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We present a model for direct semi-parametric estimation of the State PriceDensity (SPD) implied in quoted option prices. We treat the observed prices asexpected values of possible pay-offs at maturity, weighted by the unknownprobability density function. We model the logarithm of the latter as a smoothfunction while matching the expected values of the potential pay-offs with theobserved prices. This leads to a special case of the penalized composite linkmodel. Our estimates do not rely on any parametric assumption on the underlyingasset price dynamics and are consistent with no-arbitrage conditions. The modelshows excellent performance in simulations and in application to real data.

Direct semi-parametric estimation of the state price density implied in option prices