Essays in financial engineering

This thesis consists of three essays that apply techniques of operations research to problems in financial engineering. In particular, we study problems in portfolio optimization and options pricing. The first essay is motivated by the fact that derivative securities are equivalent to specific dynamic trading strategies in complete markets. This suggests the possibility of constructing buy-and-hold portfolios of options that mimic certain dynamic investment policies, e.g., asset-allocation rules. We explore this possibility by solving the following problem: given an optimal dynamic investment policy, find a set of options at the start of the investment horizon which will come closest to the optimal dynamic investment policy. We solve this problem for several combinations of preferences, return dynamics, and optimality criteria, and show that under certain conditions, a portfolio consisting of just a few european options is an excellent substitute for considerably more complex dynamic investment policies. In the second essay, we develop a method for pricing and exercising high-dimensional American options. The approach is based on approximate dynamic programming using nonlinear regression to approximate the value function. Using the approximate dynamic programming solutions, we construct upper and lower bounds on the option prices. These bounds can be evaluated by Monte Carlo simulation, and they are general enough to be used in conjunction with other approximate methods for pricing American options.

Department dc:contributor.department

Massachusetts Institute of Technology. Operations Research Center.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2001

Author dc:creator

• Haugh, Martin B. (Martin Brendan), 1971-

Advisor dc:contributor.advisor

• Andrew W. Lo.

• Operations Research Center.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/8304

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/8304