Analytical valuation of a general form of barrier option with stochastic interest rate and jumps

Abstract This article provides exact valuation formulae for barrier options with a stochastic, outside and window barrier, in a model allowing for stochastic interest rate and jumps in the underlying asset. The case of a best-of option with the same barrier and model specifications is also covered. Formulae in the classical, more restrictive Black–Scholes environment are derived too. These analytical results are numerically implemented and the obtained values are compared with Monte Carlo approx