Abstract
The introduction of financial derivatives such as futures and options on underlying as stock, currencies, interest rate etc. makes possible to decreasing of financial risks. The basic idea of a financial derivative production: to find participants in the market who are willing to share the risks and profits of future developments in the market which are subject to uncertainty. The pricing of these financial enstruments is based on an advenced mathematical theory, called Ito stochastics calculus. The basic model for a random price processes is described by Brownian motion and releted differential equations. An analitical formula for pricing of European call option was given by Black - Scholes (1973) and Merton (1973). Their approach has become the firm basis for modern financial mathematics which uses advenced tools such as martingale theory, Ito calculus and stochastics control, to find adequate solutions to the pricing of derivative securities.
Keywords
Financial Derivatives Brownian Motion Black-Scholes Formula Option Ito Stochastic Analysis Change of Measure Girsanov Transformation Martingale Equvalent Martingale Measure Arbitrage Interest Rate Semimartingale Models
References
- BACHELIER, L. (1900), Theorie de la Speculation, Ann. Sci. Ecole Norm. Sup. III- 17, 21-86, Translated in: COOTNER P. H. (Ed.) (1964). The Random Character of Stock Market Prices p.p. 17-78. MIT Press, Cambridge, Mass.
- BAXTER, M. and RENNİE, A. (1996), Financial Calculus; An Introduction to Derivative Pricing, Cambridge University Press, Cambridge.
- BJÖRK, T. (1997), Interest Rate Theory, In: Brais, B. (Ed.) Financial Mathematics Lecture Notes in Math. 1656. p.p. 53-122, Springer, Berlin.
- BLACK, F. and SCHOLES, M. (1973), The Pricing of Options and Corporate Liabilities, J. Political Economics, 81, 384-404.
- BOLLERSLEV, T. CHOU, R. Y. and KRONER, K. F., (1992), ARCH Models in Finance: A Review of the Theory and Evidence, J. Econometric, 52, 5-59.
- EMBRECHTS, P., KLÜPPELBERG, C. and MIKOSCH, T. (1997), Modelling External Events for Insurance and Finance, Springer, Berlin.
- HARRISON, M.J. and PLISKA, S. R. (1981), Martingales and Stochastic Integrals in The Theory of Continuous Trading, Stoc. Proc. Appl., 11, 215-260.
- HEADH, D., JARROW, R. and MORTON, A. (1992), Bond Pricing and the Term Structure of Interest Rates; A New Methodology for Contingent Claims Valvation, Econometrica 60, 77-105.
- HULL, J. (1997), Options, Futures and Other Derivatives, 3rd Ed. Printice Hall, Englewood Cliffs.
- JACOD, J. and SHIRYAEV, A. N.(1987) Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin-Heidelberg.
- KARATZAS, I. and SHEREVE, S.E. (1998) Methods of Mathematical Finance, Springer, Newyork.
- MERTON, R.C. (1973), Theory of Rational Options Pricing, Bell J. Econ. Manag.Sci. 4, 141-183.
- PLISKA, S.R. (1997), Introduction to Mathematical Finance: Discrete Time Models, Blackwell, Malden (MA).
- ROGERS, L. C. G. and WILLIAMS.D. (2000), Diffusions, Markov Processes and Martigales: Foundations, Cambridge (UK).
- SAMUELSON, P.A. (1965), Rational Theory of Warrant Pricing, Industrial Management Rewiev, 6, 13-31.
- SHIMPI, P.A. (Ed.) (1999), Integrating Corporate Risk Management., Swiss Re Markets, Zurich.
- TAYLOR, S.J. (1986), Modelling Financial Time Series, Wiley, Chichester.
Abstract
Hisse senedi, döviz, faiz oranı, vb. gibi mallar üzerine futures ve options gibi finansal türevlerin oluşturulması, finansal risklerin düşürülmesine imkan vermektedir. Bir finansal türev oluşturmanın altında yatan temel fikir; belirsizliğin hakim olduğu piyasada gelecekteki gelişmelere bağlı olarak ortaya çıkacak, risk ve kazancı, paylaşmaya istekli piyasa katılımcılarını bulmaktır. Bu finansal enstrümanların fiyatlandırılması, ito stokastik analizi olarak adlandırılan bir teoriye dayanmaktadır. Rassal fiyat süreci için temel model Brownian hareket ve onunla ilişkili diferansiyel denklemlerle tanımlanmaktadır. Avrupa alım opsiyonunun fiyatlandırılması için Black-Scholes (1973) ve Merton (11973) tarafından bir analitik formül verilmiştir. Onların yaklaşımı, türev menkul kıymetlerin fiyatlanmasına uygun çözümler bulmak için martingale teori, ito analizi ve stokastik kontrol gibi ileri düzeydeki araçları kullanan, modern finansal matematik için sağlam bir zemin oluşturulmuştur.
Keywords
Finansal Türev Brownian Hareket Black-Scholes Formülü Opsiyon Ito Stokastik Analizi Ölçümün Değişimi Girsinov Dönüşümü Martingale Denk Martingale Ölçümü Arbitraj Faiz Oranı Semimartingale Modelleri
References
- BACHELIER, L. (1900), Theorie de la Speculation, Ann. Sci. Ecole Norm. Sup. III- 17, 21-86, Translated in: COOTNER P. H. (Ed.) (1964). The Random Character of Stock Market Prices p.p. 17-78. MIT Press, Cambridge, Mass.
- BAXTER, M. and RENNİE, A. (1996), Financial Calculus; An Introduction to Derivative Pricing, Cambridge University Press, Cambridge.
- BJÖRK, T. (1997), Interest Rate Theory, In: Brais, B. (Ed.) Financial Mathematics Lecture Notes in Math. 1656. p.p. 53-122, Springer, Berlin.
- BLACK, F. and SCHOLES, M. (1973), The Pricing of Options and Corporate Liabilities, J. Political Economics, 81, 384-404.
- BOLLERSLEV, T. CHOU, R. Y. and KRONER, K. F., (1992), ARCH Models in Finance: A Review of the Theory and Evidence, J. Econometric, 52, 5-59.
- EMBRECHTS, P., KLÜPPELBERG, C. and MIKOSCH, T. (1997), Modelling External Events for Insurance and Finance, Springer, Berlin.
- HARRISON, M.J. and PLISKA, S. R. (1981), Martingales and Stochastic Integrals in The Theory of Continuous Trading, Stoc. Proc. Appl., 11, 215-260.
- HEADH, D., JARROW, R. and MORTON, A. (1992), Bond Pricing and the Term Structure of Interest Rates; A New Methodology for Contingent Claims Valvation, Econometrica 60, 77-105.
- HULL, J. (1997), Options, Futures and Other Derivatives, 3rd Ed. Printice Hall, Englewood Cliffs.
- JACOD, J. and SHIRYAEV, A. N.(1987) Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin-Heidelberg.
- KARATZAS, I. and SHEREVE, S.E. (1998) Methods of Mathematical Finance, Springer, Newyork.
- MERTON, R.C. (1973), Theory of Rational Options Pricing, Bell J. Econ. Manag.Sci. 4, 141-183.
- PLISKA, S.R. (1997), Introduction to Mathematical Finance: Discrete Time Models, Blackwell, Malden (MA).
- ROGERS, L. C. G. and WILLIAMS.D. (2000), Diffusions, Markov Processes and Martigales: Foundations, Cambridge (UK).
- SAMUELSON, P.A. (1965), Rational Theory of Warrant Pricing, Industrial Management Rewiev, 6, 13-31.
- SHIMPI, P.A. (Ed.) (1999), Integrating Corporate Risk Management., Swiss Re Markets, Zurich.
- TAYLOR, S.J. (1986), Modelling Financial Time Series, Wiley, Chichester.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Applied Macroeconometrics |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | April 15, 2002 |
| Published in Issue | Year 2002 Volume: 1 Issue: 1 |
