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Timing in the Presence of Directional Predictability: Optimal Stopping of Skew Brownian Motion

Listed author(s):
  • Luis H. R. Alvarez E.
  • Paavo Salminen

We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional predictability modeled by the presence of a skew point for the underlying has a nontrivial and somewhat surprising impact on the timing incentives of the decision maker. We prove that waiting is always optimal at the skew point for a large class of exercise payoffs. An interesting consequence of this finding, which is in sharp contrast with studies relying on ordinary Brownian motion, is that the exercise region for the problem can become unconnected even when the payoff is linear. We also establish that higher skewness increases the incentives to wait and postpones the optimal timing of an investment opportunity. Our general results are explicitly illustrated for a piecewise linear payoff.

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File URL: http://arxiv.org/pdf/1608.04537
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Paper provided by arXiv.org in its series Papers with number 1608.04537.

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Date of creation: Aug 2016
Handle: RePEc:arx:papers:1608.04537
Contact details of provider: Web page: http://arxiv.org/

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  1. Anatolyev, Stanislav & Gospodinov, Nikolay, 2010. "Modeling Financial Return Dynamics via Decomposition," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 232-245.
  2. Stelios Bekiros & Dimitris Georgoutsos, 2008. "Non-linear dynamics in financial asset returns: the predictive power of the CBOE volatility index," The European Journal of Finance, Taylor & Francis Journals, vol. 14(5), pages 397-408.
  3. Stéphane Villeneuve & Erik Ekstrom, 2006. "On the Value of Optimal Stopping Games," Post-Print hal-00173182, HAL.
  4. Nyberg, Henri, 2011. "Forecasting the direction of the US stock market with dynamic binary probit models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 561-578.
  5. Nyberg, Henri, 2011. "Forecasting the direction of the US stock market with dynamic binary probit models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 561-578, April.
  6. Peter F. Christoffersen & Francis X. Diebold & Roberto S. Mariano & Anthony S. Tay & Yiu Kuen Tse, 2006. "Direction-of-Change Forecasts Based on Conditional Variance, Skewness and Kurtosis Dynamics: International Evidence," PIER Working Paper Archive 06-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  7. S. D. Bekiros & D. A. Georgoutsos, 2008. "Direction-of-change forecasting using a volatility-based recurrent neural network," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(5), pages 407-417.
  8. T. R. A. Corns & S. E. Satchell, 2007. "Skew Brownian Motion and Pricing European Options," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 523-544.
  9. Anatolyev, Stanislav & Gerko, Alexander, 2005. "A Trading Approach to Testing for Predictability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 455-461, October.
  10. Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.
  11. Chevapatrakul, Thanaset, 2013. "Return sign forecasts based on conditional risk: Evidence from the UK stock market index," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2342-2353.
  12. Tina Hviid Rydberg & Neil Shephard, 2003. "Dynamics of Trade-by-Trade Price Movements: Decomposition and Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 2-25.
  13. Andrew Skabar, 2013. "Direction‐of‐Change Financial Time Series Forecasting using a Similarity‐Based Classification Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(5), pages 409-422, August.
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