{"product_id":"9783642103940","title":"Springer Finance: A New Look at Generalized Black-Scholes Formulae","description":"\u003ch1\u003eSpringer Finance: A New Look at Generalized Black-Scholes Formulae\u003c\/h1\u003e \u003ch2\u003eProfeta, Christophe; Roynette, Bernard; Yor, Marc\u003c\/h2\u003e \u003cp\u003eDiscovered 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 ? ?\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2010-02-12\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783642103940\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-642-10395-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 270\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44481726349452,"sku":"9783642103940","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783642103940.jpg?v=1775734771","url":"https:\/\/lateknightbooks.com\/products\/9783642103940","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}