Mathematical Models For Swing Options And Subprime Mortgage Derivatives.
The deregulation of the energy market and the recent soaring (and possible bubble) of commodity prices motivates the first part of the thesis. We analyze a certain kind of contract in the commodity market known as swing or take-or-pay options. These contracts are American type options where the holder has multiple exercise rights. The goal is to find the optimal consumption process for the underlying commodity. We present a pricing methodology using the theory of reflected backward stochastic differential equations and the theory of Snell envelopes. Once the model is constructed, one can use numerical techniques to solve the pricing problem and compute a replicating strategy using forward contracts. The recent burst of the real estate bubble has drawn a lot of attention to the subprime derivatives market. Existing models have proven inadequate due to their inability to account for the complexity of mortgage derivatives. Chapter 3 provides an analytical framework for understanding the mortgage market. In Chapter 4, we give a condition on the underlying securities that allows us to directly compute the loss distribution term structure of the portfolio. Then, we build a tractable model for pricing options on large credit portfolios such as Collateralized Debt Obligations of subprime Asset Backed Securities / Home Equity Loans.
dissertation or thesis