# Financial Risk Management of Insurance Enterprises - PowerPoint PPT Presentation

PPT – Financial Risk Management of Insurance Enterprises PowerPoint presentation | free to download - id: 6e0165-N2VlY

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Financial Risk Management of Insurance Enterprises

Description:

### Financial Risk Management of Insurance Enterprises Interest Rate Models ... (Brennan-Schwartz) Short term rate and volatility parameter (Longstaff-Schwartz) ... – PowerPoint PPT presentation

Number of Views:7
Avg rating:3.0/5.0
Slides: 29
Provided by: sda115
Category:
Tags:
Transcript and Presenter's Notes

Title: Financial Risk Management of Insurance Enterprises

1
Financial Risk Management of Insurance Enterprises
• Interest Rate Models

2
Interest Rate Models
• Classifications of Interest Rate Models
• Term Structure of Interest Rate Shapes
• Historical Interest Rate Movements
• Parameterizing Interest Rate Models

3
Classifications of Interest Rate Models
• Discrete vs. Continuous
• Single Factor vs. Multiple Factors
• General Equilbrium vs. Arbitrage Free

4
Discrete Models
• Discrete models have interest rates change only
at specified intervals
• Typical interval is monthly
• Daily, quarterly or annually also feasible
• Discrete models can be illustrated by a lattice
approach

5
Continuous Models
• Interest rates change continuously and smoothly
(no jumps or discontinuities)
• Mathematically tractable
• Accumulated value ert
• Example
• 1 million invested for 1 year at r 5
• Accumulated value 1 million x e.05 1,051,271

6
Single Factor Models
• Single factor is the short term interest rate for
discrete models
• Single factor is the instantaneous short term
rate for continuous time models
• Entire term structure is based on the short term
rate
• For every short term interest rate there is one,
and only one, corresponding term structure

7
Multiple Factor Models
• Variety of alternative choices for additional
factors
• Short term real interest rate and inflation (CIR)
• Short term rate and long term rate
(Brennan-Schwartz)
• Short term rate and volatility parameter
(Longstaff-Schwartz)
• Short term rate and mean reverting drift
(Hull-White)

8
General Equilibrium Models
• Derive a process for the short term interest rate
• Based on expectations of investors in the economy
• Term structure of interest rates is an output of
model
• Does not generate the current term structure
• Limited usefulness for pricing interest rate
contingent securities
• More useful for capturing time series variation
in interest rates
• Often provides closed form solutions for interest
rate movements and prices of securities

9
Arbitrage Free Models
• Designed to be exactly consistent with current
term structure of interest rates
• Current term structure is an input
• Useful for valuing interest rate contingent
securities
• Requires frequent recalibration to use model over
any length of time
• Difficult to use for time series modeling

10
Which Type of Model is Best?
• There is no single ideal term structure model
useful for all purposes
• Single factor models are simpler to use, but may
not be as accurate as multiple factor models
• General equilibrium models are useful for
modeling term structure behavior over time
• Arbitrage free models are useful for pricing
interest rate contingent securities
• How the model will be used determines which
interest rate model would be most appropriate

11
Term Structure Shapes
• Normal upward sloping
• Inverted
• Level
• Humped

12
How Do Curves Shift?
• Litterman and Scheinkmann (1991) investigated the
factors that affect yield movements
• Over 95 of yield changes are explained by a
combination of three different factors
• Level
• Steepness
• Curvature

13
Level Shifts
• Rates of maturities shift by approximately the
same amount
• Also called a parallel shift

14
Steepness Shifts
• Short rates move more (or less) than longer term
interest rates
• Changes the slope of the yield curve

15
Curvature Shifts
• Shape of curve is altered
• Short and long rates move in one direction,
intermediate rates move in the other

16
Parameterizing the Yield Curve
• Level 6 month yield
• Steepness (or slope) 10 year yield 6 month
yield
• Curvature 6 month yield 10 year yield
• 2 x 2 year yield
• Based on Brandt and Chapman (2002)

17
Characteristics of Historical Interest Rate
Movements
• Rule out negative interest rates
• Higher volatility in short-term rates, lower
volatility in long-term rates
• Mean reversion (weak)
• Correlation between rates closer together is
higher than between rates far apart
• Volatility of rates is related to level of the
rate

18
Table 1 Summary Statistics for Historical
Rates April 1953-July 1998
19
Run Graph Show of Interest Rates
• Go to
• http//www.cba.uiuc.edu/s-darcy/present/casdfa3/i
ntmodels.html
• Click on Historical (4/53-5/99)
• Click on Start Graph Show
• You may want to shorten the time interval to
speed up the process
• Note how interest rates have moved over the last
46 years
• Pay attention to the level of interest rates, the
shape of the yield curve and the volatility over
time
• Alternative source for the yield curve movements
• http//www.smartmoney.com/onebond/index.cfm?story
yieldcurve

20
Current Interest Rates
• Yields
• Spot rates
• Implied forward rates

21
(No Transcript)
22
Distortions
• U. S. Government stopped issuing 30 year bonds in
October, 2001
• Reduced supply of long term bonds has increased
their price, and reduced their yields
• Effect has distorted the yield curve

23
Parameterizing Interest Rate Models
• Vasicek
• Cox-Ingersoll-Ross (CIR)
• Heath-Jarrow-Morton (HJM)

24
Heath-Jarrow-Morton model
• Specifies process for entire term structure by
including an equation for each forward rate
• Fewer restrictions on term structure movements
• Drift and volatility can have many forms
• Simplest case is where volatility is constant
• Ho-Lee model

25
Table 2 Summary Statistics for Vasicek Model
Notes Number of simulations 10,000, ?
0.1779, 0.0866, ? 0.0200
26
Table 3 Summary Statistics for CIR Model
Notes Number of simulations 10,000, ?
0.2339, 0.0808, ? 0.0854
27
Table 4 Summary Statistics for HJM Model
Notes Number of simulations 100, ? 0.0485,
? 0.5
28
Concluding remarks
• Interest rates are not constant
• Interest rate models are used to predict interest
rate movements
• Historical information useful to determine type
of fluctuations
• Shapes of term structure
• Volatility
• Mean reversion speed
• Long run mean levels
• Dont assume best model is the one that best fits
past movements
• Pick parameters that reflect current environment
or view
• Recognize parameter error
• Analogy to a rabbit