Analytical formula for conditional expectations of path-dependent product of polynomial and exponential functions of extended Cox–Ingersoll–Ross process

Sutthimat, Phiraphat; Rujivan, Sanae; Mekchay, Khamron; Rakwongwan, Udomsak

doi:10.1007/s40687-021-00309-9

Cited by 10 publications

(6 citation statements)

References 21 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%

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%

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

2022

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“…Rujivan [10] developed a different method from the one proposed in [2] to obtain an exact formula for the ECIR processes (1.2) for any

. Sutthimat et al [13] , [14] applied Rujivan's [10] method to path-dependent product of polynomial and exponential functions. Thamrongrat and Rujivan [16] derived an exact formula for the case

for any

to compute a conditional expectation of the form:

for any integrable function r .…”

Section: Introductionmentioning

confidence: 99%

“…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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“…The motivation of the expressing form for the conditional moments is similar to that presented in [13,32,61,71,74].…”

Section: Resultsmentioning

confidence: 94%

“…, t m , as described in (1.8), for valuation of IRS described above or some other financial products having similar behaviour as IRS. The study of this work is described in Chapter 4 which is published in Research in the Mathematical Sciences, see [74].…”

Section: Interest Rate Swap Pricing By Using Ecir Processmentioning

confidence: 99%

Closed-form formulas for conditional moments of generalized cox-ingersoll-ross processes

Sutthimat

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Cox-Ingersoll-Ross (CIR) process, introduced in 1985, is a one factor model used to describe the evolution of interest rate and pricing the financial derivatives. It was later extended to have time-dependent parameters called the extended CIR (ECIR) process, which is more widely studied and used in a variety of applications. The generalized versions of CIR process are also studied and investigated for more applications in finance. However,� most of these applications rely on the knowledge and properties of conditional expectations and moments, which most of them are not yet fully developed into closed form. In this work, we propose closed-form formulas derived from applying the Feynman--Kac representation for the two generalized CIR processes: the nonlinear drift constant elasticity of variance and the Pearson diffusions which are developed from the ECIR process, as well as further study of their properties such as variance and conditional mixed moments. In addition, we also extending the result of ECIR process by applying it for valuation of interest rate swaps. The formulas derived in this work are numerically verified and validated� based on the Monte-Carlo simulations.�

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Analytical formula for conditional expectations of path-dependent product of polynomial and exponential functions of extended Cox–Ingersoll–Ross process

Cited by 10 publications

References 21 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

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

Closed-form formulas for conditional moments of generalized cox-ingersoll-ross processes

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