Statistical Inference for Partially Observed Markov-Modulated Diffusion Risk Model

Baltazar-Larios, Fernando; Esparza, Luz Judith R.

doi:10.1007/s11009-022-09932-7

Cited by 1 publication

(3 citation statements)

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“…3: E-step Using X c , we compute the corresponding statistics Nij and Ri for all i, j ∈ E in time interval [0, T ]. 4: M-step The MLEs of qij (see [2]) are given by…”

Section: Mle Of Qmentioning

confidence: 99%

“…In 1976, Merton [16] proposed a JDM for asset pricing to incorporate rare and abrupt changes in the values of {S t } t≥0 . The JDM adds, to the GBM, a compound Poisson process where jumps are independent and identically distributed; see equation (2) for a detailed definition. In Merton's model the logarithm of a jump is normally distributed [16], which renders some computations relatively easier.…”

Section: Introductionmentioning

confidence: 99%

“…Inference, when there are two states in the underlying MJP, was presented in [8]. Likelihood based estimation (including Bayesian) for MMJDM in risk theory has been investigated by [1] and [2]. Our main contribution is Section 3, where we present a methodology for the inference of the MMJDM for the general case with m ∈ N states and Laplace distribution for the logarithm of each jump; see Section 2 for a detailed definition.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Maximum Likelihood Estimation for a Markov-Modulated Jump-Diffusion Model

Reynoso¹,

Baltazar-Larios²,

Eslava³

2022

Interdisciplinary Statistics in Mexico

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We propose a method for obtaining maximum likelihood estimates (MLEs) of a Markov-Modulated Jump-Diffusion Model (MMJDM) when the data is a discrete time sample of the diffusion process, the jumps follow a Laplace distribution, and the parameters of the diffusion are controlled by a Markov Jump Process (MJP). The data can be viewed as incomplete observation of a model with a tractable likelihood function. Therefore we use the EM-algorithm to obtain MLEs of the parameters. We validate our method with simulated data. The motivation for obtaining estimates of this model is that stock prices have distinct drift and volatility at distinct periods of time. The assumption is that these phases are modulated by macroeconomic environments whose changes are given by discontinuities or jumps in prices. This model improves on the stock prices representation of classical models such as the model of Black and Scholes or Merton's Jump-Diffusion Model (JDM). We fit the model to the stock prices of Amazon and Netflix during a 15-years period and use our method to estimate the MLEs.

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“…3: E-step Using X c , we compute the corresponding statistics Nij and Ri for all i, j ∈ E in time interval [0, T ]. 4: M-step The MLEs of qij (see [2]) are given by…”

Section: Mle Of Qmentioning

confidence: 99%