Novikov, A, Alexander, S, Kordzakhia, N & Ling, T 2017, 'Pricing of asian-type and basket options via bounds', Theory of Probability and Its Applications, vol. 61, no. 1, pp. 94-106.View/Download from: UTS OPUS or Publisher's site
© 2017 Society for Industrial and Applied Mathematics. This paper sets out to provide a general framework for the pricing of average-type options via lower and upper bounds. This class of options includes Asian, basket, and options on the volume-weighted average price. The use of lower and upper bounds is proposed in response to the inherent difficulty in finding analytical representations for the true price of these options and the requirement for numerical procedures to be fast and efficient. We demonstrate that in some cases lower bounds allow for the dimensionality of the problem to be reduced and that these methods provide reasonable approximations to the price of the option.
Ling, TG & Shevchenko, PV 2016, 'Historical backtesting of local volatility model using aud/usd vanilla options', ANZIAM Journal : Electronic Supplement, vol. 57, no. 3, pp. 319-338.View/Download from: UTS OPUS or Publisher's site
Novikov, A, Kordzakhia, N & Ling, T 2014, 'Pricing of Volume-Weighted Average Options: Analytical Approximations and Numerical Results' in Kabanov, Y, Rutkowski, M & Zariphopoulou, T (eds), Inspired by Finance, Springer, London, pp. 461-474.View/Download from: UTS OPUS or Publisher's site
The volume weighted average price (VWAP) over rolling number of days in the averaging period is used as a benchmark price by market participants and can be regarded as an estimate for the price that a passive trader will pay to purchase securities in a market. The VWAP is commonly used in brokerage houses as a quantitative trading tool and also appears in Australian taxation law to specify the price of share-buybacks of publically-listed companies. Most of the existing literature on VWAP focuses on strategies and algorithms to acquire market securities at a price as close as possible to VWAP. In our setup the volume process is modeled via a shifted squared Ornstein-Uhlenbeck process and a geometric Brownian motion is used to model the asset price. We derive the analytical formulae for moments of VWAP and then use the moment matching approach to approximate a distribution of VWAP. Numerical results for moments of VWAP and call-option prices have been verified by Monte Carlo simulations.