Minicourses
T. Björk: An introduction to interest rate theory (slides 1, slides 2)
 Basic interest rate theory
 Bond markets and interest rates.
 Short rate models. The market price of risk.
 Martingale modelling.
 Affine term structures.
 Inverting the yield curve.
 Forward rate models
 Bond prices and forward rates. A toolbox.
 The HJM approach to forward rate modelling.
 Examples.
 Change of numeraire
 The normalized price system.
 Pricing.
 Forward measures.
 A general option pricing formula.
 New developments
 Credit risk.
 ``Market models''.
D. Heath: Risk Measures
 Overview of Financial Risk Management
 Risks to be managed
 How these are managed
 Measurement of risk
 Structure of the firm
 VaR
 Definitions of VaR
 Models to compute VaR
 Properties of VaR
 Consequences of requirements based on VaR
 Coherent Measures of Risk
Properties of a good risk measure
 Structure of good regulatory risk measures
 Structure of good management risk measures
 Examples of risk measures
Managing Risk using Coherent Measures
 Trading desks
 Trading floor
 Allocation of risk limits
 Charging for use of risk limits
Implications of Risk Management on Market Prices
 Valuation and stress measures
 "No good deal" pricing
 Dependence on the firm's position
 How risk limits affect prices
Special invited lectures
S. Hodges: No Good Deal Bounds
The principle of "nogooddeal" pricing can provide much tighter bounds
than noarbitrage pricing in an incomplete market without the need
for the much stronger assumptions of equilibrium pricing.
We will consider:
Bounds based on the Sharpe Ratio,
on the Generalized Sharpe Ratio,
the more general formulation of Cerny and Hodges, and also
the relationship with coherent risk measures. (slides, paper Cerny, Hodges)
A. Pelsser: Mathematical Foundation of Convexity
Correction
A broad class of exotic interest interest rate derivatives
can be valued simply by adjusting the forward interest rate. This
adjustment is known in the market as convexity correction. Various ad
hoc rules are used to calculate the convexity correction for different
products, many of them mutually inconsistent. In this paper we put
convexity correction on a firm mathematical basis by showing that it
can be interpreted as the sideeffect of a change of probability
measure. This provides us with a theoretically consistent framework to
calculate convexity corrections. Using this framework we provide exact
expressions for libor in arrears, and diff swaps. Furthermore, we
propose a simple method to calculate analytical approximations for
general instances of convexity correction.
L.C.G. Rogers: Monte Carlo Valuation of American
Options
This paper introduces a `dual' way to price
American options, based on simulating the path of the option
payoff, and of a judiciouslychosen Lagrangian martingale.
Taking the pathwise maximum of the payoff less the martingale
provides an upper bound for the price of the option, and
this bound is sharp for the optimal choice of Lagrangian
martingale. As a first exploration of this method, three
examples are investigated numerically; the accuracy
achieved with
even very simpleminded choices of Lagrangian martingale
is surprising. The method also leads naturally to candidate
hedging policies for the option, and estimates of the risk
involved in using them.
Short lectures
A.J.G. Driessen: The CrossFirm Behaviour of Credit Spread Term
Structures
We apply a term structure approach to analyze the relation between term
structures of credit spreads on corporate bonds of many different firms. We
use the intensitybased framework of Duffie and Singleton (1999) and model
the instantaneous credit spread of each firm as a function of common
factors and a firmspecific factor, thereby generalizing the purely
firmspecific model of Duffee (1999). Using data on US corporate bond
prices of 104 firms, we estimate the model for the credit spread term
structures of all firms with Quasi Maximum Likelihood based on the Kalman
filter. The results provide strong evidence for the presence of common
factors in credit spreads across firms. These common factors influence
credit spreads of all firms in the same direction. We find that the risk
associated with the common factors is priced, while the firmspecific
factor risk is not. Changes in the common factors and firmspecific factors
are negatively correlated with stock returns and positively correlated with
changes in stock return volatility.
J.K. Hoogland: Symmetries in JumpDiffusion Models with
Applications in Option Pricing and Credit Risk
It is a well known fact that local scale invariance plays a
fundamental role in the theory of derivative pricing. Specific
applications of this principle have been used quite often under
the name of `change of numeraire', but in recent work it was shown
that when invoked as a fundamental first principle, it provides
a powerful alternative method for the derivation of prices
and hedges of derivative securities, when prices of the
underlying tradables are driven by Wiener processes. In this
article we extend this work to the pricing problem in markets
driven not only by Wiener processes but also by Poisson processes,
i.e. jumpdiffusion models. It is shown that in this case too,
the focus on symmetry aspects of the problem leads to important
simplifications of, and a deeper insight into the problem.
Among the applications of the theory we consider the pricing of
stock options in the presence of jumps, and Levyprocesses. Next
we show how the same theory, by restricting the number of jumps,
can be used to model credit risk, leading to a `market model' of
credit risk. Both the traditional DuffieSingleton and
JarrowTurnbull models can be described within this framework,
but also more general models, which incorporate default
correlation in a consistent way. As an application of this theory
we look at the pricing of a credit default swap (CDS) and a
firsttodefault basket option.
J. Kerkhof: A Quantitative Assessment of Model
Risk
In this paper we propose a general approach to quantify model risk for
market risk measures. We present a theoretical framework to compute
model reserves for trading desks based on coherent market risk measures.
We decompose total model risk in a model risk premium due to estimation
risk and a model risk premium due to misspecification risk. We compute
these components using MonteCarlo simulation and the bootstrap. The
presented approach is general and can be applied to portfolios of basis
assets and all types of derivatives. We apply the procedure to the
equity, FX, and interest rate market for the heavily used BlackScholes
type models.
P. Klaassen: Loan maturity, economic cycles and bank insolvency
risk
Credit risk portfolio models usually assume a oneyear time horizon when
evaluating the credit risk of loan portfolios. The average maturity of a
bank's loan portfolio is typically significantly longer than one year,
however. We develop a stylized model to investigate how a bank's
insolvency risk changes when different holding periods are considered
for the loan portfolio. To this end, the development of the bank's
balance sheet is modelled over time. We furthermore include economic
cycles in our multiperiod model, and study how this influences a bank's
required capital for a chosen insolvency probability. (joint work with Andre Lucas)
M.R. Pistorius: Option pricing under a phase type model
One of the functions of derivatives, such as the American Put
option, is to provide the buyer an insurance against certain risks.
We will focus on the problem of pricing such derivatives
under the "phase type" model. As is well known, the classical BlackScholes
model is often uncapable of capturing certain features seen in empirical data.
As an alternative, we propose an exponential Levy model to model the risk
(price of the underlying) where the Levy process is given by a Brownian
motion with added a compound Poisson process, where
the jumps are of both signs and of "phase type", that is,
the Laplace transform of the jump sizes is the quotient of two polynomials.
In this talk, we address the question of analytical tractability of this
model, exemplified by pricing the Russian option  a perpetual expiration
version of a lookback option.
This talk is based on joint work with Soren Asmussen and Florin Avram.
M.H. Vellekoop:
Pricing Methods for Defaultable Assets
We discuss the pricing and hedging of contingent claims
on assets which may be subject to default: a sudden unpredictable
loss in value. We show that a unique price can be found
if we assume that the stochastic processes which cause
default are idiosyncratic, and we introduce a nice interpretation
of this result in terms of insurance contracts which complete
the market. Trinomial tree models which can be used to find
prices and hedges are developed, and we study in particular
the convergence properties of such methods in detail.
