I am looking to see if there is a formula or a derivation at least of an approximation of an Asian (Average Price) option under the heston model of stochastic volatility.
Please advise
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1 Answer
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There is a closed-form pricing formula for the Geometric Asian Option in the Heston model (the only non-paywalled link I can find shows the double-Heston price, Heston is a special case of double-Heston), but not for the Arithmetic Asian option (this is also the case in Black-Scholes).
For Arithmetic Asian prices, a numerical technique like Monte-Carlo will be required.
However, the prices of Geometric and Arithmetic Asian options are very similar and highly correlated, so that the geometric price can be used as a control variate in the Monte Carlo simulation, vastly increasing the accuracy of the calculation for a set number of paths.
Update 28-07-2021:
For anyone looking for implementations, analytic pricing engines for geometric asian options under Heston are available in QuantLib, and the MC pricer for arithmetic asian options supports the use of the geometric asian option as a control variate
