A closed-form formula for the conditional expectation of the extended CIR process

Abstract

This paper is an extension to a recent paper by Rujivan (2016), in which we derive a closed-form formula for the conditional expectation of the valuation process, defined by         , :        T s t t r s ds r u du T t T T s t V e f v h v e ds for 0 ,  t T where t v is assumed to follow the extended Cox-Ingersoll-Ross process, for   1 f v v  and   2 h v v  for any 1 2    , R , and any integrable function r . Our newly-derived formula can be used to price a contingent claim  f r h , ,  in which  , t f v r t , and h v t for t T 0,  represent, respectively, a terminal payoff, an interest rate process, and a payoff rate process.

Keywords

• extended cir process
• conditional expectation
• closed-form formula