(a) Financial engineering deals with the design of new assets. Draw the payoff (at t=1) of the following bull butterfly spread: Purchase 1 call with exercise price a Sell 2 calls with exercise price (atb)/2 Purchase 1 call with exercise price b as a function of the underlying stock price S at t=1 where a=120and b=140.
(a) Financial engineering deals with the design of new assets. Draw the payoff (at t=1) of the following bull butterfly spread: Purchase 1 call with exercise price a Sell 2 calls with exercise price (atb)/2 Purchase 1 call with exercise price b as a function of the underlying stock price S at t=1 where a=120and b=140.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
![(a) Financial engineering deals with the design of new assets. Draw the payoff (at t=1) of the following
bull butterfly spread: Purchase 1 call with exercise price a Sell 2 calls with exercise price (atb)/2
Purchase 1 call with exercise price b as a function of the underlying stock price S at t=1 where a=120and
b=140.
(b) An individual agent thinks that there is a high probability that the Dow Jones will have a payoff (or
points) between a=32,000 and b=36,000 at t=1. Design a digital option (see Figure 1) as a sequence of
calls on the Dow that converges to a pure bet on getting $1 on the interval [32,000, 36,000], i.e. if the
Dow lies between Se[32,000, 36,000] at t=1, then the portfolio of calls pays off exactly $1. The payoff is
O otherwise.
Figure I (Digital option)
payoff
a-32,000
b-36,000
Hint: You have to modify the sell strategies of a bull butterfly spread to obtain a payoff as
given in Figure 2 and then adjust n and õ appropriately.
Figure 2
payoff of portfolio
1-nő
a
b-8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd51db57-4539-4ba1-9709-7d3ffd19490a%2F857cbd55-4589-4b9e-bd89-fbd2565c9052%2F5i8naz3_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Financial engineering deals with the design of new assets. Draw the payoff (at t=1) of the following
bull butterfly spread: Purchase 1 call with exercise price a Sell 2 calls with exercise price (atb)/2
Purchase 1 call with exercise price b as a function of the underlying stock price S at t=1 where a=120and
b=140.
(b) An individual agent thinks that there is a high probability that the Dow Jones will have a payoff (or
points) between a=32,000 and b=36,000 at t=1. Design a digital option (see Figure 1) as a sequence of
calls on the Dow that converges to a pure bet on getting $1 on the interval [32,000, 36,000], i.e. if the
Dow lies between Se[32,000, 36,000] at t=1, then the portfolio of calls pays off exactly $1. The payoff is
O otherwise.
Figure I (Digital option)
payoff
a-32,000
b-36,000
Hint: You have to modify the sell strategies of a bull butterfly spread to obtain a payoff as
given in Figure 2 and then adjust n and õ appropriately.
Figure 2
payoff of portfolio
1-nő
a
b-8
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