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Efficient computation of option price sensitivities for options of American style

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  • Wallner, Christian
  • Wystup, Uwe

Abstract

No front-office software can survive without providing derivatives of option prices with respect to underlying market or model parameters, the so called Greeks. If a closed form solution for an option exists, Greeks can be computed analytically and they are numerically stable. However, for American style options, there is no closed-form solution. The price is computed by binomial trees, finite difference methods or an analytic approximation. Taking derivatives of these prices leads to instable numerics or misleading results, specially for Greeks of higher order. We compare the computation of the Greeks in various pricing methods and conclude with the recommendation to use Leisen-Reimer trees.

Suggested Citation

  • Wallner, Christian & Wystup, Uwe, 2004. "Efficient computation of option price sensitivities for options of American style," CPQF Working Paper Series 1, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    • Handle: RePEc:zbw:cpqfwp:1
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    References listed on IDEAS

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    1. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
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    Cited by:

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    3. Boeing, Philipp & Mueller, Elisabeth & Sandner, Philipp, 2012. "What makes Chinese firms productive? Learning from indigenous and foreign sources of knowledge," Frankfurt School - Working Paper Series 196, Frankfurt School of Finance and Management.
    4. Michael, Fredrick, 2020. "Black–Scholes like closed form formulas and numerical solutions for American style options," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    5. Werner Hürlimann, 2012. "Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 171-202, November.
    6. Boenkost, Wolfram & Schmidt, Wolfgang M., 2004. "Cross currency swap valuation," CPQF Working Paper Series 2, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    7. Kostka, Genia & Moslener, Ulf & Andreas, Jan G., 2011. "Barriers to energy efficiency improvement: Empirical evidence from small-and-medium sized enterprises in China," Frankfurt School - Working Paper Series 178, Frankfurt School of Finance and Management.
    8. Alexander Libman & Vladimir Kozlov & André Schultz, 2012. "Roving Bandits in Action: Outside Option and Governmental Predation in Autocracies," Kyklos, Wiley Blackwell, vol. 65(4), pages 526-562, November.
    9. Yu, Xiaofan, 2011. "A spatial interpretation of the persistency of China's provincial inequality," Frankfurt School - Working Paper Series 171, Frankfurt School of Finance and Management.
    10. Becker, Christoph & Wystup, Uwe, 2005. "On the cost of delayed currency fixing announcements," CPQF Working Paper Series 3, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    11. Pier Giuseppe Giribone & Simone Ligato, 2016. "Flexible-forward pricing through Leisen–Reimer trees: Implementation and performance comparison with traditional Markov chains," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 1-21, June.
    12. Boenkost, Wolfram & Schmidt, Wolfgang M., 2006. "Interest rate convexity and the volatility smile," CPQF Working Paper Series 4, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    13. Böing, Philipp & Müller, Elisabeth, 2012. "Technological Capabilities of Chinese Enterprises: Who is Going to Compete Abroad?," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62081, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    American options; Greeks; Leisen-Reimer trees;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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