Computing Greeks by Finite Difference using Monte Carlo Simulation and Variance Reduction Techniques



GIOVANI GRACIANTI(1*)

(1) Jurusan Matematika, Fakultas Sains dan Teknologi, Universitas Pelita Harapan
(*) Corresponding Author

Abstract


Makalah ini membahas penggunaan metode Monte Carlo untuk komputasi Greeks. Algoritma metode beda hingga untuk memperkirakan Greeks menggunakan teknik simulasi Monte Carlo dan teknik reduksi varians (yaitu nomor acak umum dan varians antitetis) disajikan. Model Black-Scholes digunakan sebagai model acuan untuk menganalisa dan menguji metode numerik. Hal ini menunjukkan bahwa jumlah simulasi mempengaruhi kinerja yang paling banyak, dan ada beberapa teknik untuk mengurangi kesalahan. Dalam kasus options dengan payoff diskontinu, metode ini tidak berjalan dengan baik saat waktu sekarang mendekati waktu jatuh tempo.

Kata kunci: Options, Greeks, Metode Monte Carlo, Metode Beda Hingga, dan Model Black-Scholes


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References

Asmussen, S. and Glynn P.W., 2007, Stochastic Simulation, Springer-Verlag, New York.

Atanassov, E. and Dimov, I. T., 2008, What Monte Carlo Models Can Do and Cannot Do Efficiently?, Applied mathematical Modelling 32, 1477-1500.

Bjork, T., 2003, Arbitrage Theory in Continuous Time, 2nd edition, Oxford University Press, Stockholm.

Black, F. and Scholes, M., 1973, The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81(3), 637-654.

Boyle, P., 1977, Options: A Monte Carlo Approach, Journal of Financial Economics 4, 323-338.

Boyle, P., Broadie, M., and Glasserman, P., 1997, Monte Carlo Methods for Security Pricing, Journal of Economic Dynamics and Control 21, 1267-1321.

Broadie, M., and Glasserman, P., 1996, Estimating Security Price Derivatives Using

David D. and Privault, N., 2009, Numerical Computation of Theta in a Jump Diffusion Model by Integration by Parts, Quantitative Finance 9(6), 727-735.

Fournié, E., Lasry, J.-M., Lebuchoux, J., Lions, P. -L., and Touzi, N., 1999, Applications of Malliavin Calculus to Monte Carlo Methods in Finance, Finance Stochast. 3, 391-412.

Giles, M., 2007, Monte Carlo Evaluation of Sensitivities in Computational Finance, Report no. 07/12, Oxford University Computing Laboratory.

Glasserman, P. and Yao, D.D., 1992, Some Guidelines and Guarantees for Common Random Numbers, Management Science 38(6), 884-908.

Glasserman, P., 2004, Monte Carlo Methods in Financial Engineering, Springer-Verlag New York, Inc.

Glynn, P.W., 1989, Optimization of stochastic systems via simulation, Proceedings of the 1989 Winter Simulation Conference, 90-105.

Haug, E.G., 1997, The Complete Guide to Option Pricing Formulas, McGraw-Hill.

Heston, S.L., 1993, A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, The Review of Financial Studies 6(2), 327-343.

Higham, D. J., 2004, An Introduction to Financial Option Valuation, Cambridge University Press.

Hull, J.C., 2012, Options, Futures and Other Derivatives, 8th edition, Prentice Hall.

Karatzas, I., Shreve, S., 1998, Brownian Motion and Stochastic Calculus, Springer Verlag, New York.

Klebaner, F.C., 2005, Introduction to Stochastic Calculus with Applications, 2nd edition, Imperial College Press London.

Kloden, P., Platen, E., 1992, Numerical Solution of Stochastic Differential Equations, Springer-Verlag.

Kwok, Y.K., 1998, Mathematical Models of Financial Derivatives, Springer.

Lyuu, Y.D. and Teng, H.W., 2011, Unbiased and Effcient Greeks of Financial Options, Finance Stoch. 15, 141-181.

Lyuu, Y.D., 2001, Financial Engineering and Computation: Principles, Mathematics, Algorithms, Cambridge University Press.

Mao, X., 1997, Stochastic Differential Equations and their Applications, Horwood, Chicester.

Markowitz, H., 1952, Portfolio Selection, Journal of Finance 7(1), 77-91.

Matsumoto, M. and Nishimura, T., 1998, Mersenne Twister: a 623-dimensionally Equidistributed Uniform Pseudo-random Number Generator, ACM Transactions on Modeling and Computer Simulation 8(1), 3-30.

McLeish, D.L., 2005, Monte Carlo Simulation and Finance, Wiley.

Miller, I. and Miller, M., John E. Freund's Mathematical Statistics with Applications, 7th edition, Pearson Prentice Hall, 2004.

Milstein, G. N. and Tretyakov, M.V., 2004, Stochastic Numerics for Mathematical Physics, Springer.

Milstein, G. N. and Tretyakov, M.V., 2005, Numerical analysis of Monte Carlo Evaluation of Greeks by Finite Differences, The Journal of Computational Finance 8(3).

Milstein, G. N., and Schoenmakers, J. G. M., 2002, Numerical Construction of a Hedging Strategy Against the Multi-asset European Claim, Stochastics and Stochastics Reports 73, 125-57.

Rubinstein, R.Y. and Kroese, D.P. , 2008, Simulation and the Monte Carlo method, Wiley.

Simulation, Management Science 42(2).

Van Rossum G., 1995, Python tutorial, Technical Report CS-R9526, Centrum voor Wiskunde en Informatica (CWI), Amsterdam.



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