# On the Pricing of Call-Put Parities of Asian Options by Reduced Differential Transform Algorithm

## Main Article Content

### Abstract

The key aim of the paper is to show that how the efficiently the Reduced Differential Transform Algorithm (RDTA) can be employed to price the exotic financial options. In this paper we have computed the exact solution of the parabolic partial differential equation governing the dynamics of put-call parity in the mathematical theory of Asian options, by means of RDTA.

## Article Details

### References

- A. Haghbin, S. Hesam, Reduced Differential Transform Method For Solving Seventh Order Sawada-Kotera Equations, J. Math. Computer Sci. 5 (1) (2012), 53-59.
- B. Alziary, J. P. Drcamps and P. F. Koehl, A PDE Approach to Asian Options: Analytical and Numerical Evidence, J. Bank. Finance, 21 (1997), 613-640.
- Birol Ë™IBË™IS ¸, Application of Reduced Differential Transformation Method for Solving Fourth-Order Parabolic Partial Differential Equations, J. Math. Computer Sci. 12 (2014), 124-131.
- B. K. Singh, Fractional Reduced Differential Transform Method for Numerical Computation of a System of Linear and Nonlinear Fractional PDEs, Int. J. Open Probl. Compt. Math. 9 (3) (2016), 20-38.
- C. Fan, P. Li, Y. Xue, Application of Differential Equations in Enzyme Kinetics, Chem. Eng. Trans. 71 (2018), 883-888.
- D.I. Cruz and J.M. Gonzalez., A Different Approach for Pricing Asian Options, Appl. Math. Lett. 21 (2008), 303-306.
- E. Barucci, S. Polidoro and V. Vespri, Some Results on Partial Differential Equations and Asian Options, Math. Models Methods Appl. Sci. 11 (3) (2001), 475-497.
- H. Jafari, H. Jassim, S. Moshokoa, V. Ariyan and F. Tchier, Reduced Differential Transform Method for Partial Differential Equations Within Local Fractional Derivative Operators, Adv. Mech. Eng. 8 (4) (2016), 1-6.
- H. Geman and M. Yor, Bessel Processes, Asian options, and Perpetuities, Math. Finance, 3 (4) (1993), 349-375.
- H. Rouhparvar, Computational Technique of Linear Partial Differential Equations by Reduced Differential Transform Method, Int. J. Ind. Math. 8 (4) (2016), Article ID IJIM-00651.
- J. N. dewynne and W. T. Shaw, Differential Equations and Asymptotic solutions for Arithmetic Asian Options: BlackScholes Formulae for Asian Rate Calls, Eur. J. Appl. Math. 19 (4) (2008), 353-391.
- Y. Keskin, Ph.D Thesis, Selcuk University, 2010.
- Y. Keskin, G. Oturance, Reduced Differential Transform Method for Partial Differential Equations, Int. J. Nonlinear Sci. Numer. Simul. 10 (6) (2009), 741-749.
- Y. Keskin, G. Oturance, Reduced Differential Research Transform Method for Fractional Partial Differential Equations, Nonlinear Sci. Lett. A, 1 (1) (2010), 61-72.
- Y. Keskin, G. Oturance, Application of Reduced Differential Transformation Method for Solving Gas Dynamics Equation, Int. J. Contemp. Math. Sci. 5 (22) (2010), 1091-1096.
- Y.K. Kwok, Mathematical Models of Financial derivatives, 2nd Ed., Springer, Berlin, 2008.
- J. Lishang, Mathematical Modeling and Methods of Option Pricing, World Scientific, Singapore, 2005.
- Mahmoud. R, Using the Reduced Differential Transform Method to Solve Nonlinear PDEs Arises in Biology and Physics, World Appl. Sci. J. 23 (8) (2013), 1037-1043.
- Mohammad. T., Vineet K., Srivastava: A Computational Modelling of Micro Strip Patch Antenna and Its Solution By RDTM, Alex. Eng. J. 57 (2018), 1877-1881.
- L. C. G. Rogers and Z. Shi, The Value of an Asian Option, J. Appl. Prob. 32 (4) (1995), 1077-1088.
- V. Srivastava, M. Awasthi, M. Tamsir, RDTM Solution of Caputo Time Fractional-Order Hyperbolic Telegraph Equation, AIP Adv. 3 (3) (2013), 032142.
- S. Servi, Y. Keskin, G. Oturan ¸c, Reduced Differential Transform Method for Improved Boussinesq Equation, AIP Conf. Proc. 1648 (2015), 370012.
- T.R. Ramesh Rao, Numerical Solution of Sine Gordon Equations Through Reduced Differential Transform Method, Glob. J. Pure Appl. Math. 13 (7) (2017), 3879-3888.
- Z. Ali, R. Rozita and R. Hazli, New Pricing Formula for Arithmetic Asian Options using PDE Approach, App. Math. Sci. 5 (77) (2011), 3801-3809.
- Z. Ali and R. Rozita, Solving an Asian option PDE via the Laplace Transform, ScienceAsia 39S (2013), 67-69.