Option prices as probabilities |
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| Affiliation: | 1. Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA;2. Université Henri Poincaré, Institut Elie Cartan, BP239, F-54506 Vandoeuvre-les-Nancy Cedex, France;3. Laboratoire de Probabilités et Modèles Aléatoires, Universités Paris VI et VII, 4 Place Jussieu-Case 188, F-75252 Paris Cedex 05, France;1. Department of Economics, Brown University, 64 Waterman Street, Providence RI 02912, USA;2. Department of Finance, The University of Melbourne, 198 Berkeley Street, Carlton VIC 3010, Australia;3. Econometrics and Finance Group, Netspar, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands;1. Department of Economics, University of Bologna, piazza Scaravilli n.2, I-40126 Bologna, Italy;2. Business School, Edge Hill University, St Helens Road, Ormskirk, Lancashire L39 4QP, United Kingdom;3. Department of Economics, University of Guelph, Guelph, Ontario N1G 2W1, Canada |
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| Abstract: | Four distribution functions are associated with call and put prices seen as functions of their strike and maturity. The random variables associated with these distributions are identified when the process for moneyness defined as the stock price relative to the forward price is a positive local martingale with no positive jumps that tends to zero at infinity. Results on calls require moneyness to be a continuous martingale as well. It is shown that for puts the distributions in the strike are those for the remaining supremum while for calls, they relate to the remaining infimum. In maturity we see the distribution functions for the last passage times of moneyness to strike. |
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