Model Based Default Probability And Yield Curve Information
Kamakura Risk Information Services (KRIS)TM is
a collection of financial information services that subscribers can access
on the Internet at their convenience. KRISTM
offers comprehensive information about counterparty default probabilities
and interest rate yield curves. This information is based on sophisticated
analyses of market and financial data using advanced quantitative models.
The models incorporated in KRISTM reflect
Kamakura’s extensive research in quantitative finance led by our Managing
Director of Research, Robert Jarrow. The information provided by KRISTM
is relevant to traders, investors, treasurers, risk managers and other
financial decision makers in banking, insurance, investment management,
corporations, and governments. All KRISTM
information can be used without modification by the
Kamakura Risk Manager enterprise
wide risk management suite. Credit Quality Of Issuers And Counterparties
Default Probability Estimates For Credit-Risky Entities
Participants in corporate and other credit markets need independent,
objective information about the credit quality of issuers and counterparties
to make sound lending, investment, and credit hedging decisions. KRISTM
satisfies this need in the form of default probability estimates for
individual credit-risky entities. KRISTM default probability estimates are
obtained using multiple default modeling approaches, including structural
and reduced form models based on advanced finance theory and sophisticated
statistical analysis. Updated default probability estimates are available
daily, and KRISTM subscribers can track the migration of an entity’s credit
quality by reviewing the historical series of default probabilities for the
entity. Term Structure Of Default Probabilities
Default probabilities describe the likelihood that a counterparty will
default in a specific time period. While a one-year period is often
selected, credit market participants are frequently interested in estimating
the probability of default for a shorter or longer period, e.g. 3 years, so
that the estimate corresponds to the timing of promised cash flows from
credit-risky assets they hold. So participants need a term structure of
default probabilities comprised of estimates at multiple future dates to
analyze all of their assets. To meet this need, KRISTM provides both one-year
default probability estimates as well as annualized default probability
estimates for periods ending on monthly forward dates up to five years in
the future.
Default Correlations For Credit-Risky Entities
Managers of portfolios of credit-risky investments and basket credit
derivatives are also concerned with portfolio diversification and the
correlation of the timing of defaults between multiple issuers and
counterparties. KRISTM addresses this
concern by providing an estimated correlation matrix for a specified set of
entities. Unlike the somewhat arbitrary correlation estimates often used by
managers, the estimated correlation matrices are consistent with the random
time to default conditional on macroeconomic factors assumption incorporated
in KRISTM
reduced form default probability models. Basel II Default Probabilities For Banks
Banks need to obtain estimates of default probabilities to satisfy
pending regulatory capital requirements. These requirements are embodied in
the New Basle Capital Accord (Basle II) promulgated by the
Bank for International Settlements.
Under the Internal Ratings Based (IRB) Approaches in Basle II, banks must
estimate default probabilities (PDs) for their claims against credit-risky
entities using an objective, testable modeling approach. KRISTM default
probabilities can be used to satisfy this need, since it is fully compliant
with the requirements for credit model development and testing under Basel
II. Multiple Default Probability Models
Credit market participants typically provide credit to a broad range of
different types of issuers and counterparties, ranging from large
corporations to small- and medium-enterprises (SMEs). Since the availability
and quality of market and counterparty financial data varies across
different types of counterparties, different default probability models will
be relevant to these counterparties. The most significant differentiation is
between public firms that offer publicly issued securities and private
firms, particularly SMEs. KRISTM supports this differentiation by offering
distinct default probability models for public and private firms. The models
appropriate to public firms are discussed at the
Public Firm Models Service, and
the models for SMEs are summarized at the
Private Firm Model Service.
Banks with SME clients and investors in corporate private debt placements
will find the Private Firm
Model Service of particular interest. Yield, Discount And Forward Rate Curves
Yield Curve Models
Participants in all financial markets also need information about
interest rates for arbitrary future dates to make good lending, investment,
financing and hedging decisions. Yield curve models provide estimates of
these rates, since market interest rates can be observed for only a limited
set of future dates. Yield curve models describe future interest rates in
terms of the yields on constant maturity amortizing or non-amortizing par
coupon bonds with monthly, quarterly or semi-annual coupon payments, yields
on zero coupon bonds, zero coupon bond prices (discount rates), and monthly,
quarterly or semi-annual forward rates. Estimated Yield Curves
KRISTM employs sophisticated spline curve modeling approaches to describe
each yield, discount and forward rate curve. These approaches include linear
interpolation, cubic spline interpolation, and a quartic spline technique
called maximum smoothness forward rates. KRISTM
applies these models to observed market yields to obtain the parameter
estimates for each yield curve. Updated estimates for each yield, discount
and forward rate curve are available daily, and KRISTM subscribers can track the evolution of a yield
curve over time by reviewing the historical series of yield curve estimates. Default-Free Yield Curves
KRISTM offers default-free yield curve estimates for U.S. dollar interest
rates based upon observed U.S. Treasury bond yields reported by the Federal
Reserve Board. These estimates are further described at Yield Curve Service. Interest Rate Volatilities
Financial market participants need Interest rate volatilities to value
interest rate options and other financial products. Historical yield curves
provided by KRISTM can be used to estimate the volatility of interest rates
for future dates, and these estimates can either be used for financial
product valuation or can be compared with volatilities implied by option
pricing models. The interest rate term structure models in the
Kamakura Risk Manager enterprise
wide risk management suite can also use these volatilities. Pricing And
Valuation Of Financial Instruments Using KRISTM Information
The default-free yield curves provided by KRISTM can be directly used to
price financial instruments with known default-free future cash flows, such
as U.S. Treasury bonds. Together with separately obtained yield spreads,
these curves can also be used for valuation of other financial instruments
with known future cash flows, such as municipal bonds. Interest rate options
and related instruments can be priced using the current yield curve together
with volatility estimates obtained from historical yield curves or implied
by interest rate option prices. By combining KRISTM default-free yield
curve estimates with its default probability estimates, credit-risky
financial instruments, such as corporate bonds, can also be priced.
Credit-risky price estimates are obtained from an arbitrage-free valuation
model for each instrument that incorporates a credit-risky yield curve
appropriate to the issuer or counterparty of the instrument. The
credit-risky yield curve used for this purpose is a composite of the
default-free yield curve and a credit and liquidity yield spread curve that
incorporates the default probability estimates. Advanced models for pricing
credit-risky instruments are included in the
Kamakura Risk Manager enterprise
wide risk management suite. Eligible companies can take advantage of
trial access to KRISTM information. For additional information on KRISTM please contact Kamakura Corporation at
sales@kamakuraco.com. |
