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.
Publié le : 2003-10-14
Classification:
Analytic sets,
coherent measures of risk,
conservative delta hedging,
incompleteness,
prediction,
statistical uncertainty,
value at risk,
62F25,
62G15,
62P05,
60G44,
62M99
@article{1065705113,
author = {Mykland, Per Aslak},
title = {Financial options and statistical prediction intervals},
journal = {Ann. Statist.},
volume = {31},
number = {1},
year = {2003},
pages = { 1413-1438},
language = {en},
url = {http://dml.mathdoc.fr/item/1065705113}
}
Mykland, Per Aslak. Financial options and statistical prediction intervals. Ann. Statist., Tome 31 (2003) no. 1, pp. 1413-1438. http://gdmltest.u-ga.fr/item/1065705113/