| Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae Contributor(s): Profeta, Christophe (Author), Roynette, Bernard (Author), Yor, Marc (Author) |
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ISBN: 3642103944 ISBN-13: 9783642103940 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: March 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Applied - Mathematics | Probability & Statistics - General - Business & Economics | Finance - General |
| Dewey: 519.5 |
| Series: Springer Finance |
| Physical Information: 0.7" H x 6" W x 9" (0.90 lbs) 270 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B, t? 0; F, t? 0, P) - t t note a standard Brownian motion with B = 0, (F, t? 0) being its natural ?ltra- 0 t t tion. Let E: = exp B?, t? 0 denote the exponential martingale associated t t 2 to (B, t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t): =E (K?E ) (0.1) K t and + C (t): =E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x): = e dy. (0.3) 2? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN: K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ? |