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Put-Call Parity and Market Frictions

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  • Simone Cerreia-Vioglio
  • Fabio Maccheroni
  • Massimo Marinacci

Abstract

We extend the Fundamental Theorem of Finance and the Pricing Rule Representation Theorem of Cox and Ross (see Ross [35] and [37] and Cox and Ross [9]) to the case in which market frictions are aken into account but the Put-Call Parity is still assumed to hold. In turn, we obtain a representation of the pricing rule as a discounted expectation with respect to a nonadditive risk neutral probability. As a further contribution, in so doing we endogenize the state space structure and the contingent claim representation usually assumed to represent assets and markets.

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Bibliographic Info

Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 447.

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Date of creation: 2012
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Handle: RePEc:igi:igierp:447

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  1. Stoll, Hans R, 1973. "The Relationship Between Put and Call Option Prices: Reply," Journal of Finance, American Finance Association, vol. 28(1), pages 185-87, March.
  2. Cox, John C & Ross, Stephen A, 1976. "A Survey of Some New Results in Financial Option Pricing Theory," Journal of Finance, American Finance Association, vol. 31(2), pages 383-402, May.
  3. A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 323-330.
  4. Jarrow, Robert A & O'Hara, Maureen, 1989. " Primes and Scores: An Essay on Market Imperfections," Journal of Finance, American Finance Association, vol. 44(5), pages 1263-87, December.
  5. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  6. repec:fth:inseep:9513 is not listed on IDEAS
  7. Gould, J. P. & Galai, D., 1974. "Transactions costs and the relationship between put and call prices," Journal of Financial Economics, Elsevier, vol. 1(2), pages 105-129, July.
  8. Ross, Stephen A, 1987. "Arbitrage and Martingales with Taxation," Journal of Political Economy, University of Chicago Press, vol. 95(2), pages 371-93, April.
  9. 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.
  10. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
  11. Amihud, Yakov & Mendelson, Haim, 1991. " Liquidity, Maturity, and the Yields on U.S. Treasury Securities," Journal of Finance, American Finance Association, vol. 46(4), pages 1411-25, September.
  12. Prisman, Eliezer Z, 1986. " Valuation of Risky Assets in Arbitrage Free Economies with Frictions," Journal of Finance, American Finance Association, vol. 41(3), pages 545-57, July.
  13. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2010. "Singed Integral Representations of Comonotonic Additive Functionals," Working Papers 366, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  14. Garman, Mark B. & Ohlson, James A., 1981. "Valuation of risky assets in arbitrage-free economies with transactions costs," Journal of Financial Economics, Elsevier, vol. 9(3), pages 271-280, September.
  15. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  16. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  17. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
  18. Stoll, Hans R, 1969. "The Relationship between Put and Call Option Prices," Journal of Finance, American Finance Association, vol. 24(5), pages 801-24, December.
  19. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
  20. Green, Richard C. & Jarrow, Robert A., 1987. "Spanning and completeness in markets with contingent claims," Journal of Economic Theory, Elsevier, vol. 41(1), pages 202-210, February.
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