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arXiv · 0910.2309

Closed form asymptotics for local volatility models

Wen Cheng·Nick Costanzino·John Liechty·Anna Mazzucato·Victor Nistor
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Abstract

We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for short-time asymptotic expansions of heat kernels, and obtain a family of general closed-form approximate solutions for both the pricing kernel and derivative price. A bootstrap scheme allows us to extend our method to large time. We also perform analytic as well as a numerical error analysis, and compare our results to other known methods.

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Wen Cheng, Nick Costanzino, John Liechty, Anna Mazzucato, Victor Nistor. 2010-04-21. Closed form asymptotics for local volatility models. https://arxiv.org/abs/0910.2309

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