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Teor. Veroyatnost. i Primenen., 1994, Volume 39, Issue 1, Pages 23–79 (Mi tvp3762)  

This article is cited in 17 scientific papers (total in 17 papers)

Toward the theory of pricing of options of both European and American types. I. Discrete time

A. N. Shiryaeva, Yu. M. Kabanovb, D. O. Kramkova, A. V. Melnikova

a Steklov Mathematical Institute, Russian Academy of Sciences
b Central Economics and Mathematics Institute, RAS

Abstract: This paper consisting of two parts (I — discrete time, II — continuous time [19]) considers the main concepts, statements of problems, and results of financial mathematics in connection with options and option contract pricing as a kind of derivative securities. In § 1 it is assumed that the contracts are exercised in discrete $(B,S)$-market. There are two assets: riskless bank account $B=(B_n )_{n\ge 0}$ and risky stock $S=(S_n )_{n\ge 0}$, European as well as American options are examined. Special attention is paid to the “martingale” methods of option pricing and hedging strategies in particular for call options and put options.

Keywords: security market, bonds and stocks, bank account, American and European options, rational cost (fair price), hedging strategies, martingales, Markov times, optimal stopping rules, arbitrage, market completeness.

Full text: PDF file (2629 kB)

English version:
Theory of Probability and its Applications, 1994, 39:1, 14–60

Bibliographic databases:

Received: 05.07.1993

Citation: A. N. Shiryaev, Yu. M. Kabanov, D. O. Kramkov, A. V. Melnikov, “Toward the theory of pricing of options of both European and American types. I. Discrete time”, Teor. Veroyatnost. i Primenen., 39:1 (1994), 23–79; Theory Probab. Appl., 39:1 (1994), 14–60

Citation in format AMSBIB
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\by A.~N.~Shiryaev, Yu.~M.~Kabanov, D.~O.~Kramkov, A.~V.~Melnikov
\paper Toward the theory of pricing of options of both European and American types.~I. Discrete time
\jour Teor. Veroyatnost. i Primenen.
\yr 1994
\vol 39
\issue 1
\pages 23--79
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1348190}
\zmath{https://zbmath.org/?q=an:0833.60064}
\transl
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 1
\pages 14--60
\crossref{https://doi.org/10.1137/1139002}
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    This publication is cited in the following articles:
    1. P. V. Gapeev, “Calculation of the high and low prices of European-type options”, Russian Math. Surveys, 52:4 (1997), 828–829  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Ya. Yu. Bart, “Option hedging in the binomial model with differing interest rates”, Russian Math. Surveys, 53:5 (1998), 1084–1085  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. O. V. Shataev, “On a fair price of an option of European type”, Russian Math. Surveys, 53:6 (1998), 1367–1369  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Hubalek F., Schachermayer W., “When does convergence of asset price processes imply convergence of option prices?”, Mathematical Finance, 8:4 (1998), 385–403  crossref  mathscinet  zmath  isi
    5. O. V. Shataev, “Minimization with respect to entropy in the problem of finding a martingale measure”, Russian Math. Surveys, 55:5 (2000), 1000–1002  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. S. S. Artemev, A. A. Nosikova, S. V. Soloboev, “Metod Monte-Karlo dlya modelirovaniya tseny aktsii”, Sib. zhurn. vychisl. matem., 3:1 (2000), 1–10  mathnet  zmath
    7. A. V. Melnikov, “On the Unity of Quantitative Methods of Pricing in Finance and Insurance”, Proc. Steklov Inst. Math., 237 (2002), 50–72  mathnet  mathscinet  zmath
    8. F. S. Nasyrov, “Symmetric Integrals and Their Application in Financial Mathematics”, Proc. Steklov Inst. Math., 237 (2002), 256–269  mathnet  mathscinet  zmath
    9. N. S. Demin, M. Yu. Shishirin, “Evropeiskii optsion s proizvolnym chislom tipov riskovykh tsennykh bumag v sluchae diskretnogo vremeni”, Diskretn. analiz i issled. oper., ser. 2, ser. 2, 9:1 (2002), 3–20  mathnet  mathscinet
    10. Theory Probab. Appl., 48:1 (2004), 131–140  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. R. V. Ivanov, “Calculating the American options in the default model”, Autom. Remote Control, 68:3 (2007), 513–522  mathnet  crossref  mathscinet  zmath  elib  elib
    12. Mykhailo Pupashenko, Alexander Kukush, “Reselling of european option if the implied volatility varies as Cox-Ingersoll-Ross process”, Theory Stoch. Process., 14(30):4 (2008), 114–128  mathnet
    13. N. S. Demin, A. V. Erlykova, E. A. Panshina, “Issledovanie odnogo vida ekzoticheskikh optsionov pri nalichii ottoka i pritoka kapitala v binomialnoi modeli $(B,S)$-rynka tsennykh bumag”, Diskretn. analiz i issled. oper., 16:6 (2009), 23–42  mathnet  mathscinet  zmath
    14. U. V. Andreeva, N. S. Demin, A. V. Erlykova, E. A. Pan'shina, “Exotic European options with restrictions on the payoffs”, Autom. Remote Control, 71:9 (2010), 1864–1878  mathnet  crossref  mathscinet  zmath  isi
    15. A. I. Kibzun, V. R. Sobol, “Modernizatsiya strategii posledovatelnogo khedzhirovaniya optsionnoi pozitsii”, Tr. IMM UrO RAN, 19, no. 2, 2013, 179–192  mathnet  mathscinet  elib
    16. Dhaene J. Stassen B. Devolder P. Vellekoop M., “The Minimal Entropy Martingale Measure in a Market of Traded Financial and Actuarial Risks”, J. Comput. Appl. Math., 282 (2015), 111–133  crossref  isi
    17. A. A. Shishkova, “Raschet aziatskikh optsionov dlya modeli Bleka–Shoulsa”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2018, no. 51, 48–63  mathnet  crossref  elib
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