Robust Approximations for Pricing Asian Options and Volatility Swaps Under Stochastic Volatility
AbstractWe show that if the discounted Stock price process is a continuous martingale, then there is a simple relationship linking the variance of the terminal Stock price and the variance of its arithmetic average. We use this to establish a model-independent upper bound for the price of a continuously sampled fixed-strike arithmetic Asian call option, in the presence of non-zero time-dependent interest rates (Theorem 1.2). We also propose a model-independent lognormal moment-matching procedure for approximating the price of an Asian call, and we show how to apply these approximations under the Black-Scholes and Heston models (subsection 1.3). We then apply a similar analysis to a time-dependent Heston stochastic volatility model, and we show how to construct a time-dependent mean reversion and volatility-of-variance function, so as to be consistent with the observed variance swap curve and a pre-specified term structure for the variance of the integrated variance (Theorem 2.1). We characterize the small-time asymptotics of the first and second moments of the integrated variance (Proposition 2.2) and derive an approximation for the price of a volatility swap under the time-dependent Heston model ( Equation (52)), using the Brockhaus-Long approximation (Brockhaus, and Long, 2000). We also outline a bootstrapping procedure for calibrating a piecewise-linear mean reversion level and volatility-of-volatility function (Subsection 2.3.2).
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 17 (2010)
Issue (Month): 3 ()
Contact details of provider:
Web page: http://www.tandfonline.com/RAMF20
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Li, Minqiang, 2014. "Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach," MPRA Paper 54595, University Library of Munich, Germany.
- Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty).
If references are entirely missing, you can add them using this form.