EFFICIENT FINANCIAL ENGINEERING SOLUTIONS IN OPTION PRICING
Keywords:
Quantitative Finance, computational methods, financial engineering solutions, derivatives pricing, option valuation, path-dependent options, exotics
Abstract
In this paper, together with the financial analysis in option pricing, we
make a short review of most popular and frequently used computational methods in
Quantitative Finance that could be used as a benchmark for obtaining highly accurate
numerical results. By classifying some of the most competitive methods in option pricing
according to their efficiency we try to introduce the notion of ‘efficient financial engineering
solution’ taking into account not only quantitative characteristics such as accuracy and real
time but also qualitative criteria and factors such as universality, complexity of computer
implementation and application, compatibility, understandability, and etc.
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Quantitative Methods: Advantages and Disadvantages, Trakia Journal of Sciences, Vol. 9,
Suppl. 2, 295-301, 2011, Proceedings of the Second International Scientific Conference
‘Business and Regional Development’, Faculty of Economics, Trakia University, Bulgaria,
,23-24 June 2011, ISSN 1313-7069 (print), ISSN 1313-3551 (online).
4. A. D. Andricopoulos, M. Widdicks, D. P. Newton, P. W. Duck, Extending
quadrature methods to value multi-asset and complex path dependent options, Journal of
Financial Economics, Vol. 83, Issue 2, February 2007, 471-499,
http://www.sciencedirect.com/science/article/pii/S0304405X06001620
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options, Applied Mathematical Finance, Vol. 5, 17 - 43, 1998.
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due to Discrete Dividends, Applied Mathematical Finance, Vol. 19, Issue 1, 37-58, 2012
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and accurate lattice for pricing derivatives under a jump-diffusion process, Applied
Mathematics and Computation, Vol. 217, Issue 7, 1 December 2010, 3174-3189, ISSN:
0096-3003,
http://www.sciencedirect.com/science/article/pii/S0096300310009148
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jump diffusion model, Operations Research Letters, Vol. 37, (3), 2009, 163–167,
http://www.sciencedirect.com/science/article/pii/S0167637709000364
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Barrier Options by a Markov Chain, Journal of Derivatives, Vol. 10, (n. 4), 9-31 (2003),
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.14.2335&rep=rep1&type=pdf
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http://www.wilmott.com/pdfs/071203_duffy.pdf
14. R. J. Elliott, T. K. Siu, L. Chan, Journal of Computational and Applied
Mathematics, On pricing barrier options with regime switching, 13 August 2013,
http://www.sciencedirect.com/science/article/pii/S0377042713003786
15. P. Glassermann, Monte Carlo Methods in Financial Engineering, Springer, New
York, 2004.
16. http://global-derivatives.com/index.php/pricing-models-othermenu-41
17. G. Cao, R. MacLeod, Pricing Exotic Barrier Options with Finite Differences
(2005), SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=989641
18. R. Company, L. Jódar, G. Rubio, R.J. Villanueva, Explicit solution of Black–
Scholes option pricing mathematical models with an impulsive payoff function,
Mathematical and Computer Modelling, Vol. 45, Issues 1–2, 2007, 80-92, ISSN: 0895-
7177, http://www.sciencedirect.com/science/article/pii/S0895717706001816
19. R. Company, A.L. González, L. Jódar, Numerical solution of modified Black–
Scholes equation pricing stock options with discrete dividend, Mathematical and Computer
Modelling, Vol. 44, Issues 11–12, 1058 – 1068, 2006, ISSN: 0895-7177,
http://www.sciencedirect.com/science/article/pii/S0895717706001300
20. R. Company, L. Jódar, J. Pintos, A numerical method for European Option
Pricing with transaction costs nonlinear equation, Math. and Comp. Modelling, Vol. 50, 5–
6, 2009, 910-920
http://www.sciencedirect.com/science/article/pii/S0895717709001538
21. R. Cont, P. Tankov, Financial Modeling with Jump Processes, 59Chapman &
Hall/CRC, 2004.
22. M. Costantino, C. Brebbia, Computational Finance And Its Applications II, WIT
Press, 2006, ISBN-10: 1845641744, ISBN-13: 978-1845641740.
23. M. Gaudenzi, A. Zanette, Pricing American Options with Discrete Dividends by
Binomial Trees, Decisions in Economics and Finance, Vol. 32, (2), 2009, 129 - 148,
Parisian options in:
http://hal.archives-ouvertes.fr/docs/00/72/19/58/PDF/RR-8033.pdf
24. A. Golbabai, D. Ahamadian, M. Milev, Radial Basis Functions with Application to
Finance: American Put Option under Jump Diffusion, Mathematical and Computer
Modelling, Vol. 55 (n.3-4) (2012), 1354-1362, 2012, doi:10.1016/j.mcm.2011.10.014,
http://www.sciencedirect.com/science/article/pii/S0895717711006066, ISSN: 0895-7177.
25. A. Golbabai, L. V. Ballestra, D. Ahmadian, A Highly Accurate Finite Element
Method to Price Discrete Double Barrier Options, Computational Economics, DOI
10.1007/s10614-013-9388-5, 2013
http://link.springer.com/article/10.1007%2Fs10614-013-9388-5
26. M. Gradock, D. Health, E. Platen, Numerical inversion of Laplace transforms: a
survey of techniques with application of derivative pricing,
http://www.risk.net/digital_assets/4436/v4n1a3b.pdf
27. D. Higham, An Introduction to Financial Option Valuation, Cambridge University
Press, 2004.
28. M. S. Joshi, C++ Design Patterns and Derivative Pricing, Cambridge University
Press, United Kingdom, 2004, ISBN: 0521832357.
29. N. Hilber, O. Reichmann, C. Schwab, C. Winter, Computational Methods for
Quantitative Finance: Finite Element Methods for Derivative Pricing, Springer Finance,
2013, ISBN-10: 3642354009, ISBN-13: 978-3642354007.
30. S. Howison, Barrier options in the Black-Scholes framework,
http://people.maths.ox.ac.uk/howison/barriers.pdf
31. J. C. Hull: Options, Futures & Other Derivatives with DerivaGem CD (8th
Edition), Prentice Hall, 12 February, 2011.
32. D. Jun, Continuity correction for discrete barrier options with two barriers,
Journal of Computational and Applied Mathematics, Vol. 237, Issue 1, 1 January 2013,
520-528
http://www.sciencedirect.com/science/article/pii/S0377042712002567
33. R. Kangro, R. Nicolaides, Far field boundary conditions for Black-Scholes
equations, SIAM Journal. on Numerical Analysis, 38 (4), 1357 – 1368, 2000.
34. J. Kienitz, D. Wetterau, Financial Modelling: Theory, Implementation and
Practice with MATLAB Source, The Wiley Finance Series, Wiley; 1 edition, 1 March 2013,
ISBN-10: 9780470744895, ISBN-13: 978-0470744895.
35. P. Kohl-Landgraf, PDE Valuation of Interest Rate Derivatives, 2007, ISBN-10:
3833495375, ISBN-13: 978-3833495373.
36. M. N. Koleva, L. G. Vulkov, A Splitting Numerical Scheme for Non-Linear
Models of Mathematical Finance, Lecture Notes in Computer Science, accepted 2013
37. M. N. Koleva, Positivity-preserving Numerical Method for Non-linear BlackScholes models, Lecture Notes in Computer Science, accepted 2013
38. Y. K. Kwok, Mathematical Models of Financial Derivatives, Springer-Verlag,
Heidelberg, 1998.
39. E. Larsson, K. Ahlander, A. Hall, Multi-dimensional option pricing using radial
basis functions and the generalized Fourier transform, Journal of Computational and
Applied Mathematics, Vol. 222, Issue 1, 175–192, 2008,
http://www.sciencedirect.com/science/article/pii/S0377042707005560
40. G. Levy, Computational Finance: Numerical Methods for Pricing Financial
Instruments, Butterworth-Heinemann, 2004, ISBN-10: 0750657227, ISBN-13: 978-
0750657228.
41. I-Liang Chern, Lecture Notes of Financial Mathematics, Department of
Mathematics, http://scicomp.math.ntu.edu.tw/wiki/images/e/ec/Finance.pdf, National
Taiwan University, http://scicomp.math.ntu.edu.tw/wiki/index.php/Courses.
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Published
2023-02-03
How to Cite
Milev, M., Marchev, Jr., A., Кабаиванов, С., Ilieva, I., Dobreva, M., & Markovska, V. (2023). EFFICIENT FINANCIAL ENGINEERING SOLUTIONS IN OPTION PRICING. Vanguard Scientific Instruments in Management, 7(7). Retrieved from https://vsim-journal.info/index.php?journal=vsim&page=article&op=view&path[]=421
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