Approximating Parabolic Partial Differential Equations with Applications to Financial Option Pricing
- Singh, Simranjeet
- [University Park, Pennsylvania] : Pennsylvania State University, 2017.
- Physical Description:
- 1 electronic document
- Additional Creators:
- Mazzucato, Anna L., Davis, Brian, and Schreyer Honors College
- Restrictions on Access:
- Open Access.
- Herein, we first consider the basic assumptions and derivation of the original Black-Scholes model via a generalized portfolio replication argument. Thereafter, we analyze the Dyson-Taylor commutator method for short-time expansions of the heat kernel (typically referred to as the Green's function), and apply it to the Constant Elasticity of Variance (CEV) local volatility model, in order to find closed-form approximate solutions for the pricing kernel.
- Other Subject(s):
- Dissertation Note:
- B.S. Pennsylvania State University, 2017.
- Technical Details:
- The full text of the dissertation is available as an Adobe Acrobat .pdf file ; Adobe Acrobat Reader required to view the file.
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