Binomial lattice for pricing Asian options on yields

Abstract

An efficient binomial lattice for pricing Asian options on yields is established under the affine term structure model. In order to reconnect the path of the discrete lattice, the technique of D. Nelson and K. Ramaswamy is used to transform a stochastic interest rate process into a stochastic diffusion with unit volatility. By the binomial lattice and linear interpolation, the prices of Asian options on yields can be obtained. As the number of nodes in the tree structure grows linearly with the number of time steps, the computational speed is improved. The numerical experiments to verify the validity of the lattice are also provided.

Keywords

Asian option / binomial lattice / affine term structure

References

[1] HullC JOptions, futures and derivatives, 1997the 3rd editionNew York, Prentice Hall International, Inc

[2] Chesney M, Elliott R J, Gibson R. Analytical solutions for the pricing of American bond and yield options[J]. Math Finance, 1993, (3):277–294.

[3] LeblaneB, ScailletO. Path-dependent options on yields in the affine term structure model [J]. Finance and Stochastics, 1998, 2(4): 349-367

[4] Bjork T. Interest rate theory [A]. Financial Mathematics the 3rd Session of the Centro Internazionale Matematico Estivo[C], Bressanone, Italy, 1996. 53–120.

[5] NelsonDaniel B., RamaswamyKrishna. Simple Binomial Processes as Diffusion Approximations in Financial Models. Review of Financial Studies, 1990, 3(3): 393-430

[6] AbateJ, WhiteK. The fourier-series methods for inverting transforms of probability distributions [J]. Queuing Systems, 1992, ,(14): 5-8