Derivative Model Applications

  • Jamie Rogers
Part of the Global Financial Markets book series (GFM)


The Black–Scholes GBM (geometric Brownian motion) model can be generalized to other models that are more realistic for particular markets. The various simple extensions to the Black–Scholes model assume constant parameters for ease of calculation. In reality, the properties of time series such as volatility, mean reversion, long-term levels and jump behaviour will at the very least vary through time with reasonably predictable patterns. These characteristics can be included in spot models.


  1. Black, F. The pricing of commodity contracts, The Journal of Financial Economics, 3, (Jan–March): 167–79, 1976.CrossRefGoogle Scholar
  2. Carr, P. Wu, L. Stochastic Skew Models for FX Options, 2004.Google Scholar
  3. Clewlow, L. and Strickland, C. Energy Derivatives, Pricing and Risk Management, Lacima, 2000.Google Scholar
  4. Clewlow, L. and Strickland, C. Implementing Derivative Models, Wiley, 1998.Google Scholar
  5. Copeland, T. and Antikarov, V. Real Options, Texere, 2001.Google Scholar
  6. Cox, J.S., Ross, S. and Rubinstein, M. Option pricing: a simplified approach, Journal of Financial Economics, 7 (September): 229–63, 1979.CrossRefGoogle Scholar
  7. Derman, E. Quantitative Strategies, Research Notes: Model Risk, Goldman Sachs, 1996.Google Scholar
  8. Dixit, A. and Pindyck, R. Investment Under Uncertainty, Princeton University Press, 1994.Google Scholar
  9. Geske, R. The valuation of compound options, Journal of Financial Economics, 7: 63–81, 1979.CrossRefGoogle Scholar
  10. Geske, R. and Zhou, Y. Predicting Risk and Return of the S&P 500: Evidence from Index Options, UCLA Working Paper, 2007.Google Scholar
  11. Geske, R. and Zhou, Y. Capital Structure Effects on Prices of Firm Stock Options: Tests Using Implied Market Values of Corporate Debt, UCLA Working Paper, 2007a.Google Scholar
  12. Goldman Sachs. Valuing convertible bonds as derivatives, Quantitative Strategies Research Notes, November 1994.Google Scholar
  13. Haug, E.G. The Complete Guide to Option Pricing Formulas, McGraw Hill, second edition, 2007.Google Scholar
  14. Heston, S. L. ‘A closed-form solution for options with stochastic volatility with applications to bonds and currency options’, The Review of Financial Studies 6(2), 327–343, 1993.CrossRefGoogle Scholar
  15. Hull, J. and White, A. An analysis of the bias in option pricing caused by stochastic volatility, Advances in Futures and Options Research, 3: 29–61, 1988.Google Scholar
  16. Merton, R. Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3: 125–44, 1976.CrossRefGoogle Scholar
  17. Moodley, N. The Heston Model: A Practical Approach with Matlab Code, 2005.Google Scholar
  18. Natixis Asset Management. Investing in global convertible bonds – stylized facts, pricing and strategies, research paper number eight, January 2017.Google Scholar
  19. Rebonato, R. Model risk: new challenges, new solutions, Risk, March 2001.Google Scholar
  20. Schwartz, E. The stochastic behavior of commodity prices: implications for valuation and hedging, Journal of Finance, LII(3): 923–73, 1997.CrossRefGoogle Scholar
  21. Vasicek, O. An equilibrium characterization of the term structure, Journal of Financial Economics, (5): 177–88, 1977.CrossRefGoogle Scholar
  22. Zhou, Y. Pricing Individual Stock Options on Firms with Leverage, Anderson School of Management at UCLA, 2007.Google Scholar

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© The Author(s) 2019

Authors and Affiliations

  • Jamie Rogers
    • 1
  1. 1.New YorkUSA

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