Research on Asian Option Pricing Based on Uncertain Volatility
Journal: Modern Economics & Management Forum DOI: 10.32629/memf.v5i5.2883
Abstract
In this paper, we study the impact of introducing uncertainty volatility into Asian options pricing, with emphasis on the use of Hamilton-Jacobi-Bellman (HJB) equation. The traditional Asian option pricing model usually assumes that volatility is known and constant, but in the actual market, volatility is often uncertain and volatile. This paper first reviews the pricing theory of Asian options, and then introduces the hypothesis of uncertain volatility. By constructing the HJB equation based on uncertainty volatility, a new pricing method is proposed and verified by numerical simulation. The results show that after the introduction of uncertain volatility, the price range of Asian options expands significantly, reflecting higher market uncertainty and risk.
Keywords
Asian option, HJB equation, option pricing, uncertain volatility
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[2] Sean D. Campbell, Francis X. Diebold. Weather forecasting for weather derivatives, J. Amer. Statist. Assoc. 100 (2005) 6–16.
[3] F.E. Benth, J. Saltyte Benth, S. Koekebakker. Putting a price on temperature, Scand. J. Stat. 12 (1) (2007) 53–85.
[4] Djehiche Alaton, Stillberger. On modelling and pricing weather derivatives, Appl. Math. Finance 9 (2002) 1–20.
[5] C. Harris. The Valuation of Weather Derivatives using Partial Differential Equations, Department of Mathematics, University of Reading, 2003 (Ph.DThesis).
[6] Hélèn Hamisultane. Extracting information from the market to price the weather derivatives. SSRN Electronic Journal, halshs-00079192v2, 2006.
[7] Hélèn Hamisultane. Which Method for Pricing Weather Derivatives? halshs-00355856, 2008.
[8] Edwin Kwaku Broni-Mensah. Numerical Solution of Weather Derivatives and other Incomplete Market Problems, Department of Mathematics,University of Manchester, 2012 (Ph.D Thesis).
[9] W.G. Tang, S.H. Chang. Semi-Lagrangian method for the weather options of mean-reverting Brownian motion with jump–diffusion, Comput. Math.Appl. 71 (2016) 1045–1058.
[10] Peng Li. Pricing weather derivatives with partial differential equations of the Ornstein — Uhlenbeck process, Computers & Mathematics with Applications. 75(3), 2018, 1044-1059.
[11] D. M. POOLEY, P. A. FORSYTH. Numerical convergence properties of option pricing PDEs with uncertain volatility, IMA Journal of Numerical Analysis (2003) 23, 241-267.
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