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Solving the Ivancevic Pricing Model Using the He's Frequency Amplitude Formulation

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2017

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Abstract (2. Language): 
In nancial mathematics, option pricing theory remains a core area of interest that requires e ective models. Thus, the Ivancevic option pricing model (IOPM) is a nonlinear adaptivewave alternative for the classical Black-Scholes option pricing model; it represents a controlled Brownian motion (BM) in an adaptive setting with relation to nonlinear Schrodinger equation. The importance of the IOPM cannot be overemphasized; though, it seems dicult and complex to obtain the associated exact solutions if they exist. Therefore, this paper provides exact solutions of the IOPM by means of a proposed analytical method referred to as He's frequency amplitude formulation. Cases of nonzero adaptive market potential are considered. The method is shown to e ective, ecient, simple and direct in application, even without loss of generality.
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REFERENCES

References: 

[1] B E Baaquie. Quantum Finance: Path Integrals and Hamiltonians for Options and
Interest Rates. Cambridge University Press, Cambridge, 2004.
[2] G Barles and H M Soner. Option pricing with transaction costs and a nonlinear
Black-Scholes equation. Financ. Stoch, 2: 369-397, 1998.
[3] J Biazar and H Ghazvin. Exact solutions for non-linear Schrodinger equations by He's
homotopy perturbation method. Phys. Letters A, 366: 79-84, 2007.
REFERENCES 636
[4] F Black and M Scholes. The pricing options and corporate liabilities. J. Political
Econ., 81: 637-654, 1973.
[5] R Company, E Navarro, J R Pintos and E. Ponsoda. Numerical solution of linear and
nonlinear Black-Scholes option pricing equations. Comput. Math. Appl., 56: 813-821,
2008.
[6] R Cont. Empirical properties of asset returns: stylized facts and statistical issues.
Quant. Finance, 1: 223-236, 2001.
[7] M Contreras, R Pellicer, M Villena and A Ruiz. A Quantum Model of Option Pricing:
When Black-Scholes meets Schrodinger and Its Semi-Classical Limit. Physica A, 389:
5447-5459, 2010.
[8] S O Edeki, E A Owoloko and O O Ugbebor. The Modied Black-Scholes Model
via Constant Elasticity of Variance for Stock Options Valuation. AIP Conference
proceedings, 1705: 020041, 2016.
[9] S O Edeki, O O Ugbebor and E A Owoloko. Analytical Solutions of the Black-
Scholes Pricing Model for European Option Valuation via a Projected Dierential
Transformation Method. Entropy, 17: 7510-7521, 2015.
[10] S O Edeki, O O Ugbebor and E A Owoloko. He's Polynomials for Analytical Solutions
of the Black-Scholes Pricing Model for Stock Option Valuation. Lecture Notes in En-
gineering and Computer Science: Proceedings of the World Congress on Engineering,
WCE 2016, London, U.K., 632-634, 2016.
[11] C W Gardiner. Handbook of Stochastic Methods. Springer, Berlin, 1983.
[12] O Gonzalez-Gaxiola, J Ruiz de Chavez and J A Santiago. A Nonlinear Option Pricing
Model Through the Adomian Decomposition Method. Int. J. Appl. Comput. Math.,
2: 453-467, 2016.
[13] O Gonzalez-Gaxiola and J Ruiz de Chavez. Solving the Ivancevic option pricing model
using the Elsaki-Adomian decomposition method. Int. J. of Applied Math., 28: 515-
525, 2015.
[14] J H He. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod.
Phys. B, 20(10): 1141-1199, 2006.
[15] J H He. Comment on He's frequency formulation for nonlinear oscillators. Eur. J.
Phys. 29: L19-L22, 2008.
[16] J H He. An improved amplitude-frequency formulation for nonlinear oscillators. Int.
J. Nonlinear Sci. Numer. Simul., 9(2): 211-212, 2008.
[17] V G Ivancevic. Adaptive Wave Models for Sophisticated Option Pricing. Journal of
Mathematical Finance, 1: 41-49, 2011.
REFERENCES 637
[18] V G Ivancevic. Adaptive-Wave Alternative for the Black-Scholes Option Pricing
Model. Cognitive Computation, 2: 17-30, 2010.
[19] R C Merton. Theory of Rational Option Pricing. The Bell Journal of Economics and
Management Science, 4: 141-183, 1973.
[20] J Perello, R Sircar and J Masoliver. Option pricing under stochastic volatility: the
exponential Ornstein-Uhlenbeck model. J. Stat. Mech. P06010, 2008.
[21] M R Rodrigo and R S Mamon. An alternative approach to solving the Black-Scholes
equation with time-varying parameters. Appl. Math. Lett., 19: 398-402, 2006.
[22] M Wroblewski. Nonlinear Schrodinger approach to European option pricing. Open
Phys., 15 : 280-291, 2017.
[23] J Voit. The Statistical Mechanics of Financial Markets. Springer, Berlin, 2005.
[24] O Vukovic. On the Interconnectedness of Schrodinger and Black-Scholes Equation.
Journal of Applied Mathematics and Physics, 3: 1108-1113, 2015.
[25] A M Wazwaz. A study on linear and nonlinear Schrodinger equations by the variational
iteration method. Chaos, Solitons and Fractals, 37: 1136-1142, 2008.
[26] H L Zhang. Application of He's frequency-amplitude formulation to an x1=3 force
nonlinear oscillator. Int. Journal of Nonlinear Sciences and Numerical Simulation, 9:
297-300, 2008.
[27] Y-N Zhanga, Fei Xu and Ling-ling Deng. Exact solution for nonlinear Schrodinger
equation by He's frequency formulation. Comput. Math. Appl., 58: 2449-2451, 2009.

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