The impact of Kiyoshi Itô´s stochastic calculus of financial economics
The impact of Kiyoshi Itô´s stochastic calculus of financial economics
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Ruge-Leiva, D.I. 2016. The impact of Kiyoshi Itô´s stochastic calculus of financial economics. ODEON. 10 (oct. 2016), 157–184. DOI:https://doi.org/10.18601/17941113.n10.07.
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We discuss the direct or indirect incorporation into financial economics of Kiyoshi Itô´s work on stochastic calculus, particularly the Itô formula, the relevance of his findings for option pricing theory and the way his work has been used to find a unique option pricing function in a competitive and non-arbitrage market. On that basis, we discuss how the option pricing theory may be linked with the general equilibrium theory and other aspects of conventional economics, and finally, Itô’s role in econophysics.
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Referencias (VER)
Baldwin, R., and Krugman, P. R. (1986). Persistent Trade Effects of Large
Exchange Rate Shocks. Quarterly Journal of Economics, 104, 635-54.
Bansal, V., Herbst, A., Marshall, J. and Tucker, A. (1992). Hedging Business Cycle Risk with Macro Swaps and Options. Journal of Applied
Corporate Finance, 4, 103-108.
Bansal, V., Marshall, J. and Yuyunyongwatana, R. (1994). Hedging Business Cycle Risk with Macro Economic Swaps: Some Preliminary Evidence. Journal of Derivatives, 1, 50-58.
Bansal, V., Marshall, J., and Yuyunyongwatana, R. (1995). Macroeconomic
Derivatives More Viable Than First Thought. Global Finance, 8, 101- 110.
Bick, A. (1982). Comments on the Valuation of Derivative Assets. Journal of Financial Economics, 10(3), 331-345.
Black, F., and Scholes, M. (1973). The Pricing of Options and Corporate
Liabilities. The Journal of Political Economy, 637-654.
Bodie, Z., Merton, R. C., and Samuelson, W. F. (1992). Labor Supply
Flexibility and Portfolio Choice in a Life Cycle Model. Journal of
Economic Dynamics and Control, 16(3), 427-449.
Bouchaud, J. P., Mézard, M., and Potters, M. (2002). Statistical Properties of Stock Order Books: Empirical Results and Models. Quantitative
Finance, 2(4), 251-256.
Borensztein, E., and Pennacchi, G. (1990). Valuation of Interest Payment
Guarantees on Developing Country Debt. Staff Papers-International
Monetary Fund, 806-824.
Breeden, D. T., and Litzenberger, R. H. (1978). Prices of State-Contingent
Claims Implicit in Option Prices. Journal of Business, 621-651.
Cherian, J. A., and Perotti, E. (2001). Option pricing and foreign investment under political risk. Journal of International Economics, 55(2), 359-377.
Clauset, A., Shalizi, C. R., and Newman, M. E. (2009). Power-Law
Distributions in Empirical Data. SIAM review, 51(4), 661-703.
Comte, A. (1856). Social Physics: from the Positive Philosophy. New York:
Calvin Blanchard.
Daniel, G., and Sornette, D. (2010). Econophysics: Historical Perspectives. In C. Rama (ed.). Encyclopedia of Quantitative Finance. London: Wiley.
Dixit, A. (1989). Hysteresis, Import Penetration, and Exchange-Rate Pass-
Through. Quarterly Journal of Economics, 104, 205-228.
Dixit, A. (1992). Investment and Hysteresis. Journal of Economic Perspectives, 6, 107-132.
Dothan, U., and Williams, J. (1981). Education as an Option. Journal of
Business, 117-139.
Duffie, D. (2010). Dynamic Asset Pricing Theory. Princeton University Press.
Fischer, S. (1978). Call Option Pricing When the Exercise Price is Uncertain, and the Valuation of Index Bonds. The Journal of Finance, 33(1), 169- 176.
Gabaix, X. (2009). Power Laws in Economics and Finance. Annual Review of Economics, 1, 255-293.
Gabaix, X., and Ibragimov, R. (2011). Rank − 1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents. Journal of Business and
Economic Statistics, 29(1), 24-39.
Garman, M. and Kohlhagen, S. (1980). Inflation and Foreign-Exchange Rates Under Production and Monetary Uncertainty. Journal of Financial and Quantitative Analysis, 15, 949-967.
Gennotte, G., and Pyle, D. (1991). Capital Controls and Bank Risk. Journal of Banking and Finance, 15(4), 805-824.
Gibbons, R., and Murphy, K. J. (1990). Relative Performance Evaluation for Chief Executive Officers. Industrial and Labor Relations Review, 43(3),
30S-51S.
Itô, K. (1942). On Stochastic Processes (Infinitely Divisible Laws of
Probability). Japanese Journal of Mathematics, 261-301.
Itô, K. (1944). Stochastic Integral. Proceedings of the Imperial Academy, 20(8), 519-524.
Itô, K. (1950). Stochastic Differential Equations in a Differentiable Manifold. Nagoya Mathematical Journal, 1, 35-47.
Itô, K. (1989). Special Lecture – History of Probability. Bulletin of the Institute of Actuaries of Japan, 42, in Japanese.
Itô, K. (2010). Probability and I. Iwanami Shoten Publishers, 87, in Japanese.
Jarrow, R. A. (1999). In Honor of the Nobel Laureates Robert C. Merton and Myron S. Scholes: A Partial Differential Equation that Changed the
World. The Journal of Economic Perspectives, 13(4), 229-248.
Jovanovic, F., and Schinckus, C. (2013). The Emergence of Econophysics: A New Approach in Modern Financial Theory. History of Political
Economy, 45(3), 443-474.
Jovanovic, F., and Schinckus, C. (2016). Breaking Down the Barriers between Econophysics and Financial Economics. International Review of
Financial Analysis.
Kishimoto, M. (2008). On the Black-Scholes Equation: Various derivations.
Kunita, H. (2010). Itô’s Stochastic Calculus: Its Surprising Power for
Applications. Stochastic Processes and their Applications, 120(5), 622-
652.
Lesne, A., and Laguës, M. (2012). Scale Invariance: From Phase Transitions to Turbulence. Springer Science and Business Media.
Lim, T., Lo, A. W., Merton, R. C., and Scholes, M. S. (2006). The Derivatives Sourcebook. Now Publishers Inc.
Lux, T. (2009). Applications of Statistical Physics in Finance and Economics. In B. Rosser (ed.). Handbook of Research on Complexity. Edward Elgar, Cheltenham. p. 213-258.
Mantegna, R. N., and Stanley, H. E. (1999). Introduction to Econophysics:
Correlations and Complexity in Finance. Cambridge: Cambridge
University Press.
McCauley, J. L. (2009). ARCH and GARCH Models vs. Martingale Volatility
of Finance Market Returns. International Review of Financial Analysis, 18(4), 151-153.
McCauley, J. L., Gunaratne, G. H., and Bassler, K. E. (2007). Martingale
Option Pricing. Physica A: Statistical Mechanics and its Applications, 380, 351-356.
Merton, R. C. (1973). Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science, 141-183.
Merton, R. C. (1974). On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. The Journal of Finance, 29(2), 449-470.
Merton, R. C. (1976). Option Pricing when Underlying Stock Returns Are
Discontinuous. Journal of Financial Economics, 3(1-2), 125-144.
Merton, R. C. (1992). Continuous-Time Finance. Cambridge, MA.: Blackwell.
Merton, R. C. (1998). Applications of Option-Pricing Theory: Twenty-Five
Years Later. American Economic Review, 88(3), 323-349.
Mitzenmacher, M. (2005). Editorial: The Future of Power Law Research.
Internet Mathematics, 2(4), 525-534.
Noe, T. H. (1988). Capital Structure and Signaling Game Equilibria. Review of Financial Studies, 1(4), 331-355.
Oksendal, B. (2013). Stochastic Differential Equations: An Introduction with Applications. Springer Science and Business Media.
Pesaran, M. H., and Potter, S. M. (eds.) (1993). Nonlinear Dynamics, Chaos, and Econometrics. New York: Wiley.
Potters, M., and Bouchaud, J. P. (2003). More Statistical Properties of Order Books and Price Impact. Physica A: Statistical Mechanics and its
Applications, 324(1), 133-140.
Reagan, P. and Stulz, R. (1989). Contracts, Delivery Lags, and Currency Risks. Journal of International Money and Finance, 8, 89-103.
Reagan, P., and Stulz, R. M. (1993). Contracting Costs, Inflation, and Relative Price Variability. Journal of Money, Credit and Banking, 25(3),
Richmond, P., Mimkes, J., and Hutzler, S. (2013). Econophysics and Physical Economics. Oxford: Oxford University Press.
Rickles, D. (2008). Econophysics and the Complexity of the Financial Markets. In: J. Collier and C. Hooker (eds.). Handbook of the Philosophy of Science, vol. 10: Philosophy of Complex Systems. New York: North
Holland Elsevier Editions.
Ross, S. A. (1976). Options and Efficiency. The Quarterly Journal of
Economics, 75-89.
Săvoiu, G. G., and Andronache, C. (2013). The Potential of Econophysics for the Study of Economic Processes. In G. G. Săvoiu (ed.). Econophysics:
Background and Applications in Economics, Finance, and Sociophysics
(91-113). Oxford (UK): Academic Press.
Sercu, P. (1992). Exchange Risk, Exposure, and the Option to Trade. Journal of International Money and Finance, 11, 579-593.
Sercu, P. and Vanhulle, C. (1992). Exchange-Rate Volatility, International-
Trade, and the Value of Exporting Firms. Journal of Banking and
Finance, 16, 155-182.
Sornette, D. (2014). Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models. Reports on Progress in Physics, 77(6), 062001-062028.
Weston, P. J. (1996). Defence Research and Development: Encouraging Private Venture R&D with ‘Option’ Strategies. Defence and Peace
Economics,7(4), 313-324.
Yamano, T. (2015). The First Namer of Econophysics and Immanent
Constraints. Research Gate.
Exchange Rate Shocks. Quarterly Journal of Economics, 104, 635-54.
Bansal, V., Herbst, A., Marshall, J. and Tucker, A. (1992). Hedging Business Cycle Risk with Macro Swaps and Options. Journal of Applied
Corporate Finance, 4, 103-108.
Bansal, V., Marshall, J. and Yuyunyongwatana, R. (1994). Hedging Business Cycle Risk with Macro Economic Swaps: Some Preliminary Evidence. Journal of Derivatives, 1, 50-58.
Bansal, V., Marshall, J., and Yuyunyongwatana, R. (1995). Macroeconomic
Derivatives More Viable Than First Thought. Global Finance, 8, 101- 110.
Bick, A. (1982). Comments on the Valuation of Derivative Assets. Journal of Financial Economics, 10(3), 331-345.
Black, F., and Scholes, M. (1973). The Pricing of Options and Corporate
Liabilities. The Journal of Political Economy, 637-654.
Bodie, Z., Merton, R. C., and Samuelson, W. F. (1992). Labor Supply
Flexibility and Portfolio Choice in a Life Cycle Model. Journal of
Economic Dynamics and Control, 16(3), 427-449.
Bouchaud, J. P., Mézard, M., and Potters, M. (2002). Statistical Properties of Stock Order Books: Empirical Results and Models. Quantitative
Finance, 2(4), 251-256.
Borensztein, E., and Pennacchi, G. (1990). Valuation of Interest Payment
Guarantees on Developing Country Debt. Staff Papers-International
Monetary Fund, 806-824.
Breeden, D. T., and Litzenberger, R. H. (1978). Prices of State-Contingent
Claims Implicit in Option Prices. Journal of Business, 621-651.
Cherian, J. A., and Perotti, E. (2001). Option pricing and foreign investment under political risk. Journal of International Economics, 55(2), 359-377.
Clauset, A., Shalizi, C. R., and Newman, M. E. (2009). Power-Law
Distributions in Empirical Data. SIAM review, 51(4), 661-703.
Comte, A. (1856). Social Physics: from the Positive Philosophy. New York:
Calvin Blanchard.
Daniel, G., and Sornette, D. (2010). Econophysics: Historical Perspectives. In C. Rama (ed.). Encyclopedia of Quantitative Finance. London: Wiley.
Dixit, A. (1989). Hysteresis, Import Penetration, and Exchange-Rate Pass-
Through. Quarterly Journal of Economics, 104, 205-228.
Dixit, A. (1992). Investment and Hysteresis. Journal of Economic Perspectives, 6, 107-132.
Dothan, U., and Williams, J. (1981). Education as an Option. Journal of
Business, 117-139.
Duffie, D. (2010). Dynamic Asset Pricing Theory. Princeton University Press.
Fischer, S. (1978). Call Option Pricing When the Exercise Price is Uncertain, and the Valuation of Index Bonds. The Journal of Finance, 33(1), 169- 176.
Gabaix, X. (2009). Power Laws in Economics and Finance. Annual Review of Economics, 1, 255-293.
Gabaix, X., and Ibragimov, R. (2011). Rank − 1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents. Journal of Business and
Economic Statistics, 29(1), 24-39.
Garman, M. and Kohlhagen, S. (1980). Inflation and Foreign-Exchange Rates Under Production and Monetary Uncertainty. Journal of Financial and Quantitative Analysis, 15, 949-967.
Gennotte, G., and Pyle, D. (1991). Capital Controls and Bank Risk. Journal of Banking and Finance, 15(4), 805-824.
Gibbons, R., and Murphy, K. J. (1990). Relative Performance Evaluation for Chief Executive Officers. Industrial and Labor Relations Review, 43(3),
30S-51S.
Itô, K. (1942). On Stochastic Processes (Infinitely Divisible Laws of
Probability). Japanese Journal of Mathematics, 261-301.
Itô, K. (1944). Stochastic Integral. Proceedings of the Imperial Academy, 20(8), 519-524.
Itô, K. (1950). Stochastic Differential Equations in a Differentiable Manifold. Nagoya Mathematical Journal, 1, 35-47.
Itô, K. (1989). Special Lecture – History of Probability. Bulletin of the Institute of Actuaries of Japan, 42, in Japanese.
Itô, K. (2010). Probability and I. Iwanami Shoten Publishers, 87, in Japanese.
Jarrow, R. A. (1999). In Honor of the Nobel Laureates Robert C. Merton and Myron S. Scholes: A Partial Differential Equation that Changed the
World. The Journal of Economic Perspectives, 13(4), 229-248.
Jovanovic, F., and Schinckus, C. (2013). The Emergence of Econophysics: A New Approach in Modern Financial Theory. History of Political
Economy, 45(3), 443-474.
Jovanovic, F., and Schinckus, C. (2016). Breaking Down the Barriers between Econophysics and Financial Economics. International Review of
Financial Analysis.
Kishimoto, M. (2008). On the Black-Scholes Equation: Various derivations.
Kunita, H. (2010). Itô’s Stochastic Calculus: Its Surprising Power for
Applications. Stochastic Processes and their Applications, 120(5), 622-
652.
Lesne, A., and Laguës, M. (2012). Scale Invariance: From Phase Transitions to Turbulence. Springer Science and Business Media.
Lim, T., Lo, A. W., Merton, R. C., and Scholes, M. S. (2006). The Derivatives Sourcebook. Now Publishers Inc.
Lux, T. (2009). Applications of Statistical Physics in Finance and Economics. In B. Rosser (ed.). Handbook of Research on Complexity. Edward Elgar, Cheltenham. p. 213-258.
Mantegna, R. N., and Stanley, H. E. (1999). Introduction to Econophysics:
Correlations and Complexity in Finance. Cambridge: Cambridge
University Press.
McCauley, J. L. (2009). ARCH and GARCH Models vs. Martingale Volatility
of Finance Market Returns. International Review of Financial Analysis, 18(4), 151-153.
McCauley, J. L., Gunaratne, G. H., and Bassler, K. E. (2007). Martingale
Option Pricing. Physica A: Statistical Mechanics and its Applications, 380, 351-356.
Merton, R. C. (1973). Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science, 141-183.
Merton, R. C. (1974). On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. The Journal of Finance, 29(2), 449-470.
Merton, R. C. (1976). Option Pricing when Underlying Stock Returns Are
Discontinuous. Journal of Financial Economics, 3(1-2), 125-144.
Merton, R. C. (1992). Continuous-Time Finance. Cambridge, MA.: Blackwell.
Merton, R. C. (1998). Applications of Option-Pricing Theory: Twenty-Five
Years Later. American Economic Review, 88(3), 323-349.
Mitzenmacher, M. (2005). Editorial: The Future of Power Law Research.
Internet Mathematics, 2(4), 525-534.
Noe, T. H. (1988). Capital Structure and Signaling Game Equilibria. Review of Financial Studies, 1(4), 331-355.
Oksendal, B. (2013). Stochastic Differential Equations: An Introduction with Applications. Springer Science and Business Media.
Pesaran, M. H., and Potter, S. M. (eds.) (1993). Nonlinear Dynamics, Chaos, and Econometrics. New York: Wiley.
Potters, M., and Bouchaud, J. P. (2003). More Statistical Properties of Order Books and Price Impact. Physica A: Statistical Mechanics and its
Applications, 324(1), 133-140.
Reagan, P. and Stulz, R. (1989). Contracts, Delivery Lags, and Currency Risks. Journal of International Money and Finance, 8, 89-103.
Reagan, P., and Stulz, R. M. (1993). Contracting Costs, Inflation, and Relative Price Variability. Journal of Money, Credit and Banking, 25(3),
Richmond, P., Mimkes, J., and Hutzler, S. (2013). Econophysics and Physical Economics. Oxford: Oxford University Press.
Rickles, D. (2008). Econophysics and the Complexity of the Financial Markets. In: J. Collier and C. Hooker (eds.). Handbook of the Philosophy of Science, vol. 10: Philosophy of Complex Systems. New York: North
Holland Elsevier Editions.
Ross, S. A. (1976). Options and Efficiency. The Quarterly Journal of
Economics, 75-89.
Săvoiu, G. G., and Andronache, C. (2013). The Potential of Econophysics for the Study of Economic Processes. In G. G. Săvoiu (ed.). Econophysics:
Background and Applications in Economics, Finance, and Sociophysics
(91-113). Oxford (UK): Academic Press.
Sercu, P. (1992). Exchange Risk, Exposure, and the Option to Trade. Journal of International Money and Finance, 11, 579-593.
Sercu, P. and Vanhulle, C. (1992). Exchange-Rate Volatility, International-
Trade, and the Value of Exporting Firms. Journal of Banking and
Finance, 16, 155-182.
Sornette, D. (2014). Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models. Reports on Progress in Physics, 77(6), 062001-062028.
Weston, P. J. (1996). Defence Research and Development: Encouraging Private Venture R&D with ‘Option’ Strategies. Defence and Peace
Economics,7(4), 313-324.
Yamano, T. (2015). The First Namer of Econophysics and Immanent
Constraints. Research Gate.
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