A closed-form expansion for the conditional expectations of the extended CIR process. Issue 10 (October 2022)

• Record Type: Journal Article
• Authors: Rujivan, Sanae; Thamrongrat, Nopporn
• Is Part Of: Heliyon. Volume 8:Issue 10(2022)
• Publication Date: 2022-10
• Subjects: ECIR process -- Conditional expectation -- Closed-form expansion -- Piecewise smooth function; Research -- Periodicals; Medical sciences -- Periodicals; Natural history -- Periodicals; Social sciences -- Periodicals; Earth sciences -- Periodicals; Physical sciences -- Periodicals; 507.2
• DOI: 10.1016/j.heliyon.2022.e11068
• Languages: English
• ISSNs: 2405-8440

Abstract

Abstract: This paper derives a closed-form expansion for the conditional expectation of a continuous-time stochastic process, given by V t, T : = e − ∫ t T g ( v s ) d s f ( v T ) for 0 ≤ t ≤ T, where v t evolves according to the extended Cox-Ingersoll-Ross process, for any C ∞ functions f and g . We apply the Feynman-Kac theorem to state a Cauchy problem associated with V t, T and solve the problem by using the reduction method. Furthermore, we extend our method to any piecewise C ∞ function f ; demonstrating our method can be applied to price options in financial derivative markets. In numerical study, we employ Monte Carlo simulations to demonstrate the performance of the current method. Abstract : ECIR process; Conditional expectation; Closed-form expansion; Piecewise smooth function