Application of the Heath–Platen estimator in the Fong–Vasicek short rate model

Sema Coskun; Ralf Korn; Sascha Desmettre

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The Heath-Platen estimator is modified in a suitable way to price bond options in the Fong-Vasicek model.
The application of the Heath-Platen estimator leads to a dramatic variance reduction compared to the naïve Monte Carlo estimator in the Fong-Vasicek setting.
The Heath-Platen estimator allows a valuation of bond options in the Fong-Vasicek model without the need to compute the zero bond prices (which itself is already a numerically demanding task).

Abstract

Due to the presence of stochastic volatility dynamics, the Fong–Vasicek (FV) short rate model is more complex but also more realistic than the classical Vasicek version. To enhance the numerical tractability of the FV model for the calculation of bond option prices, we suggest using the Heath–Platen (HP) estimator, which performs excellently in the related Heston stochastic volatility model. We show that the HP estimator reduces the variance, and thus the size, of confidence intervals dramatically compared with a crude Monte Carlo estimation, which leads to a drastic speed-up in price calculations across different realistic parameter sets.

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