The student will study the valuation of financial derivatives using
both solution methods for differential equations and stochastic simulations.
Typical examples of these derivatives will include installment options,
Bermuda options, variations on American options, and options on assets with market-dependent
volatility. An option is a contract that allows the holder to
buy or sell a share of stock at a certain price. The valuation of some options can be
complicated since they can be exercised anytime up to a certain expiration date,
and their value may depend on the history of the underlying stock price.
The student will have the opportunity to develop and/or compare the
simulations with recent theoretical and numerical results
obtained from partial differential equations (Black-Scholes model).
Therefore the student will be providing a standard against which
approximations can be measured and developing skills in critically assessing
different models of financial derivatives and methods of valuation.
A background in basic probability and statistics is required, together with some programming experience and some experience with differential equations. Some experience in partial differential equations would be helpful, but is not necessary. The student will learn about both binomial models and iterative methods based on partial differential equations for describing the behavior of option values. The student will also gain experience with the relationships between using continuous and discrete models and developing code for simulation or as a solution method.