The research carried out by members of the Laboratory is very
wide-ranging and cannot be captured in a single page! More information can be found by browsing the
individual pages of our members, or looking at
some of the publications and software that have come from our work.
But if you read on you'll get an insight into some of the main themes of our research:
Computational methods
Even with the explosive growth in computing power available to each of
us, a lot of time can be wasted in using the wrong algorithms when
working with financial models. In some cases, the more powerful the
model is, the more important it is to be careful in choosing the right
computational tools to get reliable information out from the model.
We have developed a range of efficient methods already: examples
include multidimensional tree algorithms for swing options, spectral
methods that price options on mean-reverting assets, and
finite-element methods for multi-factor affine models. In each case
we've been concerned to prove the reliability and
efficiency of the methods and to create software that implements them
and demonstrates their effectiveness. Currently we are working on
adaptive wavelet-based methods for solving option pricing PDEs,
multi-asset simulation codes calibrated to forward markets, and on
methods for option pricing in the presence of jumps. [back]
Energy price modelling
Mean-reversion is just the tip of the iceberg when it comes to
describing the awkward nature of energy price processes. Seasonality,
discontinuity, long-range correlations, fat tails and many other
features can be identified as well. We are interested in modelling
these processes in a way that enables us to capture the qualitative
nature of the way the prices behave, and still be able to answer
quantitative questions of interest to the investor or risk manager.
[back]
Exotic derivative pricing
It is clear that the Black-Scholes formula, despite its popularity and
power, will not be adequate for all situations. Particularly in the
energy industry, it seems, the assumptions underlying the
Black-Scholes model simply do not hold. One simple illustration of
this is the presence of mean-reversion in many energy prices. We are
interested in how to price options when the underlying price is
mean-reverting and have developed models and pricing technologies for
this situation.
We are also interested in methods for pricing structured contracts -
that cannot be regarded as combinations of simple puts and calls. One
example of such a contract is the swing option, where the holder is
given some freedom in the exercise strategy, but this freedom is
constrained. The option can be viewed as a generalisation of the
American option, where the holder cannot exercise all of the option at
one time, but must exercise with some constraints on the rate of
exercise. One application of such options is to gas storage models.
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Portfolio optimisation
Simply put, the goal of most portfolio management is to maximise
returns while simultaneously minimising risk. But how should `risk' be
measured? So we simply use the variance, or should we use some other
measure, such as Value at Risk (VaR)? What are the implications of
using VaR to determine your portfolio strategy?
[back]
Simulation technologies
Monte-Carlo simulation is a standard industry workhorse for
quantitative risk management. But it must be remembered that the
numbers it gives are always random, and have only a given
probability of being approximately right. How can that probability be
improved? It is very expensive computationally to improve it simply
by doing more simulations, and if you are doing a large-scale
simulation with hundreds of independent random variables this may be
impossible.
We are working both on more efficient Monte-Carlo simulation engines
where the accuracy and reliability are improved,
and on quasi Monte-Carlo methods as a means of getting all the
advantages of Monte-Carlo without the drawbacks.
[back]
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