Problem 2: Recall the formula for computing the price Co of an option (derivative of the BLM stock prices) That yields a payoff at time T, denote by CT: 1 Co= E* (CT), (1+r)T where* refers to the fact that we must use the value p* instead of the original (real) P for the up/down probability of the BLM. (The real value of P is not needed for pricing.) Also recall that for Cr= (ST-K)+, the European call option, the expected value, E* (ST-K) can be computed explicitly yielding the famous Black-Scholes-Merton option pricing formula: Σ(1) Φ You are to use this formula to exactly obtain the price on the one hand, and then use Monte Carlo simulation on the other hand to compare and thus see how accurate the Monte Carlo method can be. Co= #write your code here 1 (1+r)T (p*)*(1-p*)-(ud- So - K)+. T-k Here are the parameters to use: T = 10, r = 0.05, u = 1.15, d = 1.01, So= 50, K = 70. Recall that p* = 1+r-d u-d For the Monte Carlo, use n = 100, n = 1000, n = 10, 000 iid copies of Cr (for averaging) to see how it gets more accurate as n increases.

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Problem 2: Recall the formula for computing the price Co of an option (derivative of the BLM stock prices) That yields a payoff at time T, denote by CT:
1
where* refers to the fact that we must use the value p* instead of the original (real) P for the up/down probability of the BLM. (The real value of P is not
needed for pricing.) Also recall that for CT = (ST-K)+, the European call option, the expected value, E* (ST-K) can be computed explicitly yielding
the famous Black-Scholes-Merton option pricing formula:
Co =
Co=
In [7] # write your code here
4
(1 + r)T
For the Monte Carlo, use n = 100, n = 1000, n
=
#you may add more cells as needed
E* (CT),
1
=
(1 + n) ≤ ( 7 ) ² (1 - ²)² + (x^² d² * So - K)*.
Σ(1)
6-pr
(1+r)T
You are to use this formula to exactly obtain the price on the one hand, and then use Monte Carlo simulation on the other hand to compare and thus see how
accurate the Monte Carlo method can be.
Here are the parameters to use: T = 10, r = 0.05, u = 1.15, d = 1.01, So = 50, K = 70. Recall that
p* =
1+r-d
u-d
10,000 iid copies of CT (for averaging) to see how it gets more accurate as n increases.
Transcribed Image Text:Problem 2: Recall the formula for computing the price Co of an option (derivative of the BLM stock prices) That yields a payoff at time T, denote by CT: 1 where* refers to the fact that we must use the value p* instead of the original (real) P for the up/down probability of the BLM. (The real value of P is not needed for pricing.) Also recall that for CT = (ST-K)+, the European call option, the expected value, E* (ST-K) can be computed explicitly yielding the famous Black-Scholes-Merton option pricing formula: Co = Co= In [7] # write your code here 4 (1 + r)T For the Monte Carlo, use n = 100, n = 1000, n = #you may add more cells as needed E* (CT), 1 = (1 + n) ≤ ( 7 ) ² (1 - ²)² + (x^² d² * So - K)*. Σ(1) 6-pr (1+r)T You are to use this formula to exactly obtain the price on the one hand, and then use Monte Carlo simulation on the other hand to compare and thus see how accurate the Monte Carlo method can be. Here are the parameters to use: T = 10, r = 0.05, u = 1.15, d = 1.01, So = 50, K = 70. Recall that p* = 1+r-d u-d 10,000 iid copies of CT (for averaging) to see how it gets more accurate as n increases.
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