In his 2009 Letter to Investors, Buffett discussed in some details about the problems of the Black-Scholes formula when applied to extremely long-dated put options. This short comment shows that if his arguments are interpreted in the usual way, he probably made several mistakes in his Letter....

We give a simple pragmatic justification for risk neutral pricing that can be presented in a classroom without the explicit use of any advanced mathematics. We do this by exploiting a generalized binomial option pricing model developed by Arnold and Crack [2000]. This model allows for a...

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....

In this paper we discuss subdiffusive mechanism for the description of some stock markets. We analyse the fractional Black–Scholes model in which the price of the underlying instrument evolves according to the subdiffusive geometric Brownian motion. We show how to efficiently estimate the...

In this paper we consider a generalization of one of the earliest models of an asset price, namely the Black–Scholes model, which captures the subdiffusive nature of an asset price dynamics. We introduce the geometric Brownian motion time-changed by infinitely divisible inverse subordinators,...

The aim of this study is to analyse the impact of dilution and dividends on the goodness of fit of warrant pricing valuation models, to the Portuguese warrants market. In order to avoid modelling bias over the research design, and to test dividend and dilution effects we decided to keep this...

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...