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- The model allows for multiple equity-like indices.
These can be used to model multiple equity portfolios, but also asset
classes such as real estate or a foreign asset portfolio that is modeled
on a return basis. By including a dividend series for these types of
asset classes the system can produce both an income and total return
value. The equity like indices can be correlated to each other and to
the interest rate variables of the DMRP model.
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Interest Rate Model
Description
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- The DMRP interest rate model is a 2 factor interest rate model
for the stochastic process on the yield curve. The DMRP models the
logarithm of the short term rate directly. It models this logarithm as
being subject to a random shock but headed towards a target rate. This
target rate is itself moving towards a long term target rate, but is
also subject to a random shock.
The random shock on the target rate and
on the logarithm of the short term rate are correlated. The parameters
of the model are the volatilities of the two shocks, the correlation of
the two shocks, the two rates of mean reversion and the ultimate target
rate that the target rate is headed towards.
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- The DMRP model has been calibrated to historical yield curves in
both the U.S. economy and to the Canadian, Japanese, and Swiss
economies. The model has been found to be robust over these multiple
economies without dramatic alterations in its parameter values.
The
underlying logic of these values is that the rate of mean reversion of
the logarithm of the short term rate is high towards the target rate,
but the rate of mean reversion of the target rate to the ultimate target
rate is low. Because of this, the target rate determines a trading range
or a regime of the economy.
The regime changes slowly towards the long
run tendency of the economy. Thus long episodes of high, medium or low
interest rates can occur in the model. The volatility of the target rate
is lower than that of the logarithm of the short term interest rate so
that a regime can persist. However, within a regime there can still be
variation in rates.
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- The yield curve is determined at any point in time by the
so-called risk neutral values of the parameters. In the risk neutral
process, the target rate is higher than in the normal, or real
probability process. Also the ultimate target rate is higher.
These
higher values reflect the presence of risk aversion against higher
rates. The risk neutral process incorporates risk aversion by making
higher rates more likely to occur. In addition, the rate of mean
reversion of the logarithm of the short term rate towards the target
rate is higher in the risk neutral process, while the rate of mean
reversion of the target rate towards the ultimate target rate is lower.
This reflects the historical shapes of yield curves observed.
The higher
rate of mean reversion of the logarithm of the short term rate to the
target rate means that the target rate has a bigger impact on the shape
of the yield curve. This allows the yield curve to be more steeply
slowed. The lower rate of mean reversion of the target rate to the
ultimate target rate results in more allowed variation in the value of
long term yields. The two volatility and the correlation parameters are
the same from the risk neutral to the real probability.
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- By adjusting the parameter values, the different major industrial
economies can be modeled. For example, Swiss interest rates have had a
smaller variation in range historically than those in the U.S.. This
fact can be accommodated by primarily adjusting the rates of mean
reversion.
In particular, the rate of mean reversion of the target rate
to the ultimate target rate is made higher. This keeps the range of
rates more compact. Because interest rates are lower in the model, the
absolute volatility automatically becomes lower with the lower absolute
level of rates. This is because the logarithm of the interest rate is
modeled, not the absolute level itself. Thus a given numerical value of
the random shock results in a smaller change in interest rates when the
absolute level of rates is smaller.
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- Similar adjustments allow the modeling of the Canadian, Japanese
and UK interest rate history. In addition, historical sub-periods can be
modeled as well. For example, the last 10 years have been a period of
lower volatility. This primarily shows up in a lower volatility for the
shock to the logarithm of the short term interest rate.
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- Inflation Modeling
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- The rate of inflation is closely related to the level and shape
of the yield curve. When the 3 month yield is high, then inflation is
high. But also when the yield curve is flat to inverted, inflation is
high. The generator can be combined with a simple model of inflation in
terms of the yield curve plus an additional mean reverting deviation
from this implied inflation rate to generate inflation as well with the
other variables of the model. The system as currently configured
generates this inflation residual as well as supplying the model that
goes from the yield curve variables to the inflation rate.
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- Equity Indices Modeling
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- Regime switching on the parameters is an option for equity index modeling.
The software allows for multiple equity indices to be modeled.
These can be correlated to the two stochastic variables, the logarithm
of the short rate, and the target rate that are the drivers of the
interest rate model.
The equity index can be interpreted as a price
index, such as the S & P 500, or as a total return index. The
dividend yield is the dividend yield on the price index. When treating
the index as a total return index, the dividend yield is still
available, but to compute the price index, the total return series and
the dividend series must be used to calculate the price index outside
the system.
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- Averaging of Equity Index
Module
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- An additional module to the system allows averaging of equity
indices as is necessary for equity indexed annuities (EIA) or equity
indexed products (EIP). This module is not supported by a graphical user
interface but is available through a text file interface.
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- What the system produces
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- The system produces two scenario files. The merged yield file
contains scenarios of the two state variables of the interest rate model
and yield curves. The other file contains the two state variables of the
interest rate model, the equity indices and the dividend yield. These
two files are ASCII files with spaces between the variables. They are in
the following format.
- scenario index, time index, short rate, target rate, y_1,
y_2.,...,y_n
- where y_1 to y_n are the yields of bonds in the merged yield
file, or are the value of equity indices and the associated dividend
yields in the other file.
- To see an example of the format of the output files, click these
links: Merged yield
file and Equity indices and
dividend yield.
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- User-provided input
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- The user provides the following input:
- Points on the yield curve that are simulated and fit.
- Starting value of the treasury yield curve for these points.
- Number of scenarios.
- Time interval in scenarios.
- These values are entered in a screen interface. The user then
launches the calculation from the interface after having selected these
values.
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- In addition, the user can select different parameter files from
the interface corresponding to different parameter sets for the interest
rate model parameters. Examples are the real process parameters, the
risk neutral and the parameters for different economies or different
sub-periods. Parameters for different economies must be purchased
separately at a modest fee above the base fee for the system.
- Parameter Sets Available: U.S., U.S. 1950's and 1960's, US Low
Interest, US Low Volatility, Canadian, Japanese, Swiss and UK. The
Economic Scenario Generator is supported by MFC through annual upgrades of both the software and the
licensed parameter sets.
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