Abstract
The Black-Scholes formula Black and Scholes (1973) (BS hereafter) has remained a valuable tool for practitioners in pricing options as well as a precious benchmark for theoreticians. Indeed, the BS option valuation formula is a one-to-one function of the volatility parameter σ once the underlying stock level S t , the strike price K and the remaining time to expiration τ are known and fixed. Using the quoted prices of frequently traded option contracts on the same underlier, one can work out the implied volatility σ by inverting numerically the BS formula. But it is notorious that instead of being constant as assumed by the BS model, implied volatility has a stylized U-shape as it varies across different maturities and strike prices. This pattern called the “smile effect” is the starting point of the implied theories which we concentrate on thereafter.
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Sylla, A., Villa, C. (2000). Measuring Implied Volatility Surface Risk using Principal Components Analysis. In: Franke, J., Stahl, G., Härdle, W. (eds) Measuring Risk in Complex Stochastic Systems. Lecture Notes in Statistics, vol 147. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1214-0_8
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DOI: https://doi.org/10.1007/978-1-4612-1214-0_8
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