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Closed form asymptotics for local volatility models

Author

Listed:
  • Wen Cheng
  • Nick Costanzino
  • John Liechty
  • Anna Mazzucato
  • Victor Nistor

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.

Suggested Citation

  • Wen Cheng & Nick Costanzino & John Liechty & Anna Mazzucato & Victor Nistor, 2009. "Closed form asymptotics for local volatility models," Papers 0910.2309, arXiv.org, revised Apr 2010.
    • Handle: RePEc:arx:papers:0910.2309
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