Question

Rice is worth initially $256. This commodity is the underlying of a European Call and Put, having the same maturity of 11 months and the same strike price K=$275. Initially, the Call and Put are worth $9 and $22, respectively.

a) Find the theoretical risk-free rate.

b) If the observed risk-free rate is 5%, how can you extract arbitrage profits?

Answer 1

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A. 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 = 22

S= current price of share=256

X= strike price = 275

Present value of X = 275/e^0.0r

r = risk free rate.

C= value of call option = 9

22+256 = (275/e^0.0r) + 9

r= 2.2%

Theoretical risk-free rate = 2.2%

B. 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 = 22

S= current price of share=256

X= strike price = 275

Present value of X = 275/e^0.0r

r = risk free rate. 5%

C= value of call option = ?

22+256 = (275/e^0.05) + C

C= 16.41

Value/Price of call option =$16.41

If the value of the call option is $16.41, then put-call parity is violated as the actual call price is $9.

And there is an arbitrage opportunity.

Method:

Buy call, Buy risk-free, Sell put, Sell stock.