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CHAPTER 15:
ADVANCED DERIVATIVES AND STRATEGIES
ENDOFCHAPTER QUESTIONS AND PROBLEMS
1.
In both types of swaps there are two parties who make payments to each other at specific dates according
to different formulas.
In an interest rate swap the payments made by one party are based on a particular
interest rate.
The other payments can be fixed or based on another type of interest rate.
In an equity swap
the payments of at least one party are based on the performance of a stock or index.
The payments of the
other party can be based on the performance of a different stock or index or can be based on a fixed or
floating interest rate.
Thus, any swap in which one party's payments are based on a stock or index is
called an equity swap even though it might really be only partequity and partinterest rate.
2.
Most structured notes are tailored, i.e., structured, to the specific needs of an investor.
A portfolio
manager whose portfolio is exposed to loss from falling interest rates over the holding period might
purchase an inverse floating rate note as a type of hedge. If interest rates decrease, the inverse floater will
gain, thereby offsetting some or all of the loss on the rest of the portfolio.
Of course, the inverse floater
will lose if rates rise thereby offsetting some or all of the gain on the rest of the portfolio.
3.
The payoffs at expiration from the chooser are as follows:
Payoff of Chooser at Expiration
Choice made at t
S
T
≤
E
S
T
> E
designate chooser as a call
0
S
T
 E
designate chooser as put
E  S
T
0
The holder of the chooser option will designate it as a call at time t if C(S
t
,Tt,E) > P(S
t
,Tt,E).
From put
call parity, the put price can be expressed as C(S
t
,Tt,E)  S
t
+ E(1 + r)
(Tt)
.
Thus, C(S
t
,Tt,E) > P(S
t
,T
t,E) implies that C(S
t
,Tt,E) > C(S
t
,Tt,E)  S
t
+ E(1 + r)
(Tt)
, which implies that
S
t
> E(1 + r)
(Tt)
.
We are told that to replicate the chooser we hold a call expiring at T with exercise price E and a put
expiring at t with exercise price E(1 + r)
(Tt)
.
Now suppose we are at t and the following occurs:
S
t
> E(1 + r)
(Tt)
The call is still alive but the put expires outofthemoney.
At the call’s expiration at T, it will
pay off S
T
 E if S
T
> E and zero otherwise, which is exactly like the chooser.
S
t
≤
E(1 + r)
(Tt)
The call is still alive and the put expires and pays off E(1 + r)
(Tt)
 S
T
.
Take the amount E(1 + r)

(Tt)
and invest it in riskfree bonds.
At T, it will be worth E.
Short the stock at t and buy it back
at T.
Thus, the overall value at T if S
T
> E is S
T
 E (from the call) + E (from the riskfree bond)
 S
T
(from buying back the stock), for a total of 0.
If at T S
T
≤
E then you will have zero (from
the call), E (from the riskfree bond) and  S
T
(from buying back the stock), for a total of E  S
T
.
These match the payoffs of the chooser option.
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