Explicit Formula for Conditional Expectations of Product of Polynomial and Exponential Function of Affine Transform of Extended Cox-Ingersoll-Ross Process

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

“…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.…”

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

“…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 .…”

“…In addition, the outcomes presented in [11] , [12] and Rujivan and Rakwongwan [12] show that the method proposed in [10] can be used for pricing variance swaps and volatility swaps. Thamrongrat and Rujivan [17] used the outcomes proposed in [13] to the pricing of interest rate swaps in terms of bond prices when the interest rate process follows the ECIR model (1.2) .…”

“…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.…”

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

“…In this part of dissertation, we provide an extension of the recent results given by Sutthimat et al [72] and propose an analytical formula for a conditional expectation of a path-dependent product of polynomial and exponential functions described in the form…”