A jump telegraph model for option pricing

Ratanov, Nikita

doi:10.1080/14697680600991226

Cited by 64 publications

(71 citation statements)

References 17 publications

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“…The exact forms of the distribution densities p i (x, t) (with deterministic jump values) and the expectations m i (t) of the jump-telegraph processes are known; see [15].…”

Section: Corollary 21 the Set Of Equations (25) Is Equivalent To Tmentioning

confidence: 99%

Option Pricing Driven by a Telegraph Process with Random Jumps

López¹,

Ratanov²

2012

J. Appl. Probab.

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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.

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“…The exact forms of the distribution densities p i (x, t) (with deterministic jump values) and the expectations m i (t) of the jump-telegraph processes are known; see [15].…”

Section: Corollary 21 the Set Of Equations (25) Is Equivalent To Tmentioning

confidence: 99%

Option Pricing Driven by a Telegraph Process with Random Jumps

López¹,

Ratanov²

2012

J. Appl. Probab.

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“…In the framework of this model, option pricing formulae and hedging strategies are completely constructed (see [17,16]). The arbitrage-free price c of a call option with expiry payoff (S(T) − K) + can be calculated by the formula c = c s = S 0 u s y,T; λ ± ,0 − Ku s y,T; λ * ± ,r ± , s = ±, (3.12) where…”

Section: Market Model Based On Jump Telegraph Processesmentioning

confidence: 99%

Jump Telegraph Processes and Financial Markets with Memory

Ratanov

2007

Journal of Applied Mathematics and Stochastic Analysis

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The paper develops a new class of financial market models. These models are based on generalized telegraph processes with alternating velocities and jumps occurring at switching velocities. The model under consideration is arbitrage-free and complete if the directions of jumps in stock prices are in a certain correspondence with their velocity and with the behaviour of the interest rate. A risk-neutral measure and arbitrage-free formulae for a standard call option are constructed. This model has some features of models with memory, but it is more simple.

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“…However, we are interested in a description of the process where jumps condense all the stochastic behaviour of the market, as in [17], what is not so usual in the literature. In fact, in some sense, our model is able to follow the opposite path: as we will show below, we can recover the Merton-Black-Scholes results for the Wiener process under certain limits.…”

Section: Introductionmentioning

confidence: 99%

Renewal Equations for Option Pricing

Montero

2007

SSRN Journal

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In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.

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A jump telegraph model for option pricing

Abstract: ABSTRACT

Cited by 64 publications

References 17 publications

Option Pricing Driven by a Telegraph Process with Random Jumps

Option Pricing Driven by a Telegraph Process with Random Jumps

Jump Telegraph Processes and Financial Markets with Memory

Renewal Equations for Option Pricing

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