This paper proposes a new approximation method for pricing barrier options with discrete monitoring under
stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in
Malliavin calculus are effectively applied in pricing barrier options with discrete monitoring. To the best of our
knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options
with stochastic volatility models. Furthermore, it provides numerical examples for pricing double barrier call
options with discrete monitoring under Heston and λ-SABR models.
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