617
Views
0
CrossRef citations to date
0
Altmetric
Research Article

On skewed, leptokurtic returns and pentanomial lattice option valuation via minimal entropy martingale measure

| (Reviewing Editor)
Article: 1358894 | Received 26 Mar 2017, Accepted 11 Jul 2017, Published online: 07 Aug 2017

References

  • Barndorff-Nielsen, O. (1998). Process of normal inverse Gaussian type. Finance Stochastics, 2, 41–68.
  • Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 659–683.
  • Carr, P., German, H., Madan, D., & Yor, M. (2002). The fine structure of asset returns: An empirical investigation. Journal of Business, 75, 305–332.
  • Chan, W., & Maheu, J. (2002). Conditional jump dynamics in stock market returns. Journal of Business and Economic Statistics, 20, 377–389.
  • Choulli, T. & Striker, C. (2006). More on minimal entropy-hellinger martingale measure. Mathematical Finance, 16(1), 1–19.
  • Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1, 223–226.
  • Cox, J., Ross, S., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7, 229–264.
  • Derman, E., & Kani, I. (1994). Implied trinomial trinomial trees of the volatility smile. Goldman Sachs quantitative strategies research notes.
  • Duan, J., Ritchken, P., & Sun, Z. (2006). Approximating garch-jump models, jump-diffusion processes and option pricing. Mathematical Finance, 16, 21–52.
  • Esche, F., & Schweizer, M. (2005). Minimal entropy preserves the lévy property: how and why. Stochastics and their Applications, 115, 299–327.
  • Florescu, I., & Viens, F. (2008). Stochastic volatility: Option pricing using a multinomial recombining tree. Applied Mathematical Finance, 15, 151–181.
  • Frittelli, M. (2000). The minimal entropy martingale measure and valuation problem in incomplete markets. Mathematical Finance, 10, 39–52.
  • Fujiwara, T., & Miyahara, Y. (2003). The minimal entropy martingale measures for geometric lévy processes. Finance and Stochastics, 7, 509–531.
  • Harrison, M., & Kreps, M. (1979). Martingales and arbitrage in multiperiod securities markets. Economic Theory, 20, 381–408.
  • Harrison, M., & Pliska, S. (1981). Martingales and stochastic integrals in the theory of continous trading. Stochastic Processes and their Applications, 11, 215–260.
  • Hsieh, D. (1989). Testing for nonlinear dependance in daily foreign exchanges rates. Journal of Business, 62, 339–368.
  • Kamrad, B., & Ritchken, P. (1991). Multinomial approximating models for options with k state variables. Management Science, 37, 1640–1652.
  • Kargin, V. (2005). Lattice option pricing by multidimensional interpolation. Mathematical Finance, 15, 635–647.
  • Kellezi, E., & Webber, N. (2004). Valuing Bermudan options when the asset returns are Lévy processes. Quantitative Finance, 4, 87–100.
  • McNeil, A., Frey, R., & Embrechts, P. (2005). Embrechts. Quantitative risk management: Concepts techniques and tools. Priceton University Press.
  • Miyahara, Y. (2001). Geometric lévy process & memm: Pricing model and related estimation problems. Asia-Pacific Financial Markets, 8, 45–60.
  • Nieuwland, F., Verschoor, W., & Wolff, C. (1994). Stochastic trends and jumps in ems exchange rates. Journal of International Money and Finance, 13, 699–727.
  • Primbs, J., Rathianam, M., & Yamada, Y. (2007). Option Pricing with a pentanomial lattice model that incorporates skewness and kurtosis. Applied Mathematical Finance, 14, 1–17.
  • Rendleman, R., & Bartter, B. (1979). Two state option pricing pricing. Journal of Finance, 3, 1093–1110.
  • Ritchken, P., & Trevor, R. (1999). Pricing options under generalized GARCH and stochastic volatility process. Journal of Finance, 54, 337–402.
  • Ssebungenyi, C. (2008). Valuation of real options using the minimal entropy martingale measure. Applied Mathematical Sciences, 2, 2875–2800.
  • Ssebugenyi, C. S., Mwaniki, I. J., & Konlack, V. S. (2013). On the minimal entropy martingale measure and multinomial lattices with cumulants. Applied Mathematical Finance, 20, 359–379.
  • Wu, C. (2006). The GARCH option pricing model: A modification of lattice approach. Review of Qantitative Finance and Accounting, 26, 55–66.
  • Yamada, Y. & Primbs, J. (2001). Properties of multinomial lattice random walks for optimal hedges. International Conference of Computational Science, 579–588.
  • Yamada, Y., & Primbs, J. (2004). Properties of multinomial lattices with cumulants for option pricing and hedging. Asia-Pacific Fianacial Markets, 11, 335–365.