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Stochastic modeling of stock price process induced from the conjugate heat equation

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  • Paeng, Seong-Hun

Abstract

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black–Scholes equation in light of inflation and exchange rate.

Suggested Citation

  • Paeng, Seong-Hun, 2015. "Stochastic modeling of stock price process induced from the conjugate heat equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 385-394.
    • Handle: RePEc:eee:phsmap:v:419:y:2015:i:c:p:385-394
    DOI: 10.1016/j.physa.2014.09.021
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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