Diener, Nicolas. 2009. Mathematical Models For Swing Options And Subprime Mortgage Derivatives.
Doctoral Dissertation, Cornell University.
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.
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