Question

A stock currently sells for $32. A 6-month call option with a strike price of $35 has a price of $2.27. Assuming a 4% continuously compounded risk-free rate and a 6% continuous dividend yield:

a)What is the price of the associated put option?

b)What are the arbitrage opportunities if the price of the put option was $5?

c)What if this price was $6?

Answer 1

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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=32/e^0.02
X= strike price = 35
Present value of X = 35/e^0.02
r = risk free rate. 4%

P+ 31.05425 = 35/(1.0202)+ 2.27

P= $5.5229

Value/Price of put option =$5.5229

b. If the value of the put option is $5, then put-call parity is violated.

And there is an arbitrage opportunity.

We need to take benefit of this situation by conducting an arbitrage position.

A synthetic forward can be sold by
1. selling a call option (C-), selling risk free asset.
2. buying a put option (P+) of the same strike price, buying the stock.

c. If the value of the put option is $6, then put-call parity is violated.

And there is an arbitrage opportunity.

We need to take benefit of this situation by conducting an arbitrage position.

A synthetic forward can be sold by
1. Buying a call option (C-), buying risk free asset.
2. Selling a put option (P+) of the same strike price, selling the stock.