@article{Jacquier:2010:10.1080/13504860903335348,
author = {Jacquier, A and Forde, M},
doi = {10.1080/13504860903335348},
journal = {Applied Mathematical Finance},
pages = {241--259},
title = {Robust approximations for pricing Asian options and volatility swaps under stochastic volatility},
url = {http://dx.doi.org/10.1080/13504860903335348},
volume = {17},
year = {2010}
}

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TY  - JOUR
AB  - We 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).
AU  - Jacquier,A
AU  - Forde,M
DO  - 10.1080/13504860903335348
EP  - 259
PY  - 2010///
SP  - 241
TI  - Robust approximations for pricing Asian options and volatility swaps under stochastic volatility
T2  - Applied Mathematical Finance
UR  - http://dx.doi.org/10.1080/13504860903335348
UR  - http://www3.imperial.ac.uk/people/antoine.jacquier08
UR  - http://www.tandf.co.uk/journals/journal.asp?issn=1350-486X&linktype=145
VL  - 17
ER  - 

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