An extended MAS colloquium at CWI, with 4 presentations about Investment under Uncertainty.

Location: CWI, room M280

Programme

10:30 - 11:15 Sander vd Pijl (CWI - MAS)
A Numerical Method for the Control of Dike Levels in Continuous Time

11:15 - 12:00 Ulrike Laeuferts-Mau (NRG Petten)
Strategic business engineering for the next generation of nuclear energ systems: A Real Option view

12:00 - 13:30 lunch break

Continuation in Room 279

13:30 - 14:00 Lech Grzelak (TU Delft)
On the modelling of Hybrid Financial Products

14:00 - 14:30 Bowen Zhang (TU Delft)
Evaluation of a Fourier-Cosine Option Pricing Method on the GPU


10:30 - 11:15: Sander vd Pijl (CWI - MAS)
A Numerical Method for the Control of Dike Levels in Continuous Time

The optimal control of dike heights is a trade-off between the investment costs of dike increases and the expected costs due to flooding. The optimization problem is formulated in continuous time and leads to a so-called Hamilton-Jacobi-Bellman (HJB) equation. It is a system of second order partial differential equations that need to be solved backward in time.  
Given a problem formulation based on a HJB equation, a system of second order partial
differential equations needs to be solved backward in time. This is achieved by some numerical approximation.
This work will focus on the development of a numerical method that is best suited for the purpose of dike-height control. A wide variety of numerical methods for partial differential equations exists. A proper choice for a numerical method is motivated by carefully considering the properties of the problem. First of all, the state vector can be of high dimension.  
Secondly, the integration time is large and, thirdly, the equations are of convective
 type, i.e. the terms containing first-order derivatives are dominant. Fourth and finally, the boundary conditions, if carelessly chosen, can lead to boundary layers. This leads to the following propositions:
 - Due to the dimensionality of the problem, dimensional splitting on a Cartesian mesh would be preferred, leading to a finite difference approach.
 - The large integration time is expected to require some high order approximation.
 - The convective nature of the problem is expected to require a monotone or non-oscillatory scheme, such as the ENO or WENO spatial discretization schemes, in combination with some high order TVD Runge-Kutta time integration method.

11:15 - 12:00: Ulrike Laeuferts-Mau (NRG Petten)
Strategic business engineering for the next generation of nuclear energy systems: A Real Option view

The next generation of advanced nuclear energy systems is dedicated towards efficient fuel utilization and an improved waste management to minimize the long term impact on society and environment. The economics of reprocessing spent fuel and closing the fuel cycle with fast neutron reactor (FR) have shown to be unfavourable under classical investment criteria and can't prove a clear life-cycle cost advantage over other energy sources.
Most studies on academic and industrial level have concentrated on cost minimization for electricity generation, but failed to retrieve the economic potential of the system as a whole. In order to make a responsible and more sustainable fuel cycle a convincing business case, we adopt Real option theory that calls attention to the evolution and dynamics of value to the investor.
In our model we depart from today?s light water reactor (LWR) monoculture without reprocessing. We simulate exposure towards volatile energy markets, uncertainties in natural Uranium resource utilization as well as costs uncertainties for long time storage in geological repositories.
First results show that a new generation of FR systems and reprocessing facilities add value as a hedge against key uncertainties and thereby justify higher capital costs. The objective of this analysis is an innovative interpretation of advanced systems as call option on the current once through cycle in order to better comprehend the broad economic impact and financial investment challenges on utility, national and international level.

13:30 - 14:00 Lech Grzelak (TU Delft)
On the modelling of hybrid financial products

We present an extension of the stochastic volatility equity models by a stochastic Hull-White interest rate component. We place this system of stochastic differential equations in the class of affine jump diffusion - linear quadratic jump- diffusion processes (Duffie, Pan and Singleton, Cheng and Scaillet) so that the pricing of European products can be efficiently done within the Fourier cosine expansion pricing framework. We also apply the model to price some hybrid structured derivatives, which combine the different asset classes: equity and interest rate.

14:00 - 14:30 Bowen Zhang (TU Delft)
Evaluation of a Fourier-cosine option pricing method on the GPU

In this presentation, acceleration on the GPU for option pricing by the COS method based on the Fourier-cosine expansion is demonstrated. In particular, both European and Bermudan options will be discussed in detail.
For Bermudan options, we consider both the Black-Scholes model and L'evy processes of infinite activity. Moreover, the influence of the number of terms in the Fourier-cosine expansion, $N$, as well as the number of exercise dates, $M$, on the acceleration factor of the GPU is  explored.
We also give a comparison between different ways of GPU and CPU implementation. For instance, we have optimized the GPU implementation for maximum performance which is compared to a hybrid CPU/GPU version which outperforms the pure GPU or CPU versions for European options. Furthermore, for each process and each option type that is covered by this paper, we give a discussion on the precision of the GPU.

More about the MAS seminars: http://www.cwi.nl/en/MAS_Seminars