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Option Pricing Driven by a Telegraph Process with Random Jumps

Part of: Markov processes

Published online by Cambridge University Press:  04 February 2016

Oscar López  and
Nikita Ratanov
Oscar López*
Affiliation:
Universidad del Rosario
Nikita Ratanov*
Affiliation:
Universidad del Rosario
*
∗ Postal address: Universidad del Rosario, Calle 12c, No. 4-69, Bogotá, Colombia.
∗ Postal address: Universidad del Rosario, Calle 12c, No. 4-69, Bogotá, Colombia.
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Abstract

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In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies are switching. These models are typically incomplete, but the set of equivalent martingale measures can be described in detail. We provide additional suggestions which permit arbitrage-free option prices as well as hedging strategies to be obtained.

Keywords

Jump-telegraph processequivalent martingale measureoption pricinghedging

MSC classification

Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J75: Jump processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 838 - 849
Copyright
© Applied Probability Trust 

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