Financial
Mathematics and Applied Probability Seminars 20072008
Unless otherwise indicated, all
seminars take place at Lecture Theatre K2.31 (the usual room, formerly known
as 2C), King's College London, The Strand, London WC2R 2LS.
Tuesday 16
October,
5:30 pm

Dr Umut Cetin
Department of Statistics, London School of Economics
Pricing and hedging in carbon emissions markets
Joint work with M. Verschuere,
Electrabel.
We propose a model in order to
study EU markets for carbon emissions. Starting with a noarbitrage
relationship between the prices of carbon allowances belonging to
subsequent phases, we solve for the price and optimal hedging strategies of
derivatives in this market using a local risk minimisation approach under
complete and incomplete information regarding the market's collective
position in carbon credits.
Dr Cetin’s talk is available
as a PDF.

Tuesday 23 October,
5.30pm

Prof Michael Giles
Computer Laboratory, University of Oxford
Monte Carlo evaluation of Greeks
In finance, we need to know
not only the correct prices for financial derivative options, but also
their sensitivity to changes in various parameters, such as the current
asset price, interest rate, exchange rate and level of volatility 
derivatives known collectively as the "Greeks". In this talk I
will discuss various aspects of computing Greeks through Monte Carlo
simulation. I will start by presenting the three main approaches: finite
differences, likelihood ratio method (LRM) and pathwise sensitivity
calculation. The last of these leads very naturally to an adjoint
implementation which makes it possible to compute the sensitivity to a
large number of input parameters at a very low cost, little more than the
cost of evaluating the price itself. The practical development of adjoint
codes is greatly assisted by using Automatic Differentiation (AD) tools. I will
explain the underlying ideas and discuss the ise of the FADBAD++ software
package which is based on templates and operator overloading within C++.
The pathwise approach is not applicable when the payoff is not
differentiable. Even when the payoff is differentiable, the use of
scripting in realworld implementations means it can be very difficult in
practice to evaluate the derivative in very complex financial products. To
address these limitations, I will present a new idea to combine the adjoint
pathwise approach for the stochastic path evolution with LRM for the payoff
evaluation.
Prof. Giles’ talk is available
as a PDF.

Tuesday 30
October,
5.30pm

Prof. William Shaw
Department of Mathematics King's College, London
Quantile mechanics and dependency without copulas
Joint work with G.
Steinbrecher
This talk will begin by
discussing the representation of quantile functions for Monte Carlo
simulation as solutions of certain nonlinear ordinary and partial
differential equations, in particular providing an efficient method for
convering Gaussian samples to fattailed samples. The PDE representation
leads us to a natural generalization to a collection of multivariate
distributions in which quite exotic combinations of marginal distributions
are coupled together in a natural way. In this way we generate a natural
alternative to the copula philosophy, where dependency is generated via
suitably coupled stochastic differential equations.
Prof. Shaw’s talk is available
as a PDF.

Tuesday 6
November,

No seminar today
MSc Project Week & Presentations

Tuesday 13th
November,
5.30 pm

Dr Arun Verma
Bloomberg, New York
Breakeven volatility surfaces  Historical vols conditional on Moneyness
and Maturity
Joint work with Dr Bruno
Dupire
Usually, the historical volatility of a time
series is computed as the annualized standard deviation of the log returns.
It provides an estimate of the volatility parameter to be input in the
BlackScholes formula to price options of various strikes and maturities.
However, most markets exhibit a strong dependency of implied volatility on
strikes, named skew or smile, which the historical volatility estimate
misses as it provides a single number for all strikes. We propose a
methodology to extract from a time series of prices not only one historical
volatility but a whole volatility surface, corresponding to the implied
volatilities that should have been used in the past to properly price and
hedge options of various strikes and maturities. It is based on the notion
of breakeven volatilities and exploits delta hedging principles that lie
at the heart of option pricing theory and reflect trading practice. This
approach has two main applications: 1) in the case of an underlying where
no options are available, it gives an indication of where implied
volatilities should be and 2) when options are available, it provides a
rich/cheap analysis tool.
Dr Verma’s talk is available as a Microsoft
PowerPoint file.

Tuesday 20 November,
5.30 pm

Dr Christoph Reisinger
Department of Mathematics, University of Oxford
Modelling and numerical
aspects of basket credit derivatives pricing
Based on joint work with Helen
Haworth, William Shaw, and Ben Hambly.
The simulation of multiname
credit derivatives raises significant challenges, among others from the
perspective of dependence modelling, calibration, and computational
complexity. Structural models are based on the evolution of firm values,
often modelled by market and idiosyncratic factors, to create a rich
correlation structure. In addition to this, we will allow for contagious
effects, to account for the
important scenarios where the default of a number of companies has a
timedecaying impact on the credit quality of others. If any further
evidence for the importance of this was needed, the recent developments in
the credit markets have furnished it, in spades. We will give illustrations
for small nthtodefault baskets, and propose extensions to large basket
credit derivatives by exploring the limit for an increasing number of
firms.
Dr. Reisinger’s talk is available as a PDF.

Tuesday 27 November,
5:30 pm

Dr Peter Jaeckel
Head of Credit, Hybrid, Inflation, and Commodity Derivative Analytics, ABN
Amro, London
“Hyp Hyp Hooray”
A new stochasticlocal volatility model is
introduced. The new model's structural features are carefully selected to
accommodate economic principles, financial markets' reality, mathematical
consistency, and ease of numerical tractability when used for the pricing
and hedging of exotic derivative contracts. Also, we present a generic
analytical approximation for Black volatilities for plain vanilla options
implied by any parametriclocalandstochasticvolatility model, apply it
to the new model, and demonstrate its accuracy.
Dr Jaeckel’s talk is available as a PDF.

Tuesday 4 December,
5:30 pm

No seminar today

Tuesday 22 January 2008 5.30pm

Prof Xunyu Zhou
Nomura Professor of Mathematical Finance, University of Oxford
“Prospect Theory  A New Paradigm for Portfolio
Choice”
In this talk I shall report
recent progress on continuoustime behavioural portfolio choice under
Kahneman and Tversky's (cumulative) prospect theory, featuring Sshaped
utility functions and probability distortions. It is shown that the model
wellposedness becomes a prominent issue in such a behavioural model.
The optimal terminal wealth positions, derived in fairly explicit forms,
possess surprisingly simple structure reminiscent of a gambling policy
betting on a good state of the world while accepting a fixed, known loss in
case of a bad one. If time permits I will also discuss on the incomplete
market and singleperiod models as well as the equity premium puzzle.
Prof. Zhou’s talk is available as
a PDF.

Tuesday 29 January 2008 5.30pm

Prof Helyette Geman
Birkbeck, London
“Seasonal and Stochastic
Effects in Commodity Forward Curves”
Joint work with Svetlana
Borovkova, Free university of Amsterdam
In this paper we develop an original model for the
dynamics of commodity forward curves exhibiting seasonality such as natural
gas, electricity or agricultural commodities. In the existing literature on
the subject, the first state variable in multifactor models is the
commodity price, which mixes seasonal and stochastic features and may be
unobservable. We propose to use instead the average forward price, which is
devoid of seasonality and conveys a more robust representation of the
current forward curve level. The second factor in our model is a quantity
analogous to the stochastic convenience yield, which accounts for the
random changes in the forward curve shape. The wellknown costofcarry
relationship is significantly improved by introducing a deterministic
seasonal premium within the convenience yield. We develop model estimation
procedures and apply them to a number of energy markets, such as natural
gas and electricity.
The paper associated with Prof. Geman’s talk is
available as a PDF.

Tuesday 5 February 2008
5:30 pm

Dr Martijn Pistorius (Mathematics Department, King’s College
London) and Marc Jeannin
(Nomura International plc)
On the pricing and hedging of
barrier options driven by additive processes
Two ingredients encountered in many
optionpricing models are (a) stochastic volatility, and (b) jumps, where
the latter are needed to capture short maturity option prices while the
former is present to enable the model to fit simultaneously options of multiple
maturities. The class of Levy processes has been successfully employed to
model option prices at single maturities. However, it has been observed by
many authors that, due to their rigid term structure of marginal
distributions, Levy models are not in general capable of calibrating
simultaneously observed option prices across maturities. Here we consider
the generalisation of a Levy model by allowing the Levy characteristics to
be deterministically time dependent. Restricting ourselves to a specific
subclass of additive processes we present an algorithm for valuing barrier
options consistent with a given set of call and put prices. We illustrate the algorithm by
simultaneously calibrating the model to Stoxx50E options at four different
maturities and then calculating the values and Greeks of downandin call
options and comparing the outcomes with Monte Carlo
simulation results.

Tuesday 12 February 2008
5:30 pm

Prof Paul Embrechts
ETH, Zurich
Quantitative Modelling of Operational Risk:
facts and fantasies


Tuesday 26 February 2008,
5:30 pm

Benjamin Bruder
University Paris 7 (Denis Diderot), and SG Asset Management, Paris
Option pricing with uncertain volatilty and tolerance against losses

Tuesday 4 March 2008,
5:30 pm

Dr Alexander McNeil
HeriotWatt University, Edinburgh

Tuesday 18 March

No seminar today
(MSc presentations week)

Tuesday 6 May 2008, 5:30pm

Dr Peter Friz
Statistical Laboratory, DPMMS,
University of Cambridge

Tuesday 27 May 2008, 5:30pm

Dr Violetta Bernyk
Statistical Laboratory, DPMMS,
University of Cambridge
An Optimal Selling Strategy Based on Predicting
the Ultimate Maximum Price
Abtract:In this talk I will present an optimal selling strategy
for an asset in the following
sense. Suppose that an investor has a long position in one financial asset,
whose price
is modelled by some stochastic process. The investor's objective is to
determine a
``best moment'' at which to close out the position before a given
time and to sell the
asset at the highest possible price, i.e. as close as possible to the
ultimate maximum
price over the whole period. This optimal decision must be based on
continuous
observations of the asset price performance and only on the information
accumulated
to date. Hence, the investor should use a prediction of the future
evolution of the
price of the financial security.
In the case where the asset price is modelled by a spectrally positive stable
Levy
process, we describe explicitly the optimal strategy under certain conditions on the
model parameters. The optimal strategy is of the following form: the investor must
stop the observation of the price process and sell the asset as soon as the associated
reflected process crosses for the first time a particular stopping boundary. To this
connection we need to derive also the law of the associated supremum process and
the latter problem dates back to 1973. Finally we provide numerical estimates and
simulation examples of the results obtained by using this strategy.
This is a joint work with Prof. R.C.Dalang, EPFL, Lausanne and Prof. G.Peskir,
Manchester University.


