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IEOR4703 – Monte Carlo Simulation

创建日期：2024-05-21 17:43:44

所属分类：数学mathematics

标签： IEOR4703

Monte Carlo Simulation

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IEOR4703 – Monte Carlo Simulation
For all problems in this assignment, assume the stock price process follows geometric Brownian motion (GBM)
Problem 1 (Pricing American via Simulation): Use the sample code american via fd.ipynb to extract the exercise boundary for
American put for the following parameters: spot price of S0 = 100, strike price K = 80, risk-free rate r = 0.025, continuous divided rate
of q = 0.05, volatility of σ = 0.30, maturity of T = 2 years. Use the extracted exercise boundary to price the same American put option
via simulation using the sample code american via simulation given boundary.ipynb. Use 20,000, 50,000, and 100,000 simulated
paths and compare the results.
Problem 2 (Pricing No-touch Rebate): Assume spot price of S0 = 1, 000, risk-free rate r = 0.05, continuous divided rate of
q = 0.0185, volatility of σ = 0.30, and maturity of T = 2 years. Consider the following two barriers: low barrier of $700 and high barrier
of $1, 300. The holder of this option would recieve a rebate of $100 if the stock does not hit or cross the barriers at any time during the
life of the option. Estimate the price of this contract via simulation.
Problem 3 (Pricing American via Simulation): The code american via simulation extracting exercise boundary.ipynb can
be utilized for pricing an American put option. Use the code to price American option under the parameter set provided in the sample
code for the following cases:
a. for Chebyshev polynomials of 1st kind:
1. run it for first four polynomial (basis) functions
2. run it for first five polynomial (basis) functions
3. run it for first six polynomial (basis) functions
4. run it for first seven polynomial (basis) functions
b. for Chebyshev polynomials of 2nd kind:
1. run it for first four polynomial (basis) functions
2. run it for first five polynomial (basis) functions
3. run it for first six polynomial (basis) functions
4. run it for first seven polynomial (basis) functions
c. for Laguerre polynomials:
1. run it for first four polynomial (basis) functions
2. run it for first five polynomial (basis) functions
3. run it for first six polynomial (basis) functions
4. run it for first seven polynomial (basis) functions
In parts (a), (b), and (c) use 50,000, 100,000, and 200,000 simulated paths. Compare premiums and exercise boundaries and conclude.

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