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**1 - 1**of**1**### Using Lattice Rules to Value Low-Dimensional Derivative Contracts

"... This paper discusses the use of lattice rules to evaluate low and medium dimensional integrals. Lattice rules are based on the use of deterministic sequences rather than random sequences. They are a special type of so-called low discrepancy sequences. We find that as long as the integral is sufficie ..."

Abstract
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This paper discusses the use of lattice rules to evaluate low and medium dimensional integrals. Lattice rules are based on the use of deterministic sequences rather than random sequences. They are a special type of so-called low discrepancy sequences. We find that as long as the integral is sufficiently regular, lattice rules generally outperform not only basic Monte Carlo but also other types of low discrepancy sequences. We implement a specific lattice rule known as good lattice points and apply this approach to two problems of practical interest. The first application is to the valuation of the certain types of financial options known as lookback options. The second application is to the valuation of the embedded option in certain equity-indexed annuities. In the case of these examples we show that the good lattice points are dramatically more efficient than competing methods.