Abstracts

Extracting risk-neutral density (RND) functions from cross-sections of observed standard option prices is highly important for both academics and practitioners. For instance, Ross (2013), Figlewski (2009), and Figlewski and Birru (2012) employ the RND to obtain information about investors’ risk preferences and expectations. In the field of option pricing, the implied RND allows to price illiquid exotic derivatives with arbitrary payoffs and are also applicable to the copula-based pricing of multi-asset products. For example, Monteiro et al. (2011) show that the implied RND can be used to accurately price European-style binary options and Cherubini and Luciano (2002) use the implied RND to price bivariate equity options.
In this work, we propose a novel parametric approach to extract the implied risk neutral density function from a cross-section of call option prices. The method is based on the framework proposed by Orosi (2011), who presents a multi-parameter extension of the models of Figlewski (2002) and Henderson, Hobson, and Kluge (2007). By choosing a proper functional form, we show that well-behaved risk neutral densities can be generated by imposing restrictions on the parameters of the model. The results of our numerical experiments indicate that the method is capable of extracting risk neutral densities with complex characteristics. Moreover, we demonstrate the pricing performance of our method by generating arbitrage-free call option prices that can be used to produce well-behaved densities from S&P 500 Index options.
Additionally, further extensions of the model are straightforward. For example, we demonstrate that the model is capable of retrieving the risk neutral probability density function from call options written on defaultable assets.