Animations shown at a HFB seminar in Frankfurt

Sample paths of stochastic processes

Online simulator

To get a feeling for the geometric Brownian Motion have a look at the online simulator where you can provide vol and drift parameter and draw sample paths online.

Brownian Motion with a drift

brownian_motion.mpg (5.4M)

Geometric Brownian Motion

sde
solution
parameter	, ,
animation	brownian_geom.mpg (3.3M)

Vasicek (Ornstein-Uhlenbeck, Hull-White)

sde
parameter	,
animation ()	hull-white-k3.mpg (4.2M)
animation ()	hull-white-k10.mpg (3.7M)

Cox-Ingersoll-Ross

sde
parameter	,
animation ()	cox-ross-k3.mpg (5.0M)
animation ()	cox-ross-k10.mpg (4.0M)

Jump-Diffusion

sde
parameter	, , , jump parameter: , ,
animation	jump-fx.mpg (3.1M)
parameter	, jump parameter: , ,
animation	jump-share.mpg (4.6M)

Finite Difference Method

Presentation

The presentation is only available in German.

(204k)

with pauses (221k)

Explicit Method

The following files are numerical results of the examples mentioned in the paper above. Unfortunately, the domestic and foreign interest rates have been permuted.

Black-Scholes PDE with log transformed spot
fdm-expl-320.mpg (583k)
fdm-expl-330.mpg (2.6M)
Black-Scholes PDE (not transformed)
fdm-expl-nolog-160.mpg (386k)
fdm-expl-nolog-170.mpg (506k)
fdm-expl-nolog-200.mpg (517k)
fdm-expl-nolog-300.mpg (531k)

Implicit Method

fdm-cn-100.mpg (595k)

Examples with non uniform meshes

fdm-nu-expl.mpg (1.0M)

fdm-nu-mixed.mpg (1.2M)

fdm-nu-mixed2.mpg (1.5M)

fdm-nu-mixed3.mpg (808k)

fdm-nu-cn.mpg (790k)