Reference no: EM132742000
Implement in Matlab the Monte Carlo algorithm seen in class for pricing a European call option. 2. (5 points) Use your algorithm to compute the value at time 0 of a European call with maturity T = 1 year and strike price K = 100, for the current stock price S0 = 110, assuming that the annualized parameters are r = 0.01, σ = 0.2. 3. (5 points) Compare your above result with the exact value provided by the analytical formula seen in class for n = 10, 000, n = 100, 000 and n = 1, 000, 000 sample paths. A cash-or-nothing Binary call option pays nothing if the price ends up below the strike price and pays fixed amount Q if it ends up above the strike price. Its payoff function is thus VT = χ{ST ≥K}Q where χ{ST ≥K}, the indicator function, is defined by χ{ST ≥K} = 1 if ST ≥ K 0 Otherwise 4.
Problem 1: Modify your algorithm to compute the price of a Binary call option with a cash-or-nothing payoff.
Problem 2: Compute the value of the call at time 0 for the following parameters: K = 100, T = 1, σ = 0.20, Q = 1, S0 = 110, r = 0.01.
Problem 3: Derive a price in closed form for the cash-or-nothing call at time t when the value of the stock is s.
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