Closed-form formula for conditional moments of generalized nonlinear drift CEV process

Sutthimat, Phiraphat; Mekchay, Khamron; Rujivan, Sanae

doi:10.1016/j.amc.2022.127213

Cited by 6 publications

(5 citation statements)

References 22 publications

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“…The key idea involves a system with a recurrence differential equation that brings about the PDE by involving an asymmetric matrix. The form of PDE's solution associated with the conditional moment ( 4) is a polynomial expression motivated by [16,17,[19][20][21][22][23][24]. Hence, we can solve its coefficients to obtain a closed-form formula directly.…”

Section: Resultsmentioning

confidence: 99%

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Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

2022

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The stochastic differential equation (SDE) has been used to model various phenomena and investigate their properties. Conditional moments of stochastic processes can be used to price financial derivatives whose payoffs depend on conditional moments of underlying assets. In general, the transition probability density function (PDF) of a stochastic process is often unavailable in closed form. Thus, the conditional moments, which can be directly computed by applying the transition PDFs, may be unavailable in closed form. In this work, we studied an inhomogeneous nonlinear drift constant elasticity of variance (IND-CEV) process, which is a class of diffusions that have time-dependent parameter functions; therefore, their sample paths are asymmetric. The closed-form formulas for conditional moments of the IND-CEV process were derived without having a condition on eigenfunctions or the transition PDF. The analytical results were examined through Monte Carlo simulations.

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Section: Resultsmentioning

confidence: 99%

“…The process r t in (2) is called an IND-CEV process. In addition, the SDE (2) is called the extended Cox-Ingersoll-Ross (ECIR) process when = 1; see for more details in [14][15][16][17]. From (2), if the parameters κ(t), θ(t) and σ(t) are constants written by κ, θ and σ, respectively, then the SDE (2) can be rewritten as:…”

Section: Ind-cev Processmentioning

confidence: 99%

Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

2022

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“…To date, the computation of the conditional moment has only been partially solved due to the unavailability of the transitional PDF. Indeed, the problem of computing the integral on the RHS of (37) with any stochastic differential equation (SDE) is typically addressed by the Feynman-Kac theorem, where the partial differential equation (PDE) is solved analytically, and some combinatorial techniques are used to simplify the system of recursive ordinary differential equations (ODEs) associated with the conditional moment; see, for instance, [38][39][40][41], for more details.…”

Section: Comparison With Other Formulasmentioning

confidence: 99%

Analytically Computing the Moments of a Conic Combination of Independent Noncentral Chi-Square Random Variables and Its Application for the Extended Cox–Ingersoll–Ross Process with Time-Varying Dimension

et al. 2023

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This paper focuses mainly on the problem of computing the γth, γ>0, moment of a random variable Yn:=∑i=1nαiXi in which the αi’s are positive real numbers and the Xi’s are independent and distributed according to noncentral chi-square distributions. Finding an analytical approach for solving such a problem has remained a challenge due to the lack of understanding of the probability distribution of Yn, especially when not all αi’s are equal. We analytically solve this problem by showing that the γth moment of Yn can be expressed in terms of generalized hypergeometric functions. Additionally, we extend our result to computing the γth moment of Yn when Xi is a combination of statistically independent Zi2 and Gi in which the Zi’s are distributed according to normal or Maxwell–Boltzmann distributions and the Gi’s are distributed according to gamma, Erlang, or exponential distributions. Our paper has an immediate application in interest rate modeling, where we can explicitly provide the exact transition probability density function of the extended Cox–Ingersoll–Ross (ECIR) process with time-varying dimension as well as the corresponding γth conditional moment. Finally, we conduct Monte Carlo simulations to demonstrate the accuracy and efficiency of our explicit formulas through several numerical tests.

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“…For a different framework from the ones proposed in [2] , [10] , [13] , [14] , [15] , [16] , [18] , this paper develops a method for obtaining a closed-form expansion of (1.4) for any

real-valued functions f and g . Utilizing the Feynman-Kac theorem [7] , we can state an initial value problem, i.e.…”

Section: Introductionmentioning

confidence: 99%

A closed-form expansion for the conditional expectations of the extended CIR process

Rujivan

Thamrongrat

2022

Heliyon

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Closed-form formula for conditional moments of generalized nonlinear drift CEV process

Cited by 6 publications

References 22 publications

Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

Analytically Computing the Moments of a Conic Combination of Independent Noncentral Chi-Square Random Variables and Its Application for the Extended Cox–Ingersoll–Ross Process with Time-Varying Dimension

A closed-form expansion for the conditional expectations of the extended CIR process

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