Using market European option prices, a method for computing a smooth local volatility function in a 1-factor continuous diffusion model is proposed. Smoothness is introduced to facilitate accurate approximation of the local volatility function from a finite set of observation data. Assuming that the underlying indeed follows a 1-factor model, it is emphasized that accurately approximating the l...

In this paper, we examine an exchange economy with a financial market composed of three assets: a share of a stock, an European call option written on the stock, and a riskless bond. The financial market is assumed to be incomplete and the option is not a redundant asset. In such a case the construction of a riskless hedge-portfolio to valuate the option is unfeasible and therefore the pricing ...

This paper describes and analyses the history of the fundamental equation of modern financial economics: the Black-Scholes (or Black-Scholes-Merton) option pricing equation. In that history, several themes of potentially general importance are revealed. First, the key mathematical work was not rule-following but bricolage, creative tinkering. Second, it was, however, bricolage guided by the goa...

The European call option prices have well-known formulae in the CoxRoss-Rubinstein model [2], depending on the volatility of the underlying asset. Nevertheless it is hard to give a precise estimate of this volatility. S. Muzzioli and C. Toricelli [6] handle this problem by using possibility distributions. In the first part of our paper we make some critical comments on their work. In the second...