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Zbl 0982.60028
Jourdain, Benjamin; Martini, Claude
American prices embedded in European prices. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No.1, 1-17 (2001). ISSN 0294-1449

The authors analyze, in a Black-Scholes framework, relations between American options prices and European options prices. They exhibit a large class of payoffs $\psi$ for which the American option price $v^{\text{am}}_\psi(t, x)= \sup_{\tau\in{\cal T}} (0; t)$ has a closed-form expression. The main theorem is Theorem 3. Let $\widehat\varphi(x)= \inf_{t\ge 0} v_\varphi(t, x)$ where $v_\varphi(t, x)$ is the European option price for a payoff $\varphi$. Theorem 3 gives conditions on $\widehat\varphi$ to insure that $v^{\text{am}}_{\widehat\varphi}(t, x)= v_\varphi(t\vee\widehat t(x), x)$ where $\widehat t$ has to verify $v_\varphi(\widehat t(x), x)= \widehat\varphi(x)$. Examples verifying Theorem 3 hypotheses are given.
[A.Grorud (Marseille)]

MSC 2000:: *60G40 Optimal stopping
60G46 Martingales and classical analysis
91B70 Stochastic models
91B28 Finance etc.

Keywords: American options; Black-Scholes framework; derivatives

Cited in: Zbl 1033.60051

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