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Investment timing under hybrid stochastic and local volatility

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  • Kim, Jeong-Hoon
  • Lee, Min-Ku
  • Sohn, So Young

Abstract

We consider an investment timing problem under a real option model where the instantaneous volatility of the project value is given by a combination of a hidden stochastic process and the project value itself. The stochastic volatility part is given by a function of a fast mean-reverting process as well as a slowly varying process and the local volatility part is a power (the elasticity parameter) of the project value itself. The elasticity parameter controls directly the correlation between the project value and the volatility. Knowing that the project value represents the market price of a real asset in many applications and the value of the elasticity parameter depends on the asset, the elasticity parameter should be treated with caution for investment decision problems. Based on the hybrid structure of volatility, we investigate the simultaneous impact of the elasticity and the stochastic volatility on the real option value as well as the investment threshold.

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  • Kim, Jeong-Hoon & Lee, Min-Ku & Sohn, So Young, 2014. "Investment timing under hybrid stochastic and local volatility," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 58-72.
    • Handle: RePEc:eee:chsofr:v:67:y:2014:i:c:p:58-72
    DOI: 10.1016/j.chaos.2014.06.007
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    1. Patel, Kanak & Sing, Tien Foo, 2000. "Implied Volatility in the U.K. Commercial Property Market: Empirical Evidence Based on Transaction Data," The Journal of Real Estate Finance and Economics, Springer, vol. 20(1), pages 5-24, January.
    2. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, October.
    3. Brennan, Michael J. & Schwartz, Eduardo S., 1982. "An Equilibrium Model of Bond Pricing and a Test of Market Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(3), pages 301-329, September.
    4. Huang, Bing & Cao, Jiling & Chung, Hyuck, 2014. "Strategic real options with stochastic volatility in a duopoly model," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 40-51.
    5. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    6. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
    7. Sun-Yong Choi & Jean-Pierre Fouque & Jeong-Hoon Kim, 2013. "Option pricing under hybrid stochastic and local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1157-1165, July.
    8. 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.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. Bara Kim & In-Suk Wee, 2014. "Pricing of geometric Asian options under Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1795-1809, October.
    11. Zaevski, Tsvetelin S. & Kim, Young Shin & Fabozzi, Frank J., 2014. "Option pricing under stochastic volatility and tempered stable Lévy jumps," International Review of Financial Analysis, Elsevier, vol. 31(C), pages 101-108.
    12. Ting, Sai Hung Marten & Ewald, Christian-Oliver & Wang, Wen-Kai, 2013. "On the investment–uncertainty relationship in a real option model with stochastic volatility," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 22-32.
    13. Min-Ku Lee & Kyu-Hwan Jang, 2014. "Pricing Parisian Option under a Stochastic Volatility Model," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, November.
    14. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    15. Kim, Jeong-Hoon, 2004. "Asymptotic theory of noncentered mixing stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 161-174, November.
    16. McDonald, Robert & Siegel, Daniel, 1984. "Option Pricing When the Underlying Asset Earns a Below-Equilibrium Rate of Return: A Note," Journal of Finance, American Finance Association, vol. 39(1), pages 261-265, March.
    17. Shaun A. Bond & Soosung Hwang, 2003. "A Measure of Fundamental Volatility in the Commercial Property Market," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 31(4), pages 577-600, December.
    18. José Carlos Dias & João Pedro Vidal Nunes, 2011. "Pricing real options under the constant elasticity of variance diffusion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(3), pages 230-250, March.
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