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October 2003 Financial options and statistical prediction intervals
Per Aslak Mykland
Ann. Statist. 31(5): 1413-1438 (October 2003). DOI: 10.1214/aos/1065705113


The paper shows how to convert statistical prediction sets into worst case hedging strategies for derivative securities. The prediction sets can, in particular, be ones for volatilities and correlations of the underlying securities, and for interest rates. This permits a transfer of statistical conclusions into prices for options and similar financial instruments. A prime feature of our results is that one can construct the trading strategy as if the prediction set had a 100 % probability. If, in fact, the set has probability $1-\alpha$, the hedging strategy will work with at least the same probability. Different types of prediction regions are considered. The starting value $\A$ for the trading strategy corresponding to the $1-\alpha$ prediction region is a form of long term value at risk. At the same time, $\A$ is coherent.


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Per Aslak Mykland. "Financial options and statistical prediction intervals." Ann. Statist. 31 (5) 1413 - 1438, October 2003.


Published: October 2003
First available in Project Euclid: 9 October 2003

zbMATH: 1042.62094
MathSciNet: MR2012820
Digital Object Identifier: 10.1214/aos/1065705113

Primary: 62F25 , 62G15 , 62P05
Secondary: 60G44 , 62M99

Keywords: analytic sets , coherent measures of risk , conservative delta hedging , Incompleteness , prediction , statistical uncertainty , value at risk

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 5 • October 2003
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