Option Prices as Probabilities is popular PDF and ePub book, written by Christophe Profeta in 2010-01-26, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Option Prices as Probabilities can be Read Online from any device for your convenience.
Option Prices as Probabilities Book PDF Summary
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 ? ?
Detail Book of Option Prices as Probabilities PDF
- Author : Christophe Profeta
- Release : 26 January 2010
- Publisher : Springer Science & Business Media
- ISBN : 9783642103957
- Genre : Mathematics
- Total Page : 282 pages
- Language : English
- PDF File Size : 11,9 Mb
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