UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
College of Business
DEPARTMENT OF FINANCE
Finance 432 Financial Scenario Project
Spring 2008 Due Date: April 2, 2008
Maximum Number of Points: 20
This is a group project. You may work in groups of up to three people. You only need to turn in
one set of responses to the questions listed in this assignment for each group.
It is the first day at your first full-time job and you are thrilled about it. You work as a financial
risk management analyst in Cookie Life, and your career prospects are promising. After enjoying
a piece of signature cookie from your company, your manager Steve stops by and hands you a
new project to analyze a block of the company’s life annuity business. He recalls that you took
FIN 432 at the University of Illinois (excellent class) and expects you to know everything. You
are given the following instructions and several spreadsheets to assist you with working on your
first exciting and challenging project:
Assets (corporate bonds)
10 year, AAA, 4% fixed rate semi-annual coupon bond of face value $200,000, callable at par at
the beginning of any year after 5 years
20 year, BBB, 6% fixed rate semi-annual coupon bond of face value $300,000, callable at par at
the beginning of any year after 10 years
30 year, B, zero-coupon bond of face value $100,000
10 year, AA, floating rate (LIBOR+150 b.p.) semi-annual coupon bond of face value $100,000
15 year, A, floating rate (LIBOR+200 b.p.) semi-annual coupon bond of face value $400,000
$2000 monthly life annuity-immediate for aged 60
$1000 monthly deferred to age 65 life annuity-immediate for aged 55
$1800 temporary life annuity-immediate payable to age 65 for aged 50
$2000 monthly life annuity-immediate for aged 75
(A monthly life annuity-immediate makes payments at the end of every month)
All yields are nominal semi-annual unless otherwise stated.
Treasury Yields (Yield Curve)
Current Interest Rate Market
For all maturities:
AAA bonds yield 100 b.p. more than treasury bonds
AA bonds yield 140 b.p. more than treasury bonds
A bonds yield 190 b.p. more than treasury bonds
BBB bonds yield 250 b.p. more than treasury bonds
B bonds yield 350 b.p. more than treasury bonds
= 0rt + bond premium for all t, where i is the zero coupon corporate bond yield and r is the
zero coupon treasury bond yield.
LIBOR pays 30 b.p. more than treasury bonds
Bonds are called when the price is above par.
To calculate the present value of a cash flow, use a combination of the spot rate and the forward
rate (both nominal semi-annual).
For example, the appropriate way to discount a year 9.5 cash flow is:
CF9.5 / ((1+0r9/2) ^ 18) / (1+1f9/2)
The appropriate way to discount a year10 month4 cash flow is:
CF10,4/12 / ((1+0r10/2) ^ 20) / ((1 + 1f10/2) ^ (4/6))
You are asked to do the following and then provide an explanation of the results for each item:
1. Develop assets and liabilities cash flows (nominal and discounted) under the current
interest rate environment.
2. Consider the impact on assets and liabilities under the following scenarios:
a. Treasury yield curve shifts upward by 1%
b. Treasury yield curve shifts downward by 1%
c. Treasury yield curve shifts to an inverted yield curve (See spreadsheet)
d. Treasury yield curve shifts to a level yield curve of 4%
3. Use a two-factor Hull-White interest rate model to simulate 1000 nominal semi-
annual interest rates (treasury yield) scenarios (annual time step) with the following
drt r (lt rt )dt r dt dz r
dlt l ( r lt )dt l dt dzl
Short term mean-reversion speed ( r ) 1.00
Current short term rate ( r0 ) 2.10%
Short term volatility ( r ) 1.00%
Long term mean-reversion speed ( l ) 0.10
Long term mean ( r ) 4.00%
Long term volatility ( l ) 1.65%
Both the short term and the long term rates have to be positive.
Under the same simulated interest rate scenarios, consider the following:
a. Impact on the assets discounted cash flows. Graph a histogram of the present
value of the assets and indicate the 95% VaR.
b. Impact on the liabilities discounted cash flows. Graph a histogram of the present
value of the liabilities and indicated the 95% VaR.
c. Suppose your company holds a surplus of $100,000. Determine the impact on
surplus (surplus = assets – liabilities) based on the results you found in Question
4(a). Graph the results as the final output of the simulation and indicated the 95%
Do not just give numbers as your answers. Use what you have learned in the ‘explain to an
actuary/underwriter/CFO/CEO…’ exercises to give professional and comprehensive answers.