This thesis deals with theoretical and numerical questions related to affine jumpdiffusion
models used in finance. In more detail, we look at three different classes within
the affine jump-diffusion class.
The first is the Heston stochastic volatility model which has been used extensively since
its first introduction by Heston (1993). To price financial derivatives with complex payoff
structures, we have to resort to the Monte Carlo simulation. We propose new simulation
schemes for the Heston model based on the squared Bessel bridge decomposition. These
new methods perform well in different parameter settings and they are compared with two
other existing methods, first, the exact scheme of Broadie and Kaya (2006) and, second, the
QE method of Andersen (2005).
The second question is about the tail behavior of the canonical affine diffusion processes
which were introduced by Dai and Singleton (2000) in the context of financial econometrics
to study the term structure of interest rates. We show that the canonical models have light
tails or exponential bounded tails, and the explicit conditions that guarantee light tails are
given. Moreover, we prove that there exists a uniqte limiting stationary distribution for
each canonical model and the regions of finite exponential moments of such stationary
distributions are determined by the stability region of the dynamical system associated
with a given model.