Exercise 5.13 A European call and put option on the same security both expire in three months, both have a strike price of 20, and both sell for the price 3. If the nominal continuously compounded interest rate is 10% and the stock price is currently 25, identify an arbitrage.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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hi could you please help solve exercise 5.13?
Exercise 5.12 A digital (K, t) call option gives its holder 1 at expira-
tion time t if S(t) > K, or 0 if S(t) < K. A digital (K, t) put option
gives its holder 1 at expiration time t if S(t) < k, or 0 if S(t) > K. Let
C and C2 be the costs of such digital call and put options on the same
security. Derive a put-call parity relationship between C¡ and C2.
Exercise 5.13 A European call and put option on the same security
both expire in three months, both have a strike price of 20, and both sell
for the price 3. If the nominal continuously compounded interest rate is
10% and the stock price is currently 25, identify an arbitrage.
Exercise 5.14 Let Ca and Pa be the costs of American call and put op-
tions (respectively) on the same security, both having the same strike
price K and exercise time t. If S is the present price of the security, give
either an identity or an inequality that relates the quantities Ca, Pa, K,
and e-r. Briefly explain.
S
es
Exercise 5.15 Consider two put options on the same security, both of
which have expiration t. Suppose the exercise prices of the two puts are
K and Ko. where K > K2. Argue that
2...
atch
Transcribed Image Text:Exercise 5.12 A digital (K, t) call option gives its holder 1 at expira- tion time t if S(t) > K, or 0 if S(t) < K. A digital (K, t) put option gives its holder 1 at expiration time t if S(t) < k, or 0 if S(t) > K. Let C and C2 be the costs of such digital call and put options on the same security. Derive a put-call parity relationship between C¡ and C2. Exercise 5.13 A European call and put option on the same security both expire in three months, both have a strike price of 20, and both sell for the price 3. If the nominal continuously compounded interest rate is 10% and the stock price is currently 25, identify an arbitrage. Exercise 5.14 Let Ca and Pa be the costs of American call and put op- tions (respectively) on the same security, both having the same strike price K and exercise time t. If S is the present price of the security, give either an identity or an inequality that relates the quantities Ca, Pa, K, and e-r. Briefly explain. S es Exercise 5.15 Consider two put options on the same security, both of which have expiration t. Suppose the exercise prices of the two puts are K and Ko. where K > K2. Argue that 2... atch
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