A Nonparametric Approach to Derivative Asset Pricing

We utilize the method of Bertholon, Monfort and Pegoraro (2006) for pricing European call options based on nonparametric estimation of returns. Densities are estimated using kernel estimation on random samples of a Laplace and mixture of normal distributions. Additionally, an exponential-affine form of the stochastic discount factor allows derivation of closed-form solutions for option prices. Results of the closed form calculations are compared with those calculated using the nonparametric approach. Both are compared to the Black-Scholes formula. Using the Laplace and mixed Gaussian distribution, the nonparametric estimation shows evidence of mispricing by the Black-Scholes model. This technique requires no assumption regarding the form of return distributions. JEL Classifications: C1, C5, G1.

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