Calculate the price of the call numerically

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Reference no: EM132226862

Problem 1: Evaluation of a known integral using various quadratures: In this problem we are going to compute the price of a European call option with 3 month expiry, strike 12, and implied vol 20, Assume the underlying is 10 now and the interest rate is 4%.

1. Use Black-Scholes formula to compute the price of the call analytically.

2. Calculate the price of the call numerically using the following 3 quadrature methods:
(a) Left Riemann rule
(b) Midpoint rule
(c) Gauss nodes of your choice (say explicitly why you made that choice) with the number of nodes N = 5, 10, 50, 100 and compute the calculation error as a function of N for each of the methods.

3. Estimate the experimental rate of convergence of each method and compare it with the known theoretical estimate.

4. Which method is your favorite and why?

Problem 2: Calculation of Contingent Options: Let S1 be a random variable that takes on the value of SPY one year from now and let S2 take on the values of SPY 6 months from now. Assume that they are jointly normally distributed with

σ1 = 20%
σ2 = 15%
ρ = 0.95

By ρ here we mean correlation between S1 and S2. Also, assume that interest rate is zero.

1. Evaluate the price of the one year call on SPY with the strike K1 = 260. This is an example of a vanilla option.

2. Evaluate the price of the one year call on SPY with the strike K1 = 260, contingent on SPY at 6 months being below 250. This is a contingent option.

3. Calculate the contingent option again, but with ρ = 0.8, ρ = 0.5, and ρ = 0.2.

4. Does dependence on ρ make sense?

5. Calculate the contingent option again, but with SPY at 6 months below 240, 230, and 220.

6. Does the dependence on the 6 month value make sense?

7. Under what conditions do you think the price of the contingent option will equal the price of the vanilla one?

Verified Expert

I have used python code for calculate the price.It based on qudrature method.In first problem,I have used rule(left riemann rule,midpoint rule,gauss node) for calculate the price amount.In second problem,evaluate the price by using contingent option and vanilla option.

Reference no: EM132226862

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Reviews

inf2226862

7/24/2019 12:04:58 AM

here is a related material you may want to use. 31626145_1mf796-2-quadrature 1.pdf you can use either python or R to solve problems, also attach the code. you have to calculate the price in 1.2(a)(b)(c), just draw the pictures. Also in the 1.4, I think the question is that which methods in 1.2 is your favorite and why. Thank you projects team, perfect one. I was very much anxious about this assignment, but you made me calm, thanks a lot.

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