No Access

Analytical pricing of discrete arithmetic Asian options under generalized CIR process with time change

Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, K1N 6N5, Canada

Corresponding author.

and

Model Validation, Enterprise Risk and Portfolio Management, Bank of Montreal, 27th Floor, First Canadian Place, Toronto, Ontario, M5X 1A3, Canada

E-mail Address: Allen.Liu@bmo.com

Search for more papers by this author

https://doi.org/10.1142/S2424786318500020Cited by:5 (Source: Crossref)

Abstract

Starting from CIR process, we build a new model for pricing discrete arithmetic Asian options with nonlinear transformation and stochastic time change. The new model introduces the nonlinearity in both drift and diffusion components of the underlying process and allows for flexible jump processes. We are able to derive the recursive formula for the moment generating function of average price by employing the eigenfunction expansion technique. The Asian option prices can then be implemented through a Fourier transform. We also investigate the sensitivities of option prices with respect to the parameters of the new model.

Keywords:

References

Aba Oud, MA and J Goard [2015a] Stochastic models for oil prices and the pricing of futures on oil, Applied Mathematical Finance, 22, 1–12. Crossref, Google Scholar
Aba Oud, MA and J Goard [2015b] Valuation of options on oil futures under 3/4 oil price model, International Journal of Theoretical and Applied Finance, 18, 180–206. Google Scholar
Ahn, DH and B Gao [1999] A parametric nonlinear model of term structure dynamics, The Review of Financial Studies, 12, 721–762. Crossref, Google Scholar
Andersen, LB and VV Piterbarg [2010] Interest Rate Modeling. Volume 1: Foundations and Vanilla Models, London, UK: Atlantic Financial Press. Google Scholar
Bu, R, J Cheng and K Hadri [2016] Reducible diffusions with time-varying transformations with application to short-term interest rates, Economic Modelling, 52, 266–277. Crossref, Google Scholar
Bu, R, J Cheng and K Hadri [2017] Specification analysis in regime-switching continuous-time diffusion models for market volatility, Studies in Nonlinear Dynamics and Econometrics, 21, 65–80. Google Scholar
Bu, R, L Giet, K Hadri and M Lubrano [2011] Modeling multivariate interest rates using time-varying copulas and reducible nonlinear stochastic differential equations, Journal of Financial Econometrics, 9, 198–236. Crossref, Google Scholar
Carr, P and D Madan [1999] Option valuation using the fast Fourier transform, Journal of Computational Finance, 2, 61–73. Crossref, Google Scholar
Chung, SF and HY Wong [2014] Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps, Journal of Banking and Finance, 44, 130–140. Crossref, Google Scholar
Cox, JC, JE Ingersoll and SA Ross [1985] A theory of the term structure of interest rates, Econometrica, 53, 385–407. Crossref, Google Scholar
Fang, F and CW Oosterlee [2008] A novel pricing method for European options based on Fourier-cosine series expansions, SIAM Journal of Scientific Computing, 31, 826–848. Crossref, Google Scholar
Fusai, G, M Marena and A Roncoroni [2008] Analytical pricing of discretely monitored asian-style options: Theory and applcation to commodity markets, Journal of Banking and Finance, 32, 2033–2045. Crossref, Google Scholar
Goard, J and M Mazur [2013] Stochastic volatility models and the pricing of VIX options, Mathematical Finance, 23, 439–458. Crossref, Google Scholar
Huang, CS, JG O’Hara and S Mataramvura [2017] Efficient pricing of discrete arithematic Asian options under mean reversion and jumps based on Fourier-cosine expansions, Journal of Computational and Applied Mathematics, 311, 230–238. Crossref, Google Scholar
Li, J, L Li and G Zhang [2017] Pure jump models for pricing and hedging VIX derivatives, Journal of Economic Dynamics and Control, 74, 28–55. Crossref, Google Scholar
Li, L and V Linetsky [2014] Time-changed Ornstein-Uhlenbeck processes and their applications in commodity derivative models, Mathematical Finance, 24, 289–330. Crossref, Google Scholar
Li, L, R Mendoza-Arriaga, Z Mo and D Mitchell [2016] Modelling electricity prices: A time change approach, Quantitative Finance, 16, 1089–1109. Crossref, Google Scholar
Lim, D, L Li and V Linetsky [2012] Evaluating callable and putable bonds: An eigenfunction expansion approach, Journal of Economic Dynamics and Control, 36, 1888–1908. Crossref, Google Scholar
Linetsky, V [2004] The spectral decomposition of the option value, International Journal of Applied and Theoretical Finance, 7, 337–384. Link, Google Scholar
Linetsky, V and D Mitchell [2008] Spectral methods in derivatives pricing, in JR Birge and V Linetsky (editors) Handbook of Financial Engineering, Amsterdam: Elsevier, pp. 223–299. Google Scholar
Prudnikov, AP, YA Brychkov and OI Marichev [1986] Integrals and Series, Vol. 2. Gordon and Breach Science Publishers, London, UK. Google Scholar
Sato, K [1999] Lévy Processes and Infinitely Divisible Distribution, Cambridge University Press, Cambridge, UK. Google Scholar
Tong, Z [2017] Modelling VIX and VIX derivatives with reducible diffusions, International Journal of Bonds and Derivatives, 3, 153–175. Crossref, Google Scholar