Abstract
In a viable single-period model with one stock and k ≥ 2 scenarios the completeness of the market is equivalent to the uniqueness of the risk neutral probability; this equivalence allows to price every derivative security with a unique fair price. When the market is incomplete, the set of all possible risk neutral probabilities is not a singleton and for every non attainable derivative security we have a bid-ask interval of possible prices. In literature, different methods have been proposed in order to select a unique risk neutral probability starting with the real world probability p. Contrary to the complete case, in all these models \(\textbf{p}\) is really used for the option pricing and its elicitation is a crucial point for every criterion used to select a risk neutral probability. We propose a method for the valuation problem in incomplete markets which can be used when p is a partial conditional probability assessment as well as when we have different expert opinions expressed through conditional probability assessments. In fact, it is not always possible to elicit a probability distribution p over all the possible states of the world: the information that we have could be partial, conditional or even not coherent. Therefore we will select a risk neutral probability by minimizing a discrepancy measure introduced in [2] and analized in [3] between p and the set of all possible risk neutral probability, where p can be a partial conditional probability assessments or it can be given by the fusion of different expert opinions.
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References
Bingham, N.H., Kiesel, R.: Risk-Neutral Valuation: pricing and hedging of financial derivatives. Springer, London (2004)
Capotorti, A., Regoli, G.: Coherent correction of inconsistent conditional probability assessments. In: Proc. of IPMU 2008, Malaga (Es) (2008)
Capotorti, A., Regoli, G., Vattari, F.: Theoretical properties of a discrepancy measure among partial conditional probability assessments. Submitted to International Journal of Approximate Reasoning (to appear)
Capotorti, A., Regoli, G., Vattari, F.: On the use of a new discrepancy measure to correct incoherent assessments and to aggregate conflicting opinions based on imprecise conditional probabilities. In: Proc. of ISIPTA 2009, Durham (UK) (2009)
Capotorti, A., Regoli, G., Vattari, F.: Merging different probabilistic information sources through a new discrepancy measure. In: Proc. of WUPES 2009, Liblice (CR) (2009)
Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting. Trends in Logic. Kluwer, Dordrecht (2002)
Elliot, R.J., Kopp, P.E.: Mathematics of Financial Markets. Springer Finance, New York (2005)
Follmer, H., Schied, A.: Stochastic Finance: an introduction in discrete time. Walter de Gruyter, Berlin (2004)
Follmer, H., Sondermann, D.: Hedging of Non-Redundant Contingent Claim. In: Contributions to Mathematical Economics. Elsevier Science Publishers, Amsterdam (1986)
Frittelli, M.: The minimal entropy martingale measure and the valuation problem in incomplete markets. Mathematical Finance 10, 39–52 (2000)
Lad, F.: Operational Subjective Statistical Methods: a mathematical, philosophical, and historical introduction. John Wiley, New York (1996)
Musiela, M., Rutkowski, M.: Martingale Methods in Financial Modelling. Springer, New York (2005)
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Capotorti, A., Regoli, G., Vattari, F. (2010). Risk Neutral Valuations Based on Partial Probabilistic Information. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2010. Communications in Computer and Information Science, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14058-7_19
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DOI: https://doi.org/10.1007/978-3-642-14058-7_19
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