Question

A stock is worth £50 and the current 1-year risk free rate is 1%. A call option with a strike of £55 and 1-year to maturity has a premium of £2. A put option also exists with 1-year to maturity, the same strike price and a premium of £6.46 (to the nearest penny). Are there arbitrage opportunities available in this scenario? Explain how you have come to this judgement and the reasoning that underlies your logic. What are the potential shortcomings of the logic that you are using, if any?

Answer 1

As per the put-call parity equation, C + (K/(1 + r)^t) = P + S,

where C = price of call option,

P = price of put option,

S = current stock price

K = strike price of option

r = risk free rate

t = time to expiration in years

We plug in the values into the equation :

C + (K/(1 + r)^t) = P + S

2 + (55/(1 + 1%)¹) = 6.46 + 50

56.46 = 56.46

We can see that the left hand side equals the right hand side.

Therefore, there are no arbitrage opportunities as per put-call parity.

The potential shortcomings of this are :

• The risk free rate may change over time
• The effect of dividends may change the conclusion