Project 5

MGMTMFE 405
Instructor: L. Goukasian

You will need to write codes for all the parts of the project. Make sure the codes work properly
and understand the ideas behind each problem below. You may be asked to demonstrate how
the codes work, by running them, and interpret the results. Code clarity and accuracy will
determine the grades.

Submit your codes and a PDF file of your answers to questions (including graphs,
histograms, but no codes, in this PDF file) by 11PM PDT on Next Wednesday.

1. Consider the following information on the stock of company XYZ: The current stock price
is $40, and the volatility of the stock price is = 20% per annum. Assume the prevailing
risk-free rate is = 6% per annum. Use the following method to price the specified option:

(a) Use the LSMC method with N=100,000 paths simulations (50,000 plus 50,000
antithetic variates) and a time step of ∆=
1
√
to price an American Put option with
strike price of = $40 and maturity of 0.5-years, 1-year, and 2-years. Use the first
of the Laguerre Polynomials for = 2, 3, 4. (That is, you will compute 9 prices
here). Compare the prices for the 3 cases = 2, 3, 4 and comment on the choice of k.

(b) Use the LSMC method with N=100,000 paths simulations (50,000 plus 50,000
antithetic variates) and a time step of ∆=
1
√
to price an American Put option with
strike price of = $40 and maturity of 0.5-years, 1-year, and 2-years. Use the first
of the Hermite Polynomials for = 2, 3, 4. (That is, you will compute 9 prices
here). Compare the prices for the 3 cases, = 2, 3, 4, and comment on the choice of k.

(c) Use the LSMC method with N=100,000 paths simulations (50,000 plus 50,000
antithetic variates) and a time step of ∆=
1
√
to price an American Put option with
strike price of = $40 and maturity of 0.5-years, 1-year, and 2-years. Use the first
of the Simple Monomials for = 2, 3, 4. (That is, you will compute 9 prices here).
Compare the prices for the 3 cases, = 2, 3, 4, and comment on the choice of k.

(d) Compare all your findings above and comment.

Note: You will need to use weighted-polynomials as done by the authors of the method.

Inputs: 0, X, T, r, , N, k
Outputs: Values of Option Prices; writeup: comments.



















































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