On Some Risk-Reducing Derivative

Abstract

In this paper, we propose some derivative designed for small stock investors. Using the Black-Scholes model we derive an explicit formula for the price of the derivative, computing its discounted expected payoff. The payoff is modelled on the payoff of the catastrophe bonds, random occurrence of a natural disaster is replaced by a random stock price falling. Different variants of the proposed derivative are obtained by introducing a parameter to the payoff of the derivative. By Monte Carlo method, to reduce the risk of large losses associated with the investment, indicated the variant of this instrument, appropriate to selected typical values of volatility of considered stock.