Marti G Subrahmanyam, Sandra Peterson, Richard C Stapleton
ABSTRACT
We build a no-arbitrage model of the term structure, using two stochastic
factors on each date, the short-term interest rate and the forward premium.
The model is essentially an extension to two factors of the lognormal interest
rate model of Black-Karazinski. It allows for mean reversion in the short
rate and in the forward premium. The method is computationally efficient
for several reasons. First, interest rates are defined on a bankers' discount
basis, as linear functions of zero-coupon bond prices, enabling us to use
the no-arbitrage condition to compute bond prices without resorting to
cumbersome iterative methods. Second, the multivariate-binomial methodology
of Ho-Stapleton-Subrahmanyam is extended so that a multi-period tree of
rates with the no-arbitrage property can be constructed using analytical
methods. The method uses a recombining two-dimensional binomial lattice
of interest rates that minimizes the number of states and term structures.
Third, the problem of computing a large number of term structures is simplified
by using a limited number of bucket rates in each term structure scenario.
In addition to these computational advantages, a key feature of the model
is that it is consistent with the observed term structure of volatilities
implied by the prices of interest rate caps and floors. We illustrate the
use of the model by pricing American-style and Bermudan-style options on
interest rates. Option prices for realistic examples using forty time periods
are shown to be computable in seconds.
Subrahmanyam: (212) 998-0348 msubrahma@stern.nyu.edu
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