A Unified Treatment of Derivative Pricing and Forward Decision Problems Within HJM Framework

1 online resource (73 pages) : PDF

2012

University of North Carolina at Charlotte

We study the HJM approach which was originally introduced in the fixed income market by David Heath, Robert Jarrow and Andrew Morton and later was implemented in the case of European option market by Martin Schweizer, Johannes Wissel, Rene Carmona and Sergey Nadtochiy. The main contribution of this thesis is to apply HJM philosophy to the American option market. We derive the absence of arbitrage by a drift condition and compatibility between long and short rate by a spot consistency condition. In addition, we introduce a forward stopping rule which is significantly different from the classical stopping rule which requires backward induction. When It^o stochastic differential equation are used to model the dynamics of underlying asset, we discover that the drift part instead of the volatility part will determine the value function and stopping rule. As counterpart to the forward rate for the fixed income market and implied forward volatility and local volatility for the European option market, we introduce the forward drift for the American option market.

doctoral dissertations

Mathematics
Finance

Ph.D.

American Option
Forward Approach
HJM
Optimal Stopping

Applied Mathematics

Xu, Mingxin

Bishwal, Jaya
Jiang, Jiancheng
Zillante, Artie

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2012.

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Zou_uncc_0694D_10399

http://hdl.handle.net/20.500.13093/etd:705