Anna Milian
Czasopismo Techniczne, Nauki Podstawowe Zeszyt 1-NP 2016, 2016, s. 121 - 129
https://doi.org/10.4467/2353737XCT.16.145.5756In 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.
Anna Milian
Czasopismo Techniczne, Nauki Podstawowe Zeszyt 3 NP (17) 2014, 2014, s. 39 - 48
https://doi.org/10.4467/2353737XCT.14.311.3399This paper discusses Monte Carlo simulations of the Black-Scholes model. It is introduced with the simple example of the pricing of ‘European call options on a no-dividend stock and the simulation results are compared with an analytical solution. Monte-Carlo methods are then used to price simple chooser options. Moreover, it is shown that the distribution of rate of the return from investment in simple chooser options is significantly dependent on the strike price. The presented simulation is performed using MAPLE.