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SUMMARY:Jump Telegraph Processes and a Volatility Smile - Nikita Ratanov (
 University of Rosario\, Bogota)
DTSTART:20071012T143000Z
DTEND:20071012T153000Z
UID:TALK8637@talks.cam.ac.uk
CONTACT:6845
DESCRIPTION:We discuss a simple class of financial market models based on 
 inhomogeneous telegraph processes. This model capture bullish and bearish 
 trends as well as oversold/overbought market situations. The model under c
 onsideration is arbitrage-free if directions of jumps in stock prices are 
 in a certain correspondence with their current velocity and interest rate 
 behaviour. In the simplest case the model is complete. Diffusion rescaling
  of this model gives a natural representation of volatility. We provide ex
 plicit formulae for prices of standard European options are obtained\, whi
 ch permits to calculate directly implied volatilities with respect to vari
 ous moneyness and maturity times of the option.\n\n This model has a Marko
 v-modulated implied\nvolatility surface (see A.Jobert\, L.C.G. Rogers\, Op
 tion pricing with Markov-modulated dynamics). It gives an example of the i
 mplied volatility surface\, 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 implied volatility surface does not move by paralle
 l shifts.)\n\n\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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