Black_Scholes_assmt

Black_Scholes_assmt - U NIVERSITY OF E SSEX D EPARTMENT OF...

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UNIVERSITY OF ESSEX DEPARTMENT OF ECONOMICS EC372 Economics of Bond and Derivatives Markets Empirical testing of the Black-Scholes Model The Black-Scholes model should, in principle, be straightforward to apply empirically because – unlike many models in economics – it makes an unambiguous prediction: the Black-Scholes for- mula. One of the applications is to test the theory, i.e. to investigate how well empirical evidence (observed option prices) match up with the model’s predictions (the option price generated by the Black-Scholes formula). 1 Critical evaluation of any model can follow several routes, including: 1. Theoretical – are the assumptions of the theorem plausible (sensible, or reasonable, or justifi- able, or acceptable)? In the Black-Scholes model, the assumptions most commonly examined are: (i) geometric Brownian motion (gBm) of underlying asset prices; and (ii) frictionless mar- kets. Other assumptions limit the scope of the model, in particular (i) European style options; (ii) no dividend paid during the life of the option; (iii) protection against stock-splits (and other variations in the definition of the underlying asset). In some cases, it is possible to obtain empirical evidence directly about the assumptions but this is not required for testing the Black-Scholes model – just test its predictions. 2. Logical coherence – do the predictions of the model follow from its assumptions? Following several decades of analysis, this is not an issue in the Black-Scholes model: no one denies that the formula can indeed be derived from the assumptions (though some textbook expositions are untrustworthy). 3.
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This note was uploaded on 03/15/2012 for the course EC 372 taught by Professor R.e.bailey during the Spring '12 term at Uni. Essex.

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Black_Scholes_assmt - U NIVERSITY OF E SSEX D EPARTMENT OF...

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