In this paper we consider derivatives which are binary options of asset-or-nothing type with a payoff function depending on a parameter. The payoff is modelled on the payoff of catastrophe bonds. We examine the influence of the derivative on returns on shares. For this purpose two portfolios are compared: one consisting of stocks and a second additionally containing the derivative. Using the Black-Scholes model we derive an explicit formula for the standard deviation of the returns on the investment portfolios. Numerical examples show that the derivative reduces the volatility of returns on shares. For typical values of stock price volatility we indicate the value of the parameter appearing in the payoff for which the volatility of returns on shares reaches a minimum. All numerical calculations were made with MAPLE.

In this paper we consider derivatives which are binary options of asset-or-nothing type with a payoff function depending on a parameter. The payoff is modelled on the payoff of catastrophe bonds. We examine the influence of the derivative on returns on shares. For this purpose two portfolios are compared: one consisting of stocks and a second additionally containing the derivative. Using the Black-Scholes model we derive an explicit formula for the standard deviation of the returns on the investment portfolios. Numerical examples show that the derivative reduces the volatility of returns on shares. For typical values of stock price volatility we indicate the value of the parameter appearing in the payoff for which the volatility of returns on shares reaches a minimum. All numerical calculations were made with MAPLE.