The Economic Plausibility of Strict Local Martingales in Financial Modelling
AbstractThe context for this article is a continuous financial market consisting of a risk-free savings account and a single non-dividend-paying risky security. We present two concrete models for this market, in which strict local martingales play decisive roles. The first admits an equivalent risk-neutral probability measure under which the discounted price of the risky security is a strict local martingale, while the second model does not even admit an equivalent risk-neutral probability measure, since the putative density process for such a measure is itself a strict local martingale. We highlight a number of apparent anomalies associated with both models that may offend the sensibilities of the classically-educated reader. However, we also demonstrate that these issues are easily resolved if one thinks economically about the models in the right way. In particular, we argue that there is nothing inherently objectionable about either model.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 279.
Date of creation: 01 Jun 2010
Date of revision:
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strict local martingales; a rbitrage; Bessel processes; stock price bubbles; bond price bubbles; risk-neutral pricing; real-world pricing; hedging portfolios; replicating portfolios; put-call parity;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-07-24 (All new papers)
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- Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.
- Johannes Ruf & Wolfgang Runggaldier, 2013. "A Systematic Approach to Constructing Market Models With Arbitrage," Papers 1309.1988, arXiv.org, revised Dec 2013.
- Claudio Fontana & Wolfgang J. Runggaldier, 2012. "Diffusion-based models for financial markets without martingale measures," Papers 1209.4449, arXiv.org, revised Feb 2013.
- Constantinos Kardaras, 2012. "Valuation and parity formulas for exchange options," Papers 1206.3220, arXiv.org.
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