Alpha-CIR model with branching processes in sovereign interest rate modeling

Jiao, Ying; Ma, Chunhua; Scotti, Simone

doi:10.1007/s00780-017-0333-7

Cited by 56 publications

(47 citation statements)

References 32 publications

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“…The asymptotic behavior of the estimators of the parameters in the CIR-model was studied by Overbeck and Rydén (1997). In the general case, the solution to (8.12) is called a α-stable Cox-Ingersoll-Ross model (α-stable CIR-model); see, e.g., Jiao et al (2017) and Li and Ma (2015).…”

Section: )mentioning

confidence: 99%

Continuous-State Branching Processes with Immigration

2020

Mathematical Lectures From Peking University

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Section: )mentioning

confidence: 99%

Continuous-State Branching Processes with Immigration

2020

Mathematical Lectures From Peking University

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“…Handa [9] considers ergodic properties of the CIR model driven by stable processes without Markov switching. Very recently, Jiao, Ma and Scotti [10] obtain an explicit formula for the bond price and some distributions for large jumps of the model (3) with n = 1. Besides, they also show the ergodicity of this model and present the Laplace transform of the stationary distribution.…”

Section: Zhenzhong Zhang Enhua Zhang and Jinying Tongmentioning

confidence: 99%

Necessary and sufficient conditions for ergodicity of CIR model driven by stable processes with Markov switching

Zhang¹,

Zhang²,

Tong³

2018

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, we consider long time behavior of the Cox-Ingersoll-Ross (CIR) interest rate model driven by stable processes with Markov switching. Under some assumptions, we prove an ergodicity-transience dichotomy, namely, the interest rate process is either ergodic or transient. The sufficient and necessary conditions for ergodicity and transience of such interest model are given under some assumptions. Finally, an application to interval estimation of the interest rate processes is presented to illustrate our results.

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“…The clustering effect of jumps of the Hawkes [ 33 ] process is well suited to take into account the periods of turmoil in the implied volatility, typically observed in implied volatility indices. These clustering features have been studied throughout various financial asset models: see Fiura [ 28 ] for FX rates, Hainaut [ 32 ] and Jiao et al [ 39 ] for interest rates, Abergel and Jedidi [ 1 ], Horst and Xu [ 36 ], Zheng et al[ 61 ] for microstructure and limit order books, Errais et al [ 25 ] for credit risk, Jiao et al [ 40 ] for energy prices and Granelli and Veraart [ 30 ] for risk premium and contagion. In this paper, we shall insist on the stylized facts related to the clustering effects of the implied volatility indices, such as VIX index, and the related options.…”

Section: Introductionmentioning

confidence: 99%

“…Corollary 2 (Ergodic distribution) Under Assumption 1, the intensity process λ is exponential ergodic and the moment generating function of the invariant distribution is given byE e wλ ∞ = e λw 1 The variance process σ 2 is also exponential ergodic with a Gamma invariant law with the same parameters and no shift. According to Jiao et al[39, Proposition 3.7], we have to compute E e wλ ∞ = exp…”

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A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process

Bernis¹,

Brignone

Scotti

et al. 2021

Math Finan Econ

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We propose an extension of the $$\Gamma $$ Γ -OU Barndorff-Nielsen and Shephard model taking into account jump clustering phenomena. We assume that the intensity process of the Hawkes driver coincides, up to a constant, with the variance process. By applying the theory of continuous-state branching processes with immigration, we prove existence and uniqueness of strong solutions of the SDE governing the asset price dynamics. We propose a measure change of self-exciting Esscher type in order to describe the relation between the risk-neutral and the historical dynamics, showing that the $$\Gamma $$ Γ -OU Hawkes framework is stable under this probability change. By exploiting the affine features of the model we provide an explicit form for the Laplace transform of the asset log-return, for its quadratic variation and for the ergodic distribution of the variance process. We show that the proposed model exhibits a larger flexibility in comparison with the $$\Gamma $$ Γ -OU model, in spite of the same number of parameters required. We calibrate the model on market vanilla option prices via characteristic function inversion techniques, we study the price sensitivities and propose an exact simulation scheme. The main financial achievement is that implied volatility of options written on VIX is upward shaped due to the self-exciting property of Hawkes processes, in contrast with the usual downward slope exhibited by the $$\Gamma $$ Γ -OU Barndorff-Nielsen and Shephard model.

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Alpha-CIR model with branching processes in sovereign interest rate modeling

Cited by 56 publications

References 32 publications

Continuous-State Branching Processes with Immigration

Continuous-State Branching Processes with Immigration

Necessary and sufficient conditions for ergodicity of CIR model driven by stable processes with Markov switching

A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process

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