Taylor, Black and Scholes: Series Approximations and Risk Management Pitfalls

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Research Papers

Taylor, Black and Scholes: Series Approximations and Risk Management Pitfalls

March 1995 Number 9501

Author: Arturo Estrella

Risk managers make frequent use of finite Taylor approximations to option pricing formulas, particularly of first and second order (delta and gamma). This paper shows that for a plausible range of parameter values, the Taylor series for the Black-Scholes formula diverges. Using a numerical technique developed in the paper, it is also shown that even when the series converges, finite approximations of very large order are generally necessary to achieve acceptable levels of accuracy. Implications for risk management and stress testing are discussed.

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33 pages / 970 kb

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