IWORKSHOP ON MATHEMATICAL FINANCE
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The value of information: A general stochastic calculus
approach to insider trading By Bernt Øksendal
By an insider we mean a person who has access to more
information than the information that can be obtained by
observing the prices on the market. For example, an insider may
have information about the future values of a certain stock.
Insider trading is illegal in most countries and it is important
to be able to detect it, if it should occur. Central questions
are: How much extra can an insider gain compared to an honest
trader? How much different is the optimal portfolio of an
insider compared to the optimal portfolio of an honest trader?
We will give partial answers to these questions by setting up a
general stochastic analysis model for insider trading. The model
involves the forward integral, the Skorohod integral and
Malliavin calculus. The presentation is based on joint work with
Francesca Biagini, University of Bologna.
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The Stratified Estimators for Value-at-Risk of Portfolios
By Xing Jin
The standard delta and delta-gamma methods for Value-at-Risk
(VaR) estimation are difficult to apply when portfolios have
significant exposures to non-linear derivative claims, such as
portfolios containing out-of-the-money options. The Monte Carlo
simulation is a natural alternative to the delta and delta-gamma
methods and the variance reduction is a common technique to
improve the precision of Monte Carlo simulation. The purpose of
this paper is to develop stratified estimators to assess the
value-at-risk of portfolios which may have non-linear response
to underlying risk factors , e.g., options. First, we develop a
fully stratified VaR estimate for two dimension case, which is
suitable to short-term and long-term bonds, where the two risk
factors are the factor causing the parallel shifts and the
factor causing the change in slope respectively. Second, by
combining Latin Hypercube sampling and Monte Carlo sampling, we
design VaR estimators for portfolios which may contain a large
number of risk factors. Finally, numerical experiments
illustrate the potential of those methods for variance
reduction.
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Pricing American Options using Calibrated Monte Carlo
Simulations
By Liu Xiaoqing
It is a natural concern that an option pricing model should
be able to reproduce the market prices of liquid instruments. In
this regards, the weighted Monte Carlo (WMC) method was proposed
for calibrating simulation-based models by means of relative
entropy minimization. Using the calibrated simulations, it is
straightforward and effective to compute the prices of exotic
European options on the same underling instruments. The aim of
this research work with Lu Chor Sheng is to extend the
application of the WMC method to the pricing of respective
American-style options by developing a weighted least squares
Monte Carlo (WLSM) method, which is an integration of the WMC
method and the least squares Monte Carlo (LSM) method.
Simulation tests show that the WLSM method is capable of
producing more reliable prices of American options under the
assumption of stochastic volatility.
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Value Creation Through Risk Management: A Corporate
Finance Perspective
By Gunter Dufey
Corporate risk management has the potential to increase
shareholder value in the presence of capital market
imperfections, such as agency conflicts, costly external
financing, direct and indirect costs of bankruptcy, and taxes.
In particular, risk management at the firm level can lead to
higher firm value by reducing agency conflicts between
shareholders, bondholders, and managers; coordinating corporate
financing and investment policies; lowering the expected costs
of bankruptcy and financial distress; and reducing the corporate
tax burden.
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Exercise Regions and Efficient Valuation of American Lookback
Options
By Lim Tiong Wee
We presents an efficient method to compute the values and
early exercise boundaries of American fixed strike lookback
options. The method reduces option valuation to a single optimal
stopping problem for standard Brownian motion and an associated
path-dependent functional, indexed by one parameter in the
absence of dividends and by two parameters in the presence of a
dividend rate. Numerical results obtained by this method show
that, after a space-time transformation, the stopping boundaries
are well approximated by certain piecewise linear functions with
a few pieces, leading to fast and accurate approximations for
American lookback option values. Such approximations are
developed from an explicit decomposition formula for American
lookback options, which is also applied to the asymptotic
analysis of the early exercise boundary near the expiration
date.
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Arbitrage Opportunities and Integration Theories
By Donna Mary Salopek
In this talk, we will discuss how the notion of no arbitrage
is basically associated with integration theory in fractional
Brownian motion model.
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