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CATEGORIES:Statistics
SUMMARY:Jump Telegraph Processes and a Volatility Smile -
Nikita Ratanov (University of Rosario\, Bogota)
DTSTART;TZID=Europe/London:20071012T153000
DTEND;TZID=Europe/London:20071012T163000
UID:TALK8637AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/8637
DESCRIPTION:We discuss a simple class of financial market mode
ls based on inhomogeneous telegraph processes. Thi
s model capture bullish and bearish trends as well
as oversold/overbought market situations. The mod
el under consideration is arbitrage-free if direct
ions of jumps in stock prices are in a certain cor
respondence with their current velocity and intere
st rate behaviour. In the simplest case the model
is complete. Diffusion rescaling of this model giv
es a natural representation of volatility. We prov
ide explicit formulae for prices of standard Europ
ean options are obtained\, which permits to calcul
ate directly implied volatilities with respect to
various moneyness and maturity times of the option
.\n\n This model has a Markov-modulated implied\nv
olatility surface (see A.Jobert\, L.C.G. Rogers\,
Option pricing with Markov-modulated dynamics). It
gives an example of the implied volatility surfac
e\, which does not move by parallel shifts and whi
ch is based ona process different from exponential
Levy (see L.C.G. Rogers\, M.R.Tehranchi\, The imp
lied volatility surface does not move by parallel
shifts.)\n\n\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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