Abstract
A common problem is to choose a “risk-neutral” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure” by completing the market with option prices. We do this by modeling the behavior of the stock price X, together with the behavior of the option prices for a relevant family of options which are (or can theoretically be) effectively traded. In doing so, we need to ensure a kind of “compatibility” between X and the prices of our options, and this poses some significant mathematical difficulties.
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Supported in part by NSF grant DMS-0604020 and NSA grant H98230-06-1-0079.
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Jacod, J., Protter, P. Risk-neutral compatibility with option prices. Finance Stoch 14, 285–315 (2010). https://doi.org/10.1007/s00780-009-0109-9
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DOI: https://doi.org/10.1007/s00780-009-0109-9