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%% Compute Cash-or-Nothing Option Prices and Sensitivities Using the Black-Scholes Option Pricing Model % Copyright 2015 The MathWorks, Inc. %% % Consider a European call and put cash-or-nothing options on a futures % contract with an exercise price of $90, and a fixed payoff of $10 that % expires on January 1, 2009. Assume that on October 1, 2008 the contract % trades at $110, and has a volatility of 25% per annum and the risk-free % rate is 4.5% per annum. Using this data, calculate the price and sensitivity % of the call and put cash-or-nothing options on the futures contract. First, % create the |RateSpec|: Settle = 'Jan-1-2008'; Maturity = 'Oct-1-2008'; Rates = 0.045; Compounding = -1; Basis = 1; RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis) %% % Define the |StockSpec|. AssetPrice = 110; Sigma = .25; DivType = 'Continuous'; DivAmount = Rates; StockSpec = stockspec(Sigma, AssetPrice, DivType, DivAmount) %% % Define the call and put options. OptSpec = {'call'; 'put'}; Strike = 90; Payoff = 10; %% % Compute the gamma, theta, and price. OutSpec = { 'gamma';'theta';'price'}; [Gamma, Theta, Price] = cashsensbybls(RateSpec, StockSpec,... Settle, Maturity, OptSpec, Strike, Payoff, 'OutSpec', OutSpec)