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Closed-form solutions to stochastic process switching problems

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  • François, Pascal
  • Morellec, Erwan

Abstract

This paper studies the price of an asset depending on both a fundamental and possible interventions of an authority. Using the martingale approach in continuous time, we provide closed-form solutions to switching problems involving irreversible, state dependent and intramarginal switch policies. The martingale approach provides additional information regarding the switching policy, namely the average time before authority intervention, the conditional probability of intervention, or the total time of intervention. Applications in international and financial economics include exchange rates modelling, corporate claims valuation and capital budgeting decisions.

Suggested Citation

  • François, Pascal & Morellec, Erwan, 2008. "Closed-form solutions to stochastic process switching problems," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1072-1083, December.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1072-1083
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    References listed on IDEAS

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    1. Giuseppe Bertola & Lars E. O. Svensson, 1993. "Stochastic Devaluation Risk and the Empirical Fit of Target-Zone Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 689-712.
    2. Mella-Barral, Pierre & Perraudin, William, 1997. "Strategic Debt Service," Journal of Finance, American Finance Association, vol. 52(2), pages 531-556, June.
    3. Sutherland, Alan, 1995. "State- and time-contingent switches of exchange rate regime," Journal of International Economics, Elsevier, vol. 38(3-4), pages 361-374, May.
    4. Hayne E. Leland, 1998. "Agency Costs, Risk Management, and Capital Structure," Journal of Finance, American Finance Association, vol. 53(4), pages 1213-1243, August.
    5. Dixit, Avinash, 1991. "Irreversible Investment with Price Ceilings," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 541-557, June.
    6. Flood, Robert P & Garber, Peter M, 1983. "A Model of Stochastic Process Switching," Econometrica, Econometric Society, vol. 51(3), pages 537-551, May.
    7. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    8. Froot, Kenneth A. & Obstfeld, Maurice, 1991. "Exchange-rate dynamics under stochastic regime shifts : A unified approach," Journal of International Economics, Elsevier, vol. 31(3-4), pages 203-229, November.
    9. Bekaert, Geert & Gray, Stephen F., 1998. "Target zones and exchange rates:: An empirical investigation," Journal of International Economics, Elsevier, vol. 45(1), pages 1-35, June.
    10. Pascal Francois, 2004. "Capital Structure and Asset Prices: Some Effects of Bankruptcy Procedures," The Journal of Business, University of Chicago Press, vol. 77(2), pages 387-412, April.
    11. Fries, Steven & Miller, Marcus & Perraudin, William, 1997. "Debt in Industry Equilibrium," The Review of Financial Studies, Society for Financial Studies, vol. 10(1), pages 39-67.
    12. Flandreau, Marc, 1998. "The burden of intervention: externalities in multilateral exchange rates arrangements," Journal of International Economics, Elsevier, vol. 45(1), pages 137-171, June.
    13. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    14. Erwan Morellec, 2004. "Can Managerial Discretion Explain Observed Leverage Ratios?," The Review of Financial Studies, Society for Financial Studies, vol. 17(1), pages 257-294.
    15. Mundaca, B. Gabriela, 2001. "Central bank interventions and exchange rate band regimes," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 677-700, October.
    16. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    17. Andrew B. Abel & Janice C. Eberly, 1996. "Optimal Investment with Costly Reversibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 581-593.
    18. De Grauwe, Paul & Dewachter, Hans & Veestraeten, Dirk, 1999. "Price dynamics under stochastic process switching: some extensions and an application to EMU1," Journal of International Money and Finance, Elsevier, vol. 18(2), pages 195-224, February.
    19. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    20. Craine, Roger, 2002. "Exchange rate regime credibility, the agency cost of capital and devaluation," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1431-1456, August.
    21. Mello, Antonio S. & Parsons, John E. & Triantis, Alexander J., 1995. "An integrated model of multinational flexibility and financial hedging," Journal of International Economics, Elsevier, vol. 39(1-2), pages 27-51, August.
    22. Pascal Francois, 2006. "Tax loss carry-forwards and optimal leverage," Applied Financial Economics, Taylor & Francis Journals, vol. 16(14), pages 1075-1083.
    23. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176, April.
    24. Marc Flandreau, 1998. "The Burden of Intervention : Externalities in Multilateral Exchange Rates Arrangements," Post-Print hal-03416385, HAL.
    25. Froot, Kenneth A & Obstfeld, Maurice, 1991. "Stochastic Process Switching: Some Simple Solutions," Econometrica, Econometric Society, vol. 59(1), pages 241-250, January.
    26. Wilfling, Bernd & Maennig, Wolfgang, 2001. "Exchange rate dynamics in anticipation of time-contingent regime switching: modelling the effects of a possible delay," Journal of International Money and Finance, Elsevier, vol. 20(1), pages 91-113, February.
    27. Smith, Gregor W, 1991. "Solution to a Problem of Stochastic Process Switching," Econometrica, Econometric Society, vol. 59(1), pages 237-239, January.
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