a multiple of 100, i.e. they are options on 100 times the index value. How
many options do you need in order to fully hedge your portfolio?
(b) How many options do you need if the beta is 0.8, and you want to hedge
only 50% of your exposure?
(c) You decide to use the put with strike 600, and fully hedge the portfolio.
The beta is 1. What is the lowest possible value your portfolio will have
when the option expires?
(d) What is the value of your portfolio when the option expires if the stock
index ends up at 645? Assume you traded as in part (c).
1
3. Answer briefly the following questions on option pricing:
(a) Suppose a call option on ABC (ABC does not pay dividends) with exer
cise price $110 is trading at $45 and a put option with the same exercise
price and maturity is trading at $50. The forward price is $110. Is there
an arbitrage opportunity and if so how can you profit from it?
(b) Show that the prices of the following 3 call options of equal maturity,
C
(
K
),
C
(2
K
) and
C
(3
K
), where
K
, 2
K
and 3
K
are the exercise prices
of the three options, respectively, satisfy the following conditions (PV
stands for present value):
1)
C
(
K
)

C
(2
K
)
≤
PV
(
K
)
2)
C
(2
K
)
≤
1
2
C
(
K
) +
1
2
C
(3
K
)
.
You've reached the end of your free preview.
Want to read all 3 pages?
 Summer '14
 sam
 Derivatives