Question

A stock currently sells for $100. A 9-month call option with a strike of $100 has a premium of $10. Assuming a 5% continuously compounded risk-free rate and a 3% continuous dividend yield,

(a) What is the price of the otherwise identical put option? (Leave 2 d.p. for the answer)

(b) If the put premium is $10, what is the strategy for you to capture the arbitrage profit?

a. Long call, short put, long forward

b. Short call, long put, long forward

c. Long call, short put, short forward

d. Short call, long put, short forward

(c) If the put premium is $10, what is the arbitrage profit you can capture at t=0? (Leave 2 d.p. for the answer)

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

As per put-call parity

P+ S = present value of X + C

P= value of put option.

S= current price of the share

X= strike price

C= value of call option.

Present value of X = X/e^r

r = risk free rate.

Given:

P= value of put option =

S= current price of share=100/e^0.03

X= strike price = 100

Present value of X = 100/e^0.05

r = risk free rate. 5%

C = call option = 10

P+97.0445 = 100/e^0.05 +10

P= $8.08

a. Value/Price of put option =$8.08

b. Value/Price of put option =$8.08 (should be)

Value/Price of put option =$10 (Actual)

Since actual is costly

Sell put

Sell share (/forward).

Buy call

Buy Risk-free asset.

Answer: C. Long call, short put, short forward.

c. Difference b/w Actual & Should be = ,10-8.08 =$1.92