An extended set of risk neutral valuation relationships for the princing of contingent claims

• Autor(a) principal: Câmara, António de Sousa da
• Data de Publicação: 1997
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.5/23550
• topic: Hara Utility Functions; Displaced Diffusion Model; Three-Parameter Lognormal

This article establishes an extended set of risk neutral valuation relationships (RNVR's), assuming a representative agent who has an extended power utility function, of the HARA class of utility functions. The utility function of the representative agent displays either increasing, constant or decreasing proportional risk aversion. Aggregate consumption and the random payoff of the underlying asset are bivariate three-parameter lognormal distributed. As an application of the RNVR's, closed-form solutions for the price of a call written on a stock are derived. These include an extra parameter, the threshold parameter, not contained in the Black-Scholes formula. A positive threshold parameter may explain some systematic biases of the Black-Scholes model in the stock options market.