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

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Zou, W. (2012). A Unified Treatment of Derivative Pricing and Forward Decision Problems Within HJM Framework. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

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.

Details
Author

Zou, Wenhua

Title

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

Physical Description

1 online resource (73 pages) : PDF

Date

2012

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

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.

Genre

doctoral dissertations

Subjects--Topics

Mathematics
Finance

Degree

Ph.D.

Keywords

American Option
Forward Approach
HJM
Optimal Stopping

Subject Area

Applied Mathematics

Advisor(s)

Xu, Mingxin

Committee Members

Bishwal, Jaya
Jiang, Jiancheng
Zillante, Artie

Degree Note

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

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Rights Holder Information

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Identifier

Zou_uncc_0694D_10399

Permalink

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