Nonparametric option pricing with no-arbitrage constraints

Abstract

We propose a completely kernel based method of estimating the call price function or the state price density of options. The new estimator of the call price function fulfills the constraints like monotonicity and convexity given in Breeden and Litzenberger (1978) without necessarily estimating the state price density for an underlying asset price from its option prices. It can be shown that the estimator is pointwise consistent and asymptot- ically normal. In a simulation study we compare the new estimator to the unconstrained kernel estimator and to the estimator given in Aıt-Sahalia and Duarte (2003).