Question

the price of a non-dividend-paying stock is $19 and the price of a 3-month European call option on the stock with a strike price of $20 is $1, while the 3-month European put with a strike price of $20 is sold for $3. the risk-free rate is 4% (compounded quarterly). Describe the arbitrage strategy and calculate the profit.

Kindly dont forget the second part of the question

Answer 1

In this case,

c = 1,

T = 0.25,

S₀ = 19,

K = 20, and

r = 0.04

From put–call parity,

p = c + Ke^-rt - S₀

p = 1 + 20e^-0.04*0.25 - 19 = 1.80

so that the European put price is $1.80.

Now, since the put price is more than the findamental price, it is overvalued.

Arbitrage strategy to be used is as below:

1. Sell the protective put: We sell a put option and receive the $3 premium. We also short sell the stock and receive $19. The total cash inflow is $22.
2. Buy fiduciary call: We payout a total of $20.80 for the fiduciary call option. That is we pay $1 as premium for the call option and invest 19.80 in a bond for 3 months at 4%.
3. Net cash inflow: Our net cash inflow is (22 – 20.80) = $1.20.