A huge number of financial institutions and companies use the options in risk management. A particularly important issue that arises when it comes to options is fixing their value. In this paper we present the classical models for valuing options: Black-Scholes model and binomial model....

The volatility estimation is a crucial problem for pricing derivatives. The traditional implied volatility approach induces the undesired smile effect and is therefore inconsistent with the market reality. A second more realistic approach is due to Bensoussan, Crouhy and Galai (1995) who derive...

We develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a closed-form approximate solution, which relies on the expansion of the intractable model around an “auxiliary” one. We...