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Teor. Veroyatnost. i Primenen., 1994, Volume 39, Issue 1, Pages 130–149 (Mi tvp3764)  

This article is cited in 30 scientific papers (total in 30 papers)

A new look at pricing of the “Russian Option”

L. A. Sheppa, A. N. Shiryaevb

a AT&T Bell Laboratories, New Jersey, USA
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The “Russian option” was introduced and calculated with the help of the solution of the optimal stopping problem for a two-dimensional Markov process in [10]. This paper proposes a new derivation of the general results [10]. The key idea is to introduce the dual martingale measure which permits one to reduce the “two-dimensional” optimal stopping problem to a “one-dimensional” one. This approach simplifies the discussion and explain the simplicity of the answer found in [10].

Keywords: diffusion model of the $(B,S)$-market, bank account, rational option price, rational expiration time, optimal stopping rules, smooth sewing condition, the Stephan problem, diffusion with reflection.

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English version:
Theory of Probability and its Applications, 1994, 39:1, 103–119

Bibliographic databases:

Received: 05.07.1993

Citation: L. A. Shepp, A. N. Shiryaev, “A new look at pricing of the “Russian Option””, Teor. Veroyatnost. i Primenen., 39:1 (1994), 130–149; Theory Probab. Appl., 39:1 (1994), 103–119

Citation in format AMSBIB
\by L.~A.~Shepp, A.~N.~Shiryaev
\paper A new look at pricing of the ``Russian Option''
\jour Teor. Veroyatnost. i Primenen.
\yr 1994
\vol 39
\issue 1
\pages 130--149
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 1
\pages 103--119

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. N. Volkov, “Calculation of the cost of one American-type option”, Russian Math. Surveys, 50:6 (1995), 1318–1320  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Peskir G., “Optimal stopping of the maximum process: The maximality principle”, Annals of Probability, 26:4 (1998), 1614–1640  crossref  mathscinet  zmath  isi
    3. Pedersen J.L., “Discounted optimal stopping problems for the maximum process”, Journal of Applied Probability, 37:4 (2000), 972–983  crossref  mathscinet  zmath  isi
    4. L. A. Shepp, A. N. Shiryaev, “The Russian option under conditions of a possible price “freeze””, Russian Math. Surveys, 56:1 (2001), 179–181  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Proc. Steklov Inst. Math., 237 (2002), 192–202  mathnet  mathscinet  zmath
    6. O. A. Glonti, “The Pricing of an Option That Is a Combination of Russian and Integral Russian Options”, Proc. Steklov Inst. Math., 237 (2002), 270–280  mathnet  mathscinet  zmath
    7. Kyprianou A.E., Pistorius M.R., “Perpetual options and canadization through fluctuation theory”, Annals of Applied Probability, 13:3 (2003), 1077–1098  crossref  mathscinet  zmath  isi
    8. Ekstrom E., “Russian options with a finite time horizon”, Journal of Applied Probability, 41:2 (2004), 313–326  crossref  mathscinet  isi
    9. Kyprianou A.E., “Some calculations for Israeli options”, Finance and Stochastics, 8:1 (2004), 73–86  crossref  mathscinet  zmath  isi
    10. Avram F., Kyprianou A.E., Pistorius M.R., “Exit problems for spectrally negative Levy processes and applications to (canadized) Russian options”, Annals of Applied Probability, 14:1 (2004), 215–238  crossref  mathscinet  zmath  isi
    11. Asmussen S., Avram F., Pistorius M.R., “Russian and American put options under exponential phase–type Levy models”, Stochastic Processes and Their Applications, 109:1 (2004), 79–111  crossref  mathscinet  zmath  isi
    12. Duistermaat J.J., Kyprianou A.E., van Schaik K., “Finite expiry Russian options”, Stochastic Processes and Their Applications, 115:4 (2005), 609–638  crossref  mathscinet  zmath  isi
    13. Obloj J., Yor M., “On local martingale and its supremum: Harmonic functions and beyond”, From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, 2006, 517–533  isi
    14. V. I. Arkin, A. D. Slastnikov, “A Variational Approach to Optimal Stopping Problems for Diffusion Processes”, Theory Probab. Appl., 53:3 (2009), 467–480  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. Kimura T., “Valuing finite–lived Russian options”, European Journal of Operational Research, 189:2 (2008), 363–374  crossref  mathscinet  zmath  isi
    16. Eberlein E., Papapantoleon A., Shiryaev A.N., “On the duality principle in option pricing: semimartingale setting”, Finance and Stochastics, 12:2 (2008), 265–292  crossref  mathscinet  zmath  isi
    17. Theory Probab. Appl., 53:3 (2009), 481–499  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. N. S. Demin, U. V. Andreeva, “Ekzoticheskie optsiony kupli s ogranicheniem vyplat i garantirovannym dokhodom v modeli Bleka–Shoulsa”, Probl. upravl., 1 (2011), 33–39  mathnet
    19. R. V. Ivanov, A. N. Shiryaev, “On the duality principle of hedging in diffusion models”, Theory Probab. Appl., 56:3 (2011), 376–402  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    20. Gapeev P.V. Lerche H.R., “On the Structure of Discounted Optimal Stopping Problems for One-Dimensional Diffusions”, Stochastics, 83:4-6, SI (2011), 537–554  crossref  isi
    21. Dai M. Yang Zh. Zhong Y., “Optimal Stock Selling Based on the Global Maximum”, SIAM J. Control Optim., 50:4 (2012), 1804–1822  crossref  isi
    22. Andreeva U.V., Danilyuk E.Yu., Demin N.S., Rozhkova S.V., Pakhomova E.G., “Primenenie veroyatnostnykh metodov k issledovaniyu ekzoticheskikh optsionov kupli evropeiskogo tipa na osnove ekstremalnykh znachenii tseny riskovogo aktiva”, Izvestiya tomskogo politekhnicheskogo universiteta, 321:6 (2012), 5–12  elib
    23. Ott C., “Optimal Stopping Problems for the Maximum Process with Upper and Lower Caps”, Ann. Appl. Probab., 23:6 (2013), 2327–2356  crossref  isi
    24. Gapeev P.V. Rodosthenous N., “Optimal Stopping Problems in Diffusion-Type Models With Running Maxima and Drawdowns”, J. Appl. Probab., 51:3 (2014), 799–817  isi
    25. Theory Probab. Appl., 61:1 (2017), 159–167  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    26. Stiburek D., “Sequential testing of hypotheses about drift for Gaussian diffusions”, Stat. Methodol., 33 (2016), 14–30  crossref  mathscinet  isi  scopus
    27. Gapeev P.V. Rodosthenous N., “Perpetual American options in diffusion-type models with running maxima and drawdowns”, Stoch. Process. Their Appl., 126:7 (2016), 2038–2061  crossref  mathscinet  zmath  isi  elib  scopus
    28. Christensen S. Irle A., “A General Method For Finding the Optimal Threshold in Discrete Time”, Stochastics, 91:5 (2019), 728–753  crossref  isi
    29. Gapeev V P. Rodosthenous N. Chinthalapati V.L.R., “On the Laplace Transforms of the First Hitting Times For Drawdowns and Drawups of Diffusion-Type Processes”, Risks, 7:3 (2019), 87  crossref  isi
    30. Gapeev V P., “Optimal Stopping Problems For Running Minima With Positive Discounting Rates”, Stat. Probab. Lett., 167 (2020), 108899  crossref  isi
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