This talk will discuss efficient numerical methods for estimating the
probability of a large portfolio loss, and associated risk measures such
as VaR and CVaR. These involve nested expectations, and following
Bujok, Hambly & Reisinger (2015) we use the number of samples for the
inner conditional expectation as the key approximation parameter in the
Multilevel Monte Carlo formulation. The main difference in this case is
the indicator function in the definition of the probability. Here we
build on previous work by Gordy & Juneja (2010) who analyse the use of a
fixed number of inner samples , and Broadie, Du & Moallemi (2011) who
develop and analyse an adaptive algorithm. I will present the
algorithm, outline the main theoretical results and give the numerical
results for a representative model problem. I will also discuss the
extension to real portfolios with a large number of options based on
multiple underlying assets.
Joint work with Abdul-Lateef Haji-Ali