RMI Joint Seminars
March – April 2012
On 5 April 2012, Dr. Yamazaki Kazutoshi, assistant professor at
the Center for the Study of Finance and Insurance at Osaka
University, gave a talk on his paper named “Toward a
Generalization of the LelandToft Optimal Capital Structure
Model”. The talk was a joint event organized by RMI and the
Department of Mathematics. This paper generalized the problem by
allowing the values of bankruptcy costs, coupon rates and tax
benefits dependent on the firm's asset value. By using the
fluctuation identities for the spectrally negative process,
he and his coauthor obtained a candidate bankruptcy level as
well as a sufficient condition for optimality. The optimality
held in particular when, with respect to the asset value, the
coupon rate was decreasing, the value of tax benefits was
increasing, and the loss amount at bankruptcy was increasing and
concave. They argued that this solution admitted a
semiexplicit form, and this allowed for instant computation of
the optimal bankruptcy levels, equity/debt values and optimal
leverage ratios.
Earlier on 14 March 2012, Prof. Rafał
Weron from Poland’s Wrocław University of Technology discussed
his paper titled “Inference for Markov RegimeSwitching Models
of Electricity Spot Prices” at a joint seminar held by RMI and
Department of Statistics and Applied Probability. In the first
part of the talk, he presented motivation for using certain
types of Markov RegimeSwitching (MRS) models in electricity
markets and provided some illustrative empirical examples. In
the second part he covered the calibration of such models, in
particular, a new estimation method that greatly reduced the
computational burden induced by the introduction of independent
regimes. He then constructed a goodnessoffit testing scheme
for the marginal distribution of regimeswitching models. The
test was based on the KolmogorovSmirnov supremumdistance
statistic. While the existence of distinct regimes in
electricity spot prices was generally unquestionable (due to the
supply stack structure), the actual goodnessoffit of the
models required statistical validation. He applied the new
methods to a sample series of electricity spot prices from
various power markets. He then argued that the proposed MRS
models fit these datasets well and replicated the major stylized
facts of electricity spot price dynamics.
On 27 March 2012, Prof. Asger Lunde, Professor at Department of
Economics and Business from Denmark’s Aarhus University
presented a paper on “Realized Beta GARCH: A Multivariate GARCH
Model with Realized Measures of Volatility and Covolatility” at
a joint seminar coorganized by the RMI and the Department of
Economics. In his talk, Prof. Lunde introduced a multivariate
GARCH model that incorporates realized measures of volatility
and covolatility. The realized measures extract information
about the current level of volatility and covolatility from
highfrequency data, which is particularly useful for the
modeling of return volatility during periods with rapid changes
in volatility and covolatility. When applied to market returns
in conjunction with returns on an individual asset, the model
yielded a dynamic model of the conditional regression coefficient
that is known as the beta. He and his coauthors applied the
model to a large set of assets and found the conditional betas
to be far more variable than what are usually found with
rollingwindow regressions based exclusively on daily returns.
In the empirical part, they examined the crosssectional as well
as the time variation of the conditional beta series during the
financial crises.
RMI Research Seminar
23 March
2012
An RMI research seminar saw Prof. Yukio
Muromachi, professor of the Graduate School of Social Sciences, Tokyo
Metropolitan University, presenting on “Risk Evaluation of A Portfolio Including
Forwardlooking Stress Events with Probabilities”. Prof. Muromachi and his coauthors proposed a risk
evaluation model for a portfolio including stress events with probabilities
implied from market data. Their model is based on the implied copula proposed by
Hull and White (2006) for pricing Collateralized Debt Obligations (CDOs),
especially synthetic CDOs. Hull and White (2006) showed that even in prosperous periods there existed small probability masses in the extremely high
default probability regions, which implied the latent fear of the market
participants against catastrophic default events.
Calling such events “marketimplied stress scenarios”, the authors showed that
the loss distributions of CDO tranches and a bond portfolio could be constructed
numerically to include the effects of such events, and that they had strong
influences on the risk measures such as VaR. Additionally, their numerical
example showed when the extreme losses were incurred in the CDO tranches, most
of the losses came from the crash of the CDO prices, not from the actual
default losses. They concluded that their method was one of the possible ways to
connect the existing statistical models with stress tests and to obtain
useful information.
