Parameter Estimation of Local Volatility in Currency Option Valuation

S. O. Edeki; M. E. Adeosun; E. A. Owoloko; G. O. Akinlabi; I. Adinya

doi:10.15866/iremos.v9i2.8161

Parameter Estimation of Local Volatility in Currency Option Valuation

S. O. Edeki^(1*), M. E. Adeosun⁽²⁾, E. A. Owoloko⁽³⁾, G. O. Akinlabi⁽⁴⁾, I. Adinya⁽⁵⁾

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DOI: https://doi.org/10.15866/iremos.v9i2.8161

Abstract

In quantitative finance and option pricing, one of the basic determinants of option prices is the volatility of the underlying asset. In this paper, we therefore, present a concise study of volatility in option pricing in the sense of Dupire’s approach. Thereafter, we outspread such study via the application of Ito formula to the modelling and valuation of currency option with local volatility. For the purpose of efficiency, we use the daily historical prices of stock-S&P 500 for a certain period to estimate the corresponding historical volatility. Graphical representation of the analysed daily historical data of stock prices with respect to a local volatility is presented.
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Keywords

Currency Option Valuation; Local Volatility; Implied Volatility; Stochastic Model

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References

S. Mitra. A review of volatility and option pricing (2009), submitted to Elsevier, http://arxiv.org/pdf/0904.1292.pdf.

S.J. Taylor. Stochastic Volatility Modeling, (2008), https://phps.portals.mbs.ac.uk

O.O. Ugbebor and S.O. Edeki. On Duality Principle in Exponentially Levy Market, Journal of Applied Mathematics and Bioinformatics (JAMB), (2013), 3 (2), 159-170.

S.O. Edeki, I. Adinya and O.O. Ugbebor. The Effect of Stochastic Capital Reserve on Actuarial Risk Analysis via an Integro-differential Equation, IAENG International Journal of Applied Mathematics, (2014), 44 (2), 83-90.

M.E. Adeosun, S.O. Edeki, and O.O. Ugbebor. Stochastic Analysis of Stock Market Price Models: A Case Study of the Nigerian Stock Exchange (NSE), WSEAS Transactions on Mathematics, (2015), 14, 353-363.

S.O. Edeki, O.O. Ugbebor, E.A. Owoloko, “On a Dividend-Paying Stock Options Pricing Model (SOPM) Using Constant Elasticity of Variance Stochastic Dynamics”, International Journal of Pure and Applied Mathematics, 106 (4), (2016): 1029-1036.
http://dx.doi.org/10.12732/ijpam.v106i4.5

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 Differential Transformation Method, Entropy, (2015), 17 (11), 7510-7521.
http://dx.doi.org/10.3390/e17117510

B. Dupire. Pricing with a Smile, Risk, (1994), 7, 18-20.

E. Derman, and I. Kani. Riding on a Smile. Risk, (1994), 7 (2), 139-145.

M.H.A. Davis. The Dupire Formula. Finite Difference Methods Course material, Imperial College London, (2011).

F. D. Rouah. Derivaton of Local Volatility. www.javaquant.net, (1998)

E. Derman, I. Kani and M. Kamal. Trading and Hedging Local Volatility, Goldman Sachs Quantitative Strategies Research Notes, (1996).

N.R. Parasurama, and J.P. Ramudu. Historical and implied volatility: An investigation into NSE NIFTY futures. Australian Journal of Business and Management Research, (2011), 1 (7), 112-120.

N.P.B Bollen, and E. Rasiel. The performance of alternative valuation models in the OTC currency options market, Journal of International Money and Finance, (2003), 22 (1), 33-64. ISSN 0261-5606.
http://dx.doi.org/10.1016/s0261-5606(02)00073-6

M. Higgins. Stochastic Spot/Volatility Correlation in Stochastic Volatility Models and Barrier Option Pricing (2014), http://arxiv.org/pdf/1404.4028.pdf.

K. Zhang, and S. Wang. A computational scheme for uncertain volatility model in option pricing, Applied Numerical Mathematics, (2009), 59 (8), 1754-1767.
http://dx.doi.org/10.1016/j.apnum.2009.01.004

C. J. Neely. Using implied volatility to measure uncertainty about interest rates, Federal reserve bank of St. Louis Review, May/June (2005), 87(3), 407-425.

H. Berestycki, J. Busca and I. Florent. Computing the Implied Volatility in Stochastic Volatility Models, Communications on Pure and Applied Mathematics, (2004), LVII, 1352-1373, Wiley periodicals, Inc.
http://dx.doi.org/10.1002/cpa.20039

R. Cont and J. da Fonsea. Dynamics of implied Volatility. Quantitative Finance (2002), 2, 45-60, Institute of physics publishing.
http://dx.doi.org/10.1088/1469-7688/2/1/304

R. W. Lee. Implied Volatility: Statics, Dynamics and Probability Interpretation In Recent Advances in Applied Probability, Springer (2004).
http://dx.doi.org/10.1007/0-387-23394-6_11

F. Black and M. Scholes. The pricing of options and corporate liability, J. Political Economy, (1973), 81, 637-659.
http://dx.doi.org/10.1086/260062

H. Ye. A Comparison of Local Volatility and Implied Volatility. Department of Mathematics Uppsala University (2011).

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