Download here - Hong Kong Consortium of Quantitative Finance

Workshop: Quantitative Finance Day
Program at a glance
May 5, 2012 (Saturday), 9am - 6pm,
Venue: Room No. 2505, Academic Building 2, City University of Hong Kong
Welcoming Remarks
9:05am - 9:15am
Xunyu ZHOU (CUHK)
Session I
9:15am - 9:45am
9:45am - 10:15am
10:15am - 10:45am
10:45am - 11:15am
Xiren CAO (SJTU China)
Xin GUO (UC Berkeley)
Min DAI (NUS Singapore)
Break
Session II
Lunch
Session III
11:15am - 11:45am Alex KOLB (Nomura)
11:45am - 12:15pm Duan LI (CUHK)
12:15pm - 12:45pm Lixin WU (HKUST)
12:45pm - 2:00pm
2:00pm - 2:30pm
2:30pm - 3:00pm
3:00pm - 3:20pm
Andrew CARVERHILL (HKU)
Benny HON (CityU)
3:20pm - 3:50pm
3;50pm - 4:20pm
4:20pm - 4:30pm
Zuoquan XU (PolyU)
Xiaowei ZHANG (HKUST)
Session V
4:30pm
4:50pm
5:10pm
5:30pm
4:50pm
5:10pm
5:30pm
5:50pm
Jie SHEN (CityU)
Joseph SUNG (HKU)
Yingda SONG (HKUST)
Tat Wing WONG (CUHK)
Closing Remarks
5:50pm - 6:00pm
Yuekuen KWOK (HKUST)
Break
Session IV
Break
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Titles and Abstracts of Presentations
May 5, 2012 (Sat), Room. 2505, Academic Building 2, CityU HK
9:05am - 9:15am,
Welcoming Remarks by Xunyu ZHOU, Department
of Systems Engineering & Engineering Management, Chinese University of
Hong Kong
Session I: 9:15am - 10:45am, Chaired by Yuekuen KWOK, Department of
Mathematics, University of Science and Technology of Hong Kong
9:15am - 9:45am, Xiren CAO, Department of Finance, Antai school of
Business and management, Shanghai Jiaotong University
Title: Analysis of Non-linear Behavior - A Sensitivity-Based Approach
Abstract: One of the important issues in behavioral analysis is that
the law of iterated expectation is lost due to the distortion in performance probability. The standard dynamic programming fails to work
in this area. In this talk, we first give a brief review of the different
approaches in stochastic optimization and give an overview of the area
with a sensitivity-based point of view. Then we apply this sensitivitybased approach, a powerful alternative to dynamic programming, to
solve the portfolio management problem in an environment with probability distortion. We show that after changing the underlying probability measure the distorted performance becomes locally linear, and
thus the derivative of the distorted performance is simply the expectation of the sample path based derivative of the performance under
this new measure, which can be obtained by perturbation analysis. We
also provide simulation algorithms for the derivative of distorted performance and hence a gradient-based search algorithm for the optimal
policy. We apply this approach to the optimal initial allocation problem
with the distorted performance probability and obtained a closed form
optimal policy, which is consistent with the results of Jin and Zhou.
We expect that this approach is generally applicable to optimization in
other non-linear behavioral analysis.
9:45am - 10:15am,
Xin GUO, Department of IEOR, UC Berkeley, CA
Title: Economic default and Arcsine Law
Abstract: This paper develops a structural credit risk model to characterize the difference between the economic and recorded default times
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for a firm. Recorded default occurs when default is recorded in the
legal system. The economic default time is the last time when the firm
is able to pay off its debt prior to the legal default time. It has been
empirically documented that these two times are distinct (see Guo, Jarrow, and Lin (2008)). In our model, the probability distribution for the
time span between economic and recorded defaults is analyzed, and is
shown to follow a mixture of Arcsine Laws for some special cases. This
is consistent with the results contained in Guo, Jarrow, and Lin. In
addition, we show that the classical structural model is a limiting case
of our model as the time period between debt repayment dates goes to
zero. As a corollary, we show how the firm value process’s parameters
can be estimated using the tail index and correlation structure of the
firm’s return.
10:15am - 10:45am,
versity of Singapore
Min DAI, Department of Mathematics, National Uni-
Title: Portfolio Selection with Transaction Costs and Multiple Risky
Assets
Abstract: We consider the optimal consumption and investment with
transaction costs on multiple assets, using constant absolute risk aversion utility for the investor and multi-dimensional geometric Brownian motion for the prices of risky assets. We characterize the optimal
investment strategy and in particular prove by rigorous mathematical
analysis that the trading region has the shape that is very much needed
for the trading strategy to be well-defined, e.g. in the two risky asset
case, the no-trading region has four corners, the intersections of different types of trading regions are either horizontal or vertical half lines
in case of two assets. In contrast, the existing literature is restricted
to either single risky asset or multiple uncorrelated risky assets. This
work is joint with Xinfu Chen.
10:45am - 11:15am,
Break
Session II: 11:15am - 12:45am, Chaired by Ken YAN, Nomura Asset Management Hong Kong Limited
11:15am - 11:45am
Limited
Alex KOLB, Nomura Asset Management Hong Kong
Title: Hybrid Derivatives and Correlation: practical and theoretical
issues for a robust and consistent framework
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Abstract: We discuss problems encountered in practice when defining
correlations in a derivative pricing framework incorporating multiple
assets. Product areas that are susceptible to these considerations are
for example derivative payouts that depend on the co-movements of
interest rates and equity, or FX linked products that show sensitivities to stochastic interest rates. The recent focus of investment banks
on counterparty risk within a portfolio context would be another example where correlation between multiple assets and asset classes are
adamant. The lack of reliable market data for various inputs in these
kind of derivative products makes a simple but robust choice important. We propose a method how this can be achieved, even within the
context of high dimensional (multi factor) models.
11:45am - 12:15pm, Duan LI, Department of Systems Engineering & Engineering Management, Chinese University of Hong Kong
Title: Discrete-time behavioral portfolio selection under prospect theory
Abstract: We formulate and study a general multi-period behavioral
portfolio selection model under Kahneman and Tversky’s prospect theory, featuring an S-shaped value function. Unlike the classical Expected Utility maximization model, a behavioral portfolio model could
be easily ill-posed, as He and Zhou (2011) already noticed in their
single-period model. Hence, we first discuss the ill-posedness issue
and identify the conditions for the well-posedness under a multi-period
framework. Under these conditions, we derive then the semi-analytical
optimal policy and show that this optimal behavioral portfolio policy
still takes a linear feedback form.
12:15pm - 12:45pm, Lixin WU, Department of Mathematics, University of
Science and Technology of Hong Kong,
Title: Post Crisis Modeling of Interest Rate Derivatives with Credit
liquidity and Funding Risks
Abstract: We have established a new framework for derivatives pricing
under credit, liquidity and funding risks. This framework puts derivative pricing after the financial tsunami back to the track of arbitrage
pricing. For interest-rate derivatives, we have extended the affine term
structure models and LIBOR market models to accommodate credit
and funding risks, in addition to market risks.
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12:45pm - 2:00pm,
lunch
Session III: 2:00pm - 3:00pm, Chaired by Qiang ZHANG, Department of
Mathematics, City University of Hong Kong
2:00pm - 2:30pm, Andrew CARVERHILL, School of Economics and Finance, Univeristy of Hong Kong
Title: Capital Structure Dynamics - Debt, Equity, Liquidity, Dividends
and Growth
Abstract: We present our recent dynamic model of the firm’s capital
structure. The model can reflect a number of empirical regularities,
including realistic credit spreads, and liquidity (cash) holdings that do
not increase with profitability. We also discuss the issues of optimal
leverage, dividend behavior, growth and the “asset substitution problem”, in relation to the model.
In the model, liquidity is held not to facilitate investment, but to help
the firm survive hard times. We discuss empirical evidence for this and
the related measure of the “cash flow (profitability) sensitivity of cash
(liquidity)”.
2:30pm - 3:00pm, Benny HON, Department of Mathematics, City University of Hong Kong
Title: Kernel-Based Approximation Method for Option Pricing
Abstract: In this talk, we present the application of meshless computational method based on the use of kernel-based functions for solving
various option pricing problems. Properties of some special kernels such
as radial basis functions; harmonic kernels; fundamental and particular
solutions; and Greens functions will be discussed. The method requires
only a set of nodes in the domain and on the boundary from which all
governing equations are solved in strong formulation without the need
of tedious meshing and numerical integration. This makes the method
advantageous in solve free-boundary type problems such as American
options pricing and singularity type problems such as default barrier
options pricing.
3:00pm - 3:20pm,
Break
Session IV: 3:20pm - 4:20pm, Chaired by Hailiang YANG, Department of
Statistics & Actuarial Science, University of Hong Kong
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3:20pm - 3:50pm,
Zuoquan XU, Department of Applied Mathematics,
Hong Kong Polytechnic University
Title: Optimal Stopping under Probability Distortion
Abstract: Buy-and-hold, cut-loss-or-take-profit, cut-loss-and-let-profitrun are widely used trading strategies in practice. However, there is no
an existing model could explain all of them at once in the literature.
It is also well-known that people tend to apply pre-committed strategies when making decisions, however, will change their mind later. In
another words, the trading strategies are not time-consistent. By incorporating probability distortion, we formulate an optimal stopping
model to derive all the mentioned as well as other trading strategies at
once and give an explanation why people use time-inconsistent strategies.
3;50pm - 4:20pm, Xiaowei ZHANG, Department of Mathematics, University of Science and Technology
Title: Portfolio Default Losses: Typical and Atypical Behaviors
Abstract: Affine point processes are currently widely used in credit risk
for modeling portfolio default losses. More specifically, we consider a
portfolio exposed to credit risk and partition the constituent firms into
several homogeneous groups. The default dynamics of each group is
governed by a systematic risk and an idiosyncratic risk factor. All
the risk factors form a multivariate affine jump-diffusion process. The
framework we consider here incorporates both top-down and bottomup formulations, which are popular approaches in credit risk modeling.
In addition, self-excitation and cross-excitation are introduced in our
framework in order to capture the clustering feature of defaults.
In this talk, we will present the long-term characteristics of portfolio
default losses by analyzing the asymptotic behaviors of affine point processes in the large time-horizon asymptotic regime. The first half of the
talk will address the typical behaviors of affine point processes, which
are characterized by a central limit theorem (CLT). We establish such
a CLT by constructing a local martingale and leveraging the CLT for
local martingales. Thanks to the affine structure, both the asymptotic
average as well as the asymptotic variance can be calculated explicitly. Numerical results show that the Gaussian approximation for the
distribution of default losses is fairly accurate, except for the tails.
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Motivated by the perspective of risk management, which particularly
concerns rare but significant events, we will discuss the atypical behaviors of affine point processes in the second half of the talk and characterize them in terms of a large deviation principle, which is proven
by applying the Gartner-Ellis theorem. The key step is to calculate
the limiting cumulant generating function of the affine point process.
Again, thanks to the affine structure, the calculation can be conducted
explicitly. Note that the large deviations approximation is only accurate at the logarithmic level. In order to compute the rare event
probabilities more precisely, we resort to Monte Carlo simulation but
its efficiency heavily depends on the rarity of the event. Using the
large deviation result, we develop an importance sampling algorithm
for computing the probability of large default losses and prove that it
is asymptotically optimal. Numerical results show that our importance
sampling algorithm achieves significant variance reduction.
4:20pm - 4:30pm, Break
Session V: 4:30pm - 5:50pm, Chaired by Qingshuo SONG, Department of
Mathematics, City University of Hong Kong
4:30pm - 4:50pm, Jie SHEN, Department of Mathematics, City University
of Hong Kong
Title: Saddle Points of Discrete Markov Zero-Sum Game with Stopping
Abstract: We study the sufficient conditions for the existence of a
saddle point of time-dependent discrete Markov zero-sum game up to
a given stopping time. The stopping time is allowed to take either a
finite or an infinite non-negative random variable with its associated
objective function being well-defined. The result enables us to show the
existence of the saddle points of discrete games constructed by Markov
chain approximation of a class of stochastic differential games. This is
a joint work with Xun Li and Qingshuo Song.
4:50pm - 5:10pm, Joseph SUNG, Department of Statistics & Actuarial Science, University of Hong Kong
Title: A Nonzero-Sum Stochastic Differential Reinsurance Game With
Mixed Regime Switching
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Abstract: In this work, we study a class of nonzero-sum stochastic differential reinsurance games between two insurance companies. Each
insurance company is assumed to maximize the difference of the opponent’s terminal surplus from that of its own by properly arranging its
reinsurance schedule. The surplus process of each insurance company
is modeled by a mixed regime-switching Cramer-Lundberg approximation, that is, a diffusion risk process with coefficients being modulated
by both a continuous-time finite-state Markov Chain and another diffusion process. By adopting the stochastic HJB equation approach,
we provide a verification theorem to characterize the underlying Nash
Equilibrium. In particular, under the most commonly used exponential utility situation, we further obtain the explicit optimal reinsurance
schedule. The economic interpretation of the optimal strategy closely
matches with the common practice of insurance companies in realty.
(This is a joint work with A. Bensoussan, S.C.P. Yam and S.P. Yung.)
5:10pm - 5:30pm, Yingda SONG, Department of IELM, University of Science and Technology
Title: Exact Simulation of the SABR Model
Abstract: The stochastic alpha-beta-rho (SABR) model becomes popular in the financial industry because it is capable of providing good
fits to various types of implied volatility curves observed in the marketplace. However, no analytical solution to the SABR model exists that
can be simulated directly. Although we can apply discretization methods to simulate security price under the SABR model, they introduce
discretization bias to the simulation results. Therefore, we may have
to use a large number of time steps to reduce the bias to an acceptable
level. This paper proposes a Monte Carlo method for the exact simulation of the forward price and its volatility under the SABR model.
Primary difficulties involved in our exact simulation scheme are how
to simulate two random variables whose distributions can be expressed
in terms of the Hartman-Watson and the noncentral chi-squared distribution functions, respectively. Two novel simulation schemes are
proposed to achieve numerical accuracy, efficiency, and stability. One
stems from numerical Laplace inversion and Asian option literature,
and the other is based on recent developments in evaluating the noncentral chi-squared distribution functions in a robust way. Numerical
examples demonstrate that our method is fast and accurate under various market environments.
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5:30pm - 5:50pm, Tat Wing WONG, Department of Statistics, Chinese
University of Hong Kong
Title: Managing Mortality Risk with Longevity Bonds When Mortality
Rates Are Cointegrated
Abstract As a hedging vehicle for insurance companies to manage their
mortality risks, longevity bonds are linked to a selected mortality index. We investigate the dynamic mean-variance hedging problem of an
insurer using longevity bonds. Insurance liabilities are modelled by a
doubly stochastic compound Poisson process with the mortality rate
being correlated and cointegrated with the index mortality rate. We
solve this dynamic hedging problem using theory of backward stochastic differential equations. Our theory shows that cointegration materially affects the optimal hedging strategy on top of correlation. The
effect of cointegration is independent of the risk preference of insurers.
Explicit solutions of the optimal hedging strategy are derived for both
cointegrated stochastic mortality models with constant volatilities and
with state-dependent volatilities. (This is a joint work with M.C. Chiu
and H.Y. Wong)
5:50pm - 6:00pm,
Closing Remarks by Yuekuen Kwok, Department of
Mathematics, University of Science and Technology
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