Computational Methods in Finance.

A graduate course in the Mathematics in Finance program at the Courarant Institute of Mathematical Sciences of New York University.

Comments and hints on assignments.

• In C and C++, include files that you wrote for the assignment are part of your program. You should include them in what you hand in.
• Don't expect floating point computations to round exactly as you want. For example, if you have a time step dt = .2 and a tfinal = 30, then the statement: nsteps = tfinal/dt (assuming dt and tfinal are floats while nsteps is an int, this will automatically compute the quotient in floating point and truncate the result to get an integer. You might get 120 (presumable the intended answer) or 119 (if rounding errors in the division lead to a result less than 120 in floating point, a distinct possibility.
• Comment on the running time of the program. Be sure to say what computer you used.
• Comment on the checks for correctness you did. For example, in assignment 1, it is easy to compute the total payments if no refinancing is allowed. The result with refinancing cannot be more. Does the result have to be greater than 1?
• Don't cut down trees to make mind numbing printouts that I won't have time to read. Do think carefully about how to present the results graphically whenever possible. Try to present several results on the same graph if possible.
• A note on C++ programming: C++ is (claimed to be) a good language for medium to large scale software projects. The programming and debugging overhead of defining classes may not pay off for small coursework assignments.
• Remember to give the answer, for example, "total cost = ...".
• Always put in comments saying what the program is doing. For example, the assignment 1 program would have a section:

/* Compute the new cost go value. */ ........... code ....... /* Compute the expected cost if you don't refinance now */ .......code........................ ....cost_without = ..... /* Compute the expected cost if you do refinance now. */ ...........code .......... ....cost_with = ........ /* The cost to go from here is the smaller of these numbers. */ f(...) = min(cost_without, cost_with);

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