Processo de Meixner: teoria e aplicações no mercado financeiro brasileiro
DOI:
https://doi.org/10.1590/S0101-41612011000200007Palavras-chave:
processo de Meixner, apreçamento de opções, caudas pesadasResumo
Modelos consagrados e amplamente utilizados no mercado, como o modelo de Black-Scholes, assumem que os retornos diários dos ativos têm distribuição Normal. Na prática, porém, evidencia-se que esses retornos são frequentemente assimétricos e com caudas mais pesadas. Sendo assim, este trabalho busca avaliar se a distribuição de Meixner seria mais apropriada para a modelagem dos retornos. Adicionalmente, será analisado se o processo de Lévy que surge a partir dessa distribuição, o processo de Meixner, é eficiente na precificação de derivativos financeiros. Para tanto, propõe-se a substituição do movimento Browniano pelo processo de Meixner em Black-Scholes.
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Referências
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Bakshi , G.; CaoAO, C. & Chen , Z. Empirical performance of alternative option pricing models. Journal of Finance, v. 52, n. 5, 1997, p. 2003-49,
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BATES, D. The crash of ‘87: was it expected? The evidence from options markets. Journal of Finance, v. 46, n. 3,p., 1991, 1009-44.
BATES, D. Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options. Review of Financial Studies, v. 9, n. 1, 1996, p. 69-108.
BATES, D. Post ‘87 crash fears in S&P 500 futures options. NBER Working Paper, n. 5894, jan. 1997.
BertoinERTOIN, J. Lévy processes. Cambridge University Press, 1996.
BlackLACK, F. & Scholes , M. The pricing of options and corporate liabilities. Journal of Political Economy, v. 81, 1973, p. 637–654.
Carr , P.; Geman , H.; MadanADAN, D.H. & Yor , M. The fi ne structure of asset returns: an empirical investigation. Journal of Business, v. 75, n. 2, 2002.
Delbaen , F. & SchachermayerCHACHERMAYER, W. A general version of the fundamental theorem of asset pricing. Mathematische Annalen, v. 300, 1994p. 463-520.
Duffie , D.; Pan , J. & Singleton , K. Transform analysis and asset pricing for affine jump-diffusions. Econometrica, v. 68, n. 6, 2000, p.1343-1376.
Eberlein , E.; Keller , U. & PRAUSE, K. New insights into smile, mispricing and value at risk. Journal of Business, v. 71, n. 3, 1998, p. 371-405.
EsscherSSCHER, F. On the probability function in the collective theory of risk. Skandinavisk Aktuarietidskrift, v. 15, p. 175-195, 1932.
FAJARDO, J.; Schuschny A. & A. Lévy Processes and The Brazilian Market. Brazilian Review of Econometrics, v.21, n. 2, 2001, p. 263-289.
FAJARDO, J. & Farias , A. R. Generalized Hyperbolic Distributions and Brazilian Data. Brazilian Review of Econometrics, v.24, n. 2, 2004, p. 1-21.
FAJARDO, J. & Farias , A. R. Multivariate affine generalized hyperbolic distributions: An empirical investigation, International Review of Financial Analysis, v. 18, n. 4, Sept. 2009, p. 174-184.
FAJARDO, J. & Farias , A. R. Derivative pricing using multivariate affine generalized hyperbolic distributions, Journal of Banking &Finance, v. 34, n. 7, July 2010, p. 1607-1617.
FAJARDO, J.; ORNELAS. J. R. H. & FARIAS, A. R. Analyzing the use of generalized hyperbolic distributions to value at risk calculations. Revista de Economia Aplicada, v. 9, 2005, p. 25-38.
French , d. w. & Martin l. j. The measurement of option mispricing. Journal of Banking and Finance, v. 12, 1988, p. 537-550.
GERBER, H.U. & Shiu , E.S.W. Option pricing by Esscher transforms. Transactions of the Society of Actuaries, v. 46, 1994, p. 99–191.
GERBER, H.U. & Shiu , E.S.W. Actuarial bridges to dynamic hedging and option pricing. Insurance: Mathematics and Economics, v. 18, n. 3, 1996, p. 183–218.
Grigelionis , B. Processes of Meixner type. Lithuanian Mathematical Journal, v. 39, n. 1, 1999, p. 33-41.
Grigelionis , B. Generalized z-distributions and related stochastic processes. Lithuanian Mathematical Journal, v. 41, n. 3, 2001, p. 303-319.
Heston , S. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, v. 6, n. 2, 1993, p. 327-343.
Jones , E. P. Option arbitrage and strategy with large price changes. Journal of Financial Economics, v.13, n. 1, 1984, p. 91-113.
MERTON, R. C. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, v. 3, 1976, p. 125-144.
Naik , V. & Lee , M. General equilibrium pricing of options on the market portfolio with discontinuous returns. Review of Financial Studies, v. 3, n. 4, 1990, p. 493-521.
MADAN, D.; Carr P. & Chang , E. The variance gamma process and option pricing. European Finance Review, v. 2, 1998, p. 79-105.
Schoutens , W. Meixner processes in finance. Eindhoven, Eurandom Report, n. 002, 2001.
Schoutens , W. Lévy processes in finance: pricing financial derivatives. John Wiley & Sons, 2003.
Schoutens , W. & Teugels , J.L. Lévy processes, polynomials and martingales. Communication in Statistics Stochastic Models, v. 14, n. 1 e 2, 1998, p. 335–349.
STEPHENS, M. A. Asymptotic results for goodness of fi t statistics with unknown parameters. The Annals of Statistics, v. 4, n. 2, 1976, p. 357-369.
Bakshi , G.; CaoAO, C. & Chen , Z. Empirical performance of alternative option pricing models. Journal of Finance, v. 52, n. 5, 1997, p. 2003-49,
Barndorff -Nielsen, O.E. Processes of normal inverse Gaussian type. Finance and Stochastics, v. 2, n. 1, 1998, p. 41-68.
Barndorff -Nielsen, O.E & SHEPPARD, N. Non-gaussian Ornstein-Uhlenbeck based models and some of their uses in financial economics. Journal of the Royal Statistical Society, v. 63, n. 2, 2001, p. 167-241.
BATES, D. The crash of ‘87: was it expected? The evidence from options markets. Journal of Finance, v. 46, n. 3,p., 1991, 1009-44.
BATES, D. Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options. Review of Financial Studies, v. 9, n. 1, 1996, p. 69-108.
BATES, D. Post ‘87 crash fears in S&P 500 futures options. NBER Working Paper, n. 5894, jan. 1997.
BertoinERTOIN, J. Lévy processes. Cambridge University Press, 1996.
BlackLACK, F. & Scholes , M. The pricing of options and corporate liabilities. Journal of Political Economy, v. 81, 1973, p. 637–654.
Carr , P.; Geman , H.; MadanADAN, D.H. & Yor , M. The fi ne structure of asset returns: an empirical investigation. Journal of Business, v. 75, n. 2, 2002.
Delbaen , F. & SchachermayerCHACHERMAYER, W. A general version of the fundamental theorem of asset pricing. Mathematische Annalen, v. 300, 1994p. 463-520.
Duffie , D.; Pan , J. & Singleton , K. Transform analysis and asset pricing for affine jump-diffusions. Econometrica, v. 68, n. 6, 2000, p.1343-1376.
Eberlein , E.; Keller , U. & PRAUSE, K. New insights into smile, mispricing and value at risk. Journal of Business, v. 71, n. 3, 1998, p. 371-405.
EsscherSSCHER, F. On the probability function in the collective theory of risk. Skandinavisk Aktuarietidskrift, v. 15, p. 175-195, 1932.
FAJARDO, J.; Schuschny A. & A. Lévy Processes and The Brazilian Market. Brazilian Review of Econometrics, v.21, n. 2, 2001, p. 263-289.
FAJARDO, J. & Farias , A. R. Generalized Hyperbolic Distributions and Brazilian Data. Brazilian Review of Econometrics, v.24, n. 2, 2004, p. 1-21.
FAJARDO, J. & Farias , A. R. Multivariate affine generalized hyperbolic distributions: An empirical investigation, International Review of Financial Analysis, v. 18, n. 4, Sept. 2009, p. 174-184.
FAJARDO, J. & Farias , A. R. Derivative pricing using multivariate affine generalized hyperbolic distributions, Journal of Banking &Finance, v. 34, n. 7, July 2010, p. 1607-1617.
FAJARDO, J.; ORNELAS. J. R. H. & FARIAS, A. R. Analyzing the use of generalized hyperbolic distributions to value at risk calculations. Revista de Economia Aplicada, v. 9, 2005, p. 25-38.
French , d. w. & Martin l. j. The measurement of option mispricing. Journal of Banking and Finance, v. 12, 1988, p. 537-550.
GERBER, H.U. & Shiu , E.S.W. Option pricing by Esscher transforms. Transactions of the Society of Actuaries, v. 46, 1994, p. 99–191.
GERBER, H.U. & Shiu , E.S.W. Actuarial bridges to dynamic hedging and option pricing. Insurance: Mathematics and Economics, v. 18, n. 3, 1996, p. 183–218.
Grigelionis , B. Processes of Meixner type. Lithuanian Mathematical Journal, v. 39, n. 1, 1999, p. 33-41.
Grigelionis , B. Generalized z-distributions and related stochastic processes. Lithuanian Mathematical Journal, v. 41, n. 3, 2001, p. 303-319.
Heston , S. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, v. 6, n. 2, 1993, p. 327-343.
Jones , E. P. Option arbitrage and strategy with large price changes. Journal of Financial Economics, v.13, n. 1, 1984, p. 91-113.
MERTON, R. C. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, v. 3, 1976, p. 125-144.
Naik , V. & Lee , M. General equilibrium pricing of options on the market portfolio with discontinuous returns. Review of Financial Studies, v. 3, n. 4, 1990, p. 493-521.
MADAN, D.; Carr P. & Chang , E. The variance gamma process and option pricing. European Finance Review, v. 2, 1998, p. 79-105.
Schoutens , W. Meixner processes in finance. Eindhoven, Eurandom Report, n. 002, 2001.
Schoutens , W. Lévy processes in finance: pricing financial derivatives. John Wiley & Sons, 2003.
Schoutens , W. & Teugels , J.L. Lévy processes, polynomials and martingales. Communication in Statistics Stochastic Models, v. 14, n. 1 e 2, 1998, p. 335–349.
STEPHENS, M. A. Asymptotic results for goodness of fi t statistics with unknown parameters. The Annals of Statistics, v. 4, n. 2, 1976, p. 357-369.
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Publicado
30-06-2011
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Copyright (c) 2011 José Santiago Fajardo Barbachan, Felipe Gomes Pereira Coutinho
Este trabalho está licenciado sob uma licença Creative Commons Attribution-NonCommercial 4.0 International License.
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O detentor dos direitos autorais da revista é o Departamento de Economia da Faculdade de Economia, Administração, Contabilidade e Atuária da Universidade de São Paulo.
Como Citar
Barbachan, J. S. F., & Coutinho, F. G. P. (2011). Processo de Meixner: teoria e aplicações no mercado financeiro brasileiro. Estudos Econômicos (São Paulo), 41(2), 383-408. https://doi.org/10.1590/S0101-41612011000200007
