Abstract
Interest rate derivatives are a vitally important, and highly diverse, class of financial instruments. The LIBOR market model (LMM) framework greatly simplifies pricing the simpler types by modeling the forward rate at every maturity as being lognormal. But path-dependent payoffs, such as for a callable instrument or a range accrual note, introduce major problems. The workhorse for valuing such contracts in the equity space is the binomial or trinomial lattice. In this article, Xiao develops a pricing lattice within the LMM, with a grid-type architecture (rather than a tree), and shows that performance of the lattice-based model is orders of magnitude faster than Monte Carlo simulation.
Highlights
The LIBOR Market Model has become one of the most popular models for pricing interest rate products
It is believed that Monte Carlo simulation is the only viable numerical method available for the LIBOR Market Model (LMM)
We propose a lattice approach within the LMM
Summary
As a matter of fact, without this linear transformation, a lattice method in the LMM either does not exist or introduces too much error for longer maturities After applying this variable substitution (8), equation (6) can be expressed as (0). Drift Approximation Under terminal measure, the drifts of forward rate dynamics are statedependent, which gives rise to sufficiently complicated non-lognormal distributions. This means that an explicit analytic solution to the forward rate stochastic differential equations cannot be obtained. Based on the conditional expectation of the forward rate Fj (s) , the drift of Fk (t) can be expressed as j E0[Fj (s) |Fj (0),Fj (t) ] j E0[Fj (s) |Fj (0),Fj (t).
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