Short Positions, Rally Fears and Option Markets

23 Pages Posted: 28 Jan 2010 Last revised: 13 May 2010

See all articles by Ernst Eberlein

Ernst Eberlein

University of Freiburg

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: July 26, 2009

Abstract

Index option pricing on world market indices are investigated using Lévy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a Rally Before a Crash (RBC). Three models are used to effectively calibrate index options at an annual maturity and it is observed that positive jumps may be needed for FTSE, N225 and HSI. RBC probabilities are shown to have fallen by 10 points after July 2007. Typical implied volatility curves for such models are also described and illustrated. They have smirks and never smile.

Keywords: U-shaped measure change, Spectrally Negative Process, Scale Functions

JEL Classification: G1, G12, G13

Suggested Citation

Eberlein, Ernst and Madan, Dilip B., Short Positions, Rally Fears and Option Markets (July 26, 2009). Robert H. Smith School Research Paper No. RHS 06-120, Available at SSRN: https://ssrn.com/abstract=1540817 or http://dx.doi.org/10.2139/ssrn.1540817

Ernst Eberlein

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
++49 761 203 5661 (Fax)

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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