University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Test 2 October 8, 2013
NAME
Do not open this test booklet until you are told to do so.
You will have 1 hour and 15 minutes to complete this test.
You must stop work as soon as t
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Test 3 October 31, 2013
NAME
Solutions
1. You purchase 100 shares of a stock on November 1, 2013, and sell the 100 shares on
November 1, 2015. Assume that the stock will pay an
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Examples Module 12
11/7/2013
1. Stock A is currently trading at 50. For each of the following situations, calculate the
1-year forward price and 1-year pre-paid forward price, g
DERIVATIVES BACKGROUND INFORMATION
Buying & Selling Stock
Exchange
stock
stock
pmt2
Broker
pmt1
You
(Buyer)
stock
pmt3
Broker
stock
pmt4
Seller
pmt1 = ask price + broker commission
pmt2 = ask price (price at which the market-maker is willing to sell the s
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
11/14/13 Examples ACTEX Module 14
1
A farmer expects to grow and sell 100,000 bushels of wheat each year. In order to
eliminate variability in the prices he will receive when se
TI Financial Calculator Functions TVM Workbook Underlying formula in familiar form:
( [ PV ] + m [ PMT ] anm ) + [ FV ] (1 + i ) n = 0
where: m = payments per year i = annual effective interest rate n = number of years of payments (= number of years betwe
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 1
- INTEREST RATES a(t) is the accumulation function; it represents the accumulated value at time t of an
investment of 1 unit that was made at time 0.
A(t) is the amount f
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Name
Homework Assignment 6 due Tuesday 10/24/13
1. Stock A, a non-dividend-paying stock, traded at the following prices per share at each of the
indicated times:
Time
(in years)
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Name
Homework Assignment 8 due Tuesday 11/19/13
1. A stock is currently trading at 105. The continuously compounded risk-free interest rate is
0.06. For each of the following si
Interest Functions
v=
1
(1 + i )
d = 1 v =
i=
i
= iv
1+ i
d
d
=
1 d v
i d = id
= ln(1 + i )
Accumulation function:
a (n) = (1 + i ) n = e n - for constant force of interest
n
(t ) dt
a (n) = e 0
- for variable force of interest
Definition of force of in
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 2
- ANNUITIES a + a r + a r 2 + . + a r n 1 = a
Finite Geometric series:
a + a r + a r 2 + . =
Infinite Geometric series:
1 rn
r n 1
= a
, where r 1
1 r
r 1
a
, where r <
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 3
- LOAN REPAYMENT Outstanding Loan Balance
There are three methods for calculating the outstanding balance of a loan. The one to be
used in a particular situation depends
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 4
- BONDS Definitions:
F = face value or par value
r = coupon rate (per coupon payment period)
Fr = coupon amount
n = number of coupon payment periods remaining until redem
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 5
- YIELD RATE OF AN INVESTMENT To find the internal rate of return (IRR) for a series of cash flows, solve the following
equation for v:
C0 + C1v + C 2 v 2 + Cn v n = 0
Th
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 6
- TERM STRUCTURE OF INTEREST RATES Spot Rate (sn) the level annual interest rate that applies to a currently-issued n-year
zero-coupon bond
Yield Curve spot rates for zer
University of Connecticut
Math 3615: Financial Mathematics Problems
Summary Module 7
Asset-Liability Management, Duration, and Immunization
Duration (or Macaulay Duration) D or MacD
The duration of a stream of payments is a weighted average of the number
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University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2013
Test 1 September 17, 2013
NAME
Solutions
1. A deferred annuity consists of 25 payments of 1,000 each.
A payment is made every 2nd year, with the first payment occurring at t=5.
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2011
Test 3 November 1, 2011
NAME
Do not open this test booklet until you are told to do so.
You will have 1 hour and 15 minutes to complete this test.
You must stop work as soon as
University of Connecticut Math 3615: Financial Mathematics Problems Fall 2008 Test 3 October 23, 2008 ACTEX Modules 10 14
NAME *For all problems on this test, ignore the effect of commissions and bid-ask spreads.*
Only SOA-approved calculators are permitt
University of Connecticut Math 280: Financial Mathematics Problems Spring 2008 Test 3 April 3, 2008
NAME
Only SOA-approved calculators are permitted for this test. No books or notes are permitted. Do not open this test booklet until you are told to do so.
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2009
Test 2 October 13, 2009
NAME
Only SOA-approved calculators are permitted in this test.
No books or notes are permitted.
Do not open this test booklet until you are told to do so
University of Connecticut Math 280: Financial Mathematics Problems Spring 2008 Test 4 April 24, 2008
NAME
Only SOA-approved calculators are permitted for this test. No books or notes are permitted. Do not open this test booklet until you are told to do so
University of Connecticut Math 280: Financial Mathematics Problems Spring 2008 Test 2 February 28, 2008
Please write your name in the space provided at the top of the next page.
Only SOA-approved calculators are permitted for this test. No books or notes
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2009
Test 3 October 29, 2009
NAME
Only SOA-approved calculators are permitted in this test.
No books or notes are permitted.
Do not open this test booklet until you are told to do so
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2009
Test 4 November 17, 2009
NAME
Only SOA-approved calculators are permitted in this test.
No books or notes are permitted.
Do not open this test booklet until you are told to do s
University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2009
Test 3 October 29, 2009
NAME
Only SOA-approved calculators are permitted in this test.
No books or notes are permitted.
Do not open this test booklet until you are told to do so
University of Connecticut Math 3615: Financial Mathematics Problems Spring 2009 Test 2 March 5, 2009 ACTEX Modules 5 7 (plus end of Module 4)
NAME
Only SOA-approved calculators are permitted in this test. No books or notes are permitted. Do not open this
University of Connecticut
Math 3615: Financial Mathematics Problems
Spring 2009
Test 3 April 5, 2009 - SOLUTIONS
ACTEX Modules 8-10, plus Section 7.8 in Module 7
1. You purchase 100 shares of Stock A on April 2, 2009, and sell the 100 shares on April 2,
2