Question

A three-month European put option on a non-dividend-paying stock is currently selling for $3. The stock price is $20, the strike price is $25, and the risk-free interest rate is 5% per annum. Is there an arbitrage opportunity? Show the arbitrage transactions now and in three months.

Answer 1

Strike price = $ 25

Stock price = $20

Risk free rate = 5% p.a.

3 month risk free rate = 5%/4 =1.24% or 0.0125

Actual value of Put option = $3

Price of put option = PV of strike price - current market price)

PV of strike price = Strike price/(1+interest rate for period)

VP = (25/1.0125) - 20

VP = $4.69

Actual value is less i.e. $3.00. it means it is cheaper. So put option shall be long. There will be net gain of $1.69. Along with put option, 1 share is to be long.

So, at current time

Long 1 stock for $20

Long 1 put for $3

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Cash outflow $23

At 3 months (Assume market price = $20)

Value of put option = $ 5

(Strike price - Market price)

(25-20)

Sale price of stock $20

Borrowing cost (23*0.0125)= -0.29

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Cash inflow . $24.71

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Net inflow = $1.71

P.V. of net inflow or arbitrage profit = 1.71/1.025 = $1.69.

So, it is clear that $1.69 arbitrage profit shall accrue from buying put option with share.

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