On prices' evolutions based on geometric telegrapher's process

Crescenzo, Antonio Di; Pellerey, Franco

doi:10.1002/asmb.456

Cited by 57 publications

(37 citation statements)

References 13 publications

(25 reference statements)

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“…However, a 'telegraph analog' of the Black-Scholes model was considered by, e.g. Di Crescenzo and Pellerey [2] and Pogorui and Rodríguez-Dagnino [14]. It should be noted that the asset pricing models proposed in the above works are based on pure telegraph processes without jump components.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Option Pricing Driven by a Telegraph Process with Random Jumps

López¹,

Ratanov²

2012

J. Appl. Probab.

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“…Many authors analyzed over the years the telegraph process, see for example Orsingher (1985Orsingher ( , 1990, Foong and Kanno (1994), Stadje and Zacks (2004). Di Crescenzo and Pellerey (2002) proposed the geometric telegraph process as a model to describe the dynamics of the price of risky assets S(t). In the Black-Scholes (1973) -Merton (1973) model the process S(t) is described by means of geometric Brownian motion S(t) = s 0 exp{αt + σW (t)}, t > 0.…”

Section: Introductionmentioning

confidence: 99%

Parametric Estimation for the Standard and Geometric Telegraph Process Observed at Discrete Times

Iacus

Gregorio

2006

SSRN Journal

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The telegraph process X(t), t > 0, (Goldstein, 1951) and the geometric telegraph process S(t) = s 0 exp{(µ− 1 2 σ 2 )t+σX(t)} with µ a known constant and σ > 0 a parameter are supposed to be observed at n+1 equidistant time points t i = i∆ n , i = 0, 1, . . . , n. For both models λ, the underlying rate of the Poisson process, is a parameter to be estimated. In the geometric case, also σ > 0 has to be estimated. We propose different estimators of the parameters and we investigate their performance under the high frequency asymptotics, i.e. ∆ n → 0, n∆ = T < ∞ as n → ∞, with T > 0 fixed. The process X(t) in non markovian, non stationary and not ergodic thus we use approximation arguments to derive estimators. Given the complexity of the equations involved only estimators on the first model can be studied analytically. Therefore, we run an extensive Monte Carlo analysis to study the performance of the proposed estimators also for small sample size n. key words: telegraph process, discretely observed process, inference for stochastic processes.MSC: primary 60K99; secondary 62M99

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“…Many authors analyzed over the years the telegraph process, see for example Orsingher (1990Orsingher ( , 1995, Foong and Kanno (1994), Stadje and Zacks (2004). Di Crescenzo and Pellerey (2002) proposed the geometric telegraph process as a model to describe the dynamics of the price of risky assets S(t). In the Black-Scholes (1973) -Merton (1973 model the process S(t) is described by means of geometric Brownian motion S(t) = s 0 exp{αt + σ W (t)}, t ≥ 0.…”

mentioning

confidence: 99%

“…Di Crescenzo and Pellerey (2002) assume that S(t) evolves in time according to the following process…”

mentioning

confidence: 99%

Parametric estimation for the standard and geometric telegraph process observed at discrete times

Gregorio

Iacus

2007

Stat Infer Stoch Process

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The telegraph process X(t), t ≥ 0, (Goldstein, Q J Mech Appl Math 4:129-156, 1951) and the geometric telegraph process S(t) = s0 exp{μ -1/2σ2)t + σ X(t)}with μ a known real constant and σ > 0 a parameter are supposed to be observed at n + 1 equidistant time points t i = iΔ n ,i = 0,1,..., n. For both models λ, the underlying rate of the Poisson process, is a parameter to be estimated. In the geometric case, also σ > 0 has to be estimated. We propose different estimators of the parameters and we investigate their performance under the asymptotics, i.e. Δ n → 0, nΔ n = T < ∞ as n → ∞, with T > 0 fixed. The process X(t) in non markovian, non stationary and not ergodic thus we build a contrast function to derive an estimator. Given the complexity of the equations involved only estimators on the first model can be studied analytically. Therefore, we run an extensive Monte Carlo analysis to study the performance of the proposed estimators also for small sample size n. © 2007 Springer Science+Business Media B.V

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On prices' evolutions based on geometric telegrapher's process

Cited by 57 publications

References 13 publications

Option Pricing Driven by a Telegraph Process with Random Jumps

Option Pricing Driven by a Telegraph Process with Random Jumps

Parametric Estimation for the Standard and Geometric Telegraph Process Observed at Discrete Times

Parametric estimation for the standard and geometric telegraph process observed at discrete times

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