Option pricing with the control variate technique beyond Monte Carlo simulation

Although mostly used alongside Monte Carlo simulation, the control-variate (CV) technique can be applied to other numerical algorithms in option pricing. This paper studies the conditions under which a numerical method (simulation-based or not) can benefit from the CV technique and what approximators can serve as CVs. We demonstrate the ideas with Carr and Madan’s Fourier transform-based algorithm, convolution-based pricing algorithms, and classic binomial trees. Numerical results are provided to show that the CV-enhanced versions are more efficient than the original algorithms. •Analytical solutions to the prices of complex derivatives are mostly not available.•The control variate (CV) technique can reduce the errors in the price estimation.•In addition to Monte Carlo simulation, it can also enhance other numerical methods.•That includes binomial trees, Fourier transform- and convolution-based algorithms.•The CV-enhanced versions are more efficient than the original algorithms.