ESTIMATING THE PARAMETER DELTA IN THE BLACK MODEL USING THE FINITE DIFFERENCE METHOD FOR FUTURES OPTIONS
Abstract
Financial derivatives are a widely used tool for investors to hedge against the risk caused by changes in asset prices in the financial markets. A usual type of hedging derivative is an asset option. In case of unexpected changes in asset prices, in the investment portfolio, the investor will exercise the option to eliminate losses resulting from these changes. Therefore, it is necessary to include the options in the investor´s portfolio in such a ratio that the losses caused by decreasing of assets prices will be covered by profits from those options. Futures option is a type of call or put option to buy or to sell an option contract at a designated strike price. The change in price of the underlying assets or underlying futures contract causes a change in the prices of options themselves. For investor exercising option as a tool for risk insurance, it is important to quantify these changes. The dependence of option price changes, on the underlying asset or futures option price changes, can be expressed by the parameter delta. The value of delta determines the composition of the portfolio to be risk-neutral. The parameter delta is calculated as a derivation of the option price with respect to the price of the underlying asset, if the option price formula exists. But for some types of more complex options, the analytical formula does not exist, so calculation of delta by derivation is not possible. However, it is possible to estimate the value of delta numerically using the principles of the numerical method called “Finite Difference Method.” In the paper the parameter delta for a Futures call option calculated from the analytical formula and estimated from the Finite difference method are compared.References
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