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Asymptotic Solutions for Australian Options with Low Volatility

Asymptotic Solutions for Australian Options with Low Volatility AbstractIn this paper we derive asymptotic expansions for Australian options in the case of low volatility using the method of matched asymptotics. The expansion is performed on a volatility scaled parameter. We obtain a solution that is of up to the third order. In case that there is no drift in the underlying, the solution provided is in closed form, for a non-zero drift, all except one of the components of the solutions are in closed form. Additionally, we show that in some non-zero drift cases, the solution can be further simplified and in fact written in closed form as well. Numerical experiments show that the asymptotic solutions derived here are quite accurate for low volatility. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Asymptotic Solutions for Australian Options with Low Volatility

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Asymptotic Solutions for Australian Options with Low Volatility

Abstract

AbstractIn this paper we derive asymptotic expansions for Australian options in the case of low volatility using the method of matched asymptotics. The expansion is performed on a volatility scaled parameter. We obtain a solution that is of up to the third order. In case that there is no drift in the underlying, the solution provided is in closed form, for a non-zero drift, all except one of the components of the solutions are in closed form. Additionally, we show that in some non-zero drift...
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Publisher
Taylor & Francis
Copyright
© 2014 Taylor & Francis
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2014.906973
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper we derive asymptotic expansions for Australian options in the case of low volatility using the method of matched asymptotics. The expansion is performed on a volatility scaled parameter. We obtain a solution that is of up to the third order. In case that there is no drift in the underlying, the solution provided is in closed form, for a non-zero drift, all except one of the components of the solutions are in closed form. Additionally, we show that in some non-zero drift cases, the solution can be further simplified and in fact written in closed form as well. Numerical experiments show that the asymptotic solutions derived here are quite accurate for low volatility.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Nov 2, 2014

Keywords: Asian options; Australian options; stochastic volatility; asymptotic expansions

References

  • Differential equations and asymptotic solutions for arithmetic Asian options: ‘Black-Scholes Formulae’ for Asian Rate Calls
  • Asian and Australian options: A common perspective
  • Bessel processes, Asian options and perpetuities
  • Variable purchase options
  • An empirical test of the pricing of VPO contracts
  • On the equivalence of floating and fixed-strike Asian options
  • Spectral expansions for Asian (average price) options
  • Australian options
  • Essentially exact asymptotic solutions for Asian derivatives
  • Unified Asian pricing
  • Pricing Asian options in a semimartingale model