[SOLVED] NTUIB Assignment 1

Assignment 1

Derive the closed-form formula for an option with the following payoff function:

Payoff at T

K2 K1

0

ST

KKKK

1234

• Basic requirement
  (i) Utilize the martingale pricing method to derive the closed-form formula by hands.

  (ii) Based on the formula you derive, implement a program to price this option. (Inputs: S0, r, q, σ, T, K1, K2, K3, K4. Output: Option value.)

• Bonus (10 points):
  Employ the Monte Carlo simulation to price this option.

  Based on lnST ∼ NDQ(lnS0 + (r − q − σ2/2)T,σ2T), draw 10,000 random samples for ST
  to compute an option price. Repeat the above step 20 times to obtain the 95% confidence interval for the option value:

  [mean of 20 repetitions − 2×(s.d. of 20 repetitions), mean of 20 repetitions + 2×(s.d. of 20 repetitions)].

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