  We propose a very efficient method for pricing various types of lookback
options under Markov models. We utilize the model-free representations of
lookback option prices as integrals of first passage probabilities. We combine
efficient numerical quadrature with continuous-time Markov chain approximation
for the first passage problem to price lookbacks. Our method is applicable to a
variety of models, including one-dimensional time-homogeneous and
time-inhomogeneous Markov processes, regime-switching models and stochastic
local volatility models. We demonstrate the efficiency of our method through
various numerical examples.
