Abstract

This paper proposes an analytical formula for the conditional expectations of path-dependent product of polynomial and exponential function in the form of (∑j=0nλj(l)rtlj)e∑k=1mαk(l)rtkfor n, m∈ N, l= 1 , 2 ,.. , m, 0 ≤ t<inf>1</inf>< t<inf>2</inf>< ⋯ < t<inf>m</inf>= T< ∞ and λj(l),αk(l)∈R, where {rt}t∈[0,T] corresponds to the extended Cox–Ingersoll–Ross (ECIR) process. The validation of the analytical formula is illustrated for several examples by comparing the results from the formula with those from Monte Carlo (MC) simulations. The efficiency of the formula is also presented via the computational run-times as compared with MC simulation. Moreover, the application of the analytical formula of this work is demonstrated for pricing arrears interest rate swaps under the ECIR process.