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the risk-free rate pounded continuously is 6%.
you are also given the following selected values from the standard normal cumulative
distribution function:
z n(z) z n(z) z n(z)
.01 0.5040 .11 0.5438 .21 0.5832
.02 0.5090 .12 0.5478 .22 0.5871
.03 0.5120 .13 0.5517 .23 0.5910
.04 0.5160 .14 0.5557 .24 0.5948
.05 0.5199 .15 0.5596 .25 0.5987
.06 0.5239 .16 0.5636 .26 0.6026
.08 0.5279 .17 0.5675 .27 0.6064
.09 0.5319 .18 0.5714 .28 0.6103
.09 0.5359 .19 0.5753 .29 0.6141
.10 0.5398 .20 0.5793 .30 0.6179
(a) list the assumptions required for put-call parity.
(b) use the black-scholes formula to calculate the price of a one-year european call
option on stock xyz with a strike price of 52.
(c) calculate the price of a one-year european put option on stock xyz with a strike
price of 52.
show all work.
course 6: spring 2005 - 6 - go on to next page
morning session
6. (6 points) you are given the following with respect to a portfolio of bonds:
bond
annual
coupon par
market
value
option
features
years to
maturity
a 4.50% 100 100 none 2
b 6.00% 100
callable in one
year at 101 2
you are given the following with respect to a binomial lattice:
• rl : 4%
• σ : 15%
• time interval between nodes: 1 year
(a) calculate the one-year spot rate.
(b) calculate the two-year spot rate.
(c) calculate the one-year implied forward rate.
(d) calculate the value of the option in bond b.
show all work.
7. (4 points) outline the risks faced by a u.s. investor in purchasing a 10-year privatelyplaced
u.s. corporate callable bond.
course 6: spring 2005 - 7 - go on to next page
morning session
course 6
morning session
section b – multiple choice
course 6: spring 2005 - 8 - go on to next page
morning session
1-5. each of questions 1 through 5 consists of two lists. in the list at the left are two items,
lettered x and y. in the list at the right are three items, numbered i, ii and iii. one of
the lettered items is related in some way to exactly two of the numbered items.
indicate the related items using the following answer code:
lettered item
is related to numbered items
(a)
x
i and ii only
(b)
x
ii and iii only
(c)
y
i and ii only
(d)
y
i and iii only
(e)
the correct answer is not given by (a), (b), (c) or (d).
1. x. yield-to-maturity return method i. requires an explicit reinvestment
rate assumption
y. total return method ii. is monly used for pricing and
trading
iii. ignores the capital gain or loss from
security sales
2. x. effective duration matching i. very expensive to implement
y. cash flow matching ii. only works for small changes in
interest rates
iii. accounts for options embedded in
the assets and liabilities
course 6: spring 2005 - 9 - go on to next page
morning session 本文共7页： www.gaofen123.com www.gaofen123.com
(a) 4.3%
(b) 4.5%
(c) 4.7%
(d) 9.6%
(e) 10.0%
course 6: spring 2005 - 19 - go on to next page
morning session
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course 6: spring 2005 - 20 - go on to next page
morning session
16-20. each of questions 16 through 20 consists of two lists. in the list at the left are two items,
lettered x and y. in the list at the right are three items, numbered i, ii and iii. one of
the lettered items is related in some way to exactly two of the numbered items.
indicate the related items using the following answer code:
lettered item
is related to numbered items
(a)
x
i and ii only
(b)
x
ii and iii only
(c)
y
i and ii only
(d)
y
i and iii only
(e)
the correct answer is not given by (a), (b), (c) or (d).
16. x. bonds i. residual claim
y. mon stock ii. limited liability
iii. maturity date
17. x. bination by formula i. equivalent to purchasing an option
y. multiple asset performance ii. assumes that the immunization
target return exceeds either the
minimum return or the expected
worst case active return
iii. active management proportion will
vary inversely with the minimal
accep推荐 return
course 6: spring 2005 - 21 - go on to next page
morning session
18. x. immunization strategy i. transactions are a function of
volatility and time
y. total-return strategy ii. explicitly considers real-world
constraints such as tax effects,
regulatory restrictions and gaap
accounting
iii. manager may take advantage of a
perceived change in value in the
market
19. x. rainbow options i. knockout options
y. barrier options ii. based on the maximum or minimum
of the values of several assets
iii. often arise as part of a structured
security
20. x. spread analysis i. pares the total return and
duration of various assets
y. relative return value analysis ii. analyzes prices and yields by bond
market sector
iii. uses regression to determine
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