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Telegraph Processes and Option PricingAsymmetric Jump-Telegraph Processes

Telegraph Processes and Option Pricing: Asymmetric Jump-Telegraph Processes [In this chapter we examine the more general jump-telegraph process with alternating velocities and alternating transition intensities in the presence of deterministic jumps at random time instants. The existence of the unique martingale measure is very important for financial modelling. Exploiting the analogue of Doob-Meyer decomposition (see e.g. [1]) we characterise the martingales based on the telegraph processes with jumps. A version of Girsanov’s Theorem for jump-telegraph processes is obtained as well. The explicit formulae for the moments of the asymmetric telegraph process are also derived.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Telegraph Processes and Option PricingAsymmetric Jump-Telegraph Processes

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Publisher
Springer Berlin Heidelberg
Copyright
© The Author(s) 2013
ISBN
978-3-642-40525-9
Pages
69 –88
DOI
10.1007/978-3-642-40526-6_4
Publisher site
See Chapter on Publisher Site

Abstract

[In this chapter we examine the more general jump-telegraph process with alternating velocities and alternating transition intensities in the presence of deterministic jumps at random time instants. The existence of the unique martingale measure is very important for financial modelling. Exploiting the analogue of Doob-Meyer decomposition (see e.g. [1]) we characterise the martingales based on the telegraph processes with jumps. A version of Girsanov’s Theorem for jump-telegraph processes is obtained as well. The explicit formulae for the moments of the asymmetric telegraph process are also derived.]

Published: Oct 18, 2013

Keywords: Jump-telegraph process; Expectations; Variances; Moments; Martingales; Girsanov’s Theorem

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