In this paper we present a numerical valuation of variable annuities with combined Guaranteed Minimum Withdrawal Benefit (GMWB) and Guaranteed Minimum Death Benefit (GMDB) under optimal policyholder behaviour solved as an optimal stochastic control problem. This product simultaneously deals with...

It is a well known fact that recovery rates tend to go down when the number of defaults goes up in economic downturns. We demonstrate how the loss given default model with the default and recovery dependent via the latent systematic risk factor can be estimated using Bayesian inference...

There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct...

An efficient adaptive direct numerical integration (DNI) algorithm is developed for computing high quantiles and conditional Value at Risk (CVaR) of compound distributions using characteristic functions. A key innovation of the numerical scheme is an effective tail integration approximation that...

Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and...

The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that...

Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and...

The t copula is often used in risk management as it allows for modeling the tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof)...

Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed scheme involve tracking of multiple one-dimensional...

A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal withdrawal...