Comparison of methods to estimate option implied risk-neutral densities

Abstract

This paper is a comparison study of non-parametric techniques used to estimate risk-neutral densities from option prices. Cross-sectional option prices are first generated using Monte Carlo simulation. Using these simulated options data, risk-neutral densities of the underlying asset are estimated using three different non-parametric methods. The performances of these non-parametric estimation methods are then evaluated by comparing the estimated densities with the theoretical density. Unlike previous comparison studies that use traded options data without knowing the true risk-neutral densities, this study uses simulated option data with known data-generating processes and their corresponding risk-neutral densities, hence giving a real evaluation of the non-parametric estimation methods. This study finds that the kernel regression method yields the best performance, followed by the spline interpolation method and the neural network models.

Keywords:

• Risk neutral distributions
• Financial options
• Applied mathematical finance
• Monte Carlo methods

JEL Classification::

• C1
• C14
• C15
• G1
• G13

Acknowledgements

The author would like to thank Pierre Batteau, Felix Goltz, Patrick Navatte, Patrick Rousseau and Patrick Roger for helpful comments and suggestions. Any errors are the responsibility of the author.

Notes

†See Bakshi et al. (1997) and Garcia et al. (2003) for a comprehensive survey of option pricing models.

†See Cont (1997) and Jackwerth (1999) for a detailed description and review of the parametric methods to estimate RNDs from option prices.

¹Studies have shown that option pricing models with stochastic volatility and jumps produce the ‘volatility smile’ as seen in traded options (see Bakshi et al. (1997) for a comprehensive review on such models).

†The personal computer used in the computations in this study has an Intel Core Duo processor 1.66 GHz with 1 Gb RAM.