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Simple Formulas to Option Pricing and Hedging in the Black- Scholes Model

Paolo Pianca

Finance from University Library of Munich, Germany

Abstract: For option whose striking price equals the forward price of the underlying asset, the Black-Scholes pricing formula can be approximated in closed-form. A interesting result is that the derived equation is not only very simple in structure but also that it can be immediately inverted to obtain an explicit formula for implied volatility. In this contribution we present and compare the accuracy of three of such approximation formulas. The numerical analysis shows that the first order approximations are close only for small maturities, Polya approximations are remarkably accurate for a very large range of parameters, while logistic values are the most accurate only for extreme maturities.

Keywords: Option pricing; hedging; Taylor, Polya and logistic approximations (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fin
Date: 2005-11-15
Note: Type of Document - pdf; pages: 9
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