at each node. Checking that the model is arbitrage-free and that bond price processes have suitable properties (e.g. implied interest rates are always non-negative) can be a cumbersome task. As a result, we usually work with term structure models where we directly specify an EMM, Q, and price all securities using this EMM. By construction, such a model is arbitrage free. Moreover, by leaving some parameters initially unspecified (e.g. short-rate values at nodes or Q-probabilities along branches in a lattice model) we can then calibrate them so that security prices in the model coincide with security prices observed in the market.

In the lecture notes of Term Structure Models-Spring 2005 professor Martin Haugh introduces how to price a Bermudan swaption with term structure lattice, precisely speaking, binomial tree, there he cailibrates both Ho-Lee and Black Derman Toy Model and use the calibrated interested rate model to price a Bermudan swaption as an example.

lecture notes about this topic is http://www.columbia.edu/~mh2078/TS05/lattice_models.pdf and
sample spreedsheet is http://www.columbia.edu/~mh2078/TS05/Term_Structure_Lattices.xls
wiki(Bermudan swaption)

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