(f) The price of Stock Y, which is currently $80, can go to $120, $90, or $60 in 6 months' time. Security A pays $1 if the price of Stock Y in 6 months is $120, and zero otherwise. Security B pays $1 if the price of Stock Y in 6 months is $90, and zero otherwise. Security C pays $1 if the price of Stock Y in 6 months is $60, and zero otherwise. The prices of these securities are pa, PB , and pc, respectively. The discretely compounded risk-free interest rate is 5% per half-year (not annualised). When answering the questions below, explain your calculations. i. In the absence of arbitrage, what is the total cost of purchasing one unit each of securities A, B, and C? ii. If PB 0.2/1.05 - 0.190476, what is the value of a 6-month European call on Stock Y with an exercise price of $75?
(f) The price of Stock Y, which is currently $80, can go to $120, $90, or $60 in 6 months' time. Security A pays $1 if the price of Stock Y in 6 months is $120, and zero otherwise. Security B pays $1 if the price of Stock Y in 6 months is $90, and zero otherwise. Security C pays $1 if the price of Stock Y in 6 months is $60, and zero otherwise. The prices of these securities are pa, PB , and pc, respectively. The discretely compounded risk-free interest rate is 5% per half-year (not annualised). When answering the questions below, explain your calculations. i. In the absence of arbitrage, what is the total cost of purchasing one unit each of securities A, B, and C? ii. If PB 0.2/1.05 - 0.190476, what is the value of a 6-month European call on Stock Y with an exercise price of $75?
Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter13: Capital, Interest, Entrepreneurship, And Corporate Finance
Section: Chapter Questions
Problem 13PAE
Related questions
Question
![(f) The price of Stock Y, which is currently $80, can go to $120, $90, or $60 in 6
months' time. Security A pays $1 if the price of Stock Y in 6 months is $120, and
zero otherwise. Security B pays $1 if the price of Stock Y in 6 months is $90, and
zero otherwise. Security C pays $1 if the price of Stock Y in 6 months is $60, and
zero otherwise. The prices of these securities are pa, PB , and pc, respectively.
The discretely compounded risk-free interest rate is 5% per half-year (not
annualised). When answering the questions below, explain your calculations.
i.
In the absence of arbitrage, what is the total cost of purchasing one unit
each of securities A, B, and C?
ii.
If pg = 0.2/1.05 × 0.190476, what is the value of a 6-month European
call on Stock Y with an exercise price of $75?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa51da7e8-0885-47de-856c-eeb528497fff%2F7671192f-9440-4e00-84ef-41be9ea463c0%2F9gat2qh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(f) The price of Stock Y, which is currently $80, can go to $120, $90, or $60 in 6
months' time. Security A pays $1 if the price of Stock Y in 6 months is $120, and
zero otherwise. Security B pays $1 if the price of Stock Y in 6 months is $90, and
zero otherwise. Security C pays $1 if the price of Stock Y in 6 months is $60, and
zero otherwise. The prices of these securities are pa, PB , and pc, respectively.
The discretely compounded risk-free interest rate is 5% per half-year (not
annualised). When answering the questions below, explain your calculations.
i.
In the absence of arbitrage, what is the total cost of purchasing one unit
each of securities A, B, and C?
ii.
If pg = 0.2/1.05 × 0.190476, what is the value of a 6-month European
call on Stock Y with an exercise price of $75?
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