Question

Option market on a particular stock gives ? = $31, ? = $30, ? = 10%, for a 3-month option, ? = $3, ? = $2.25.

Identify an arbitrage opportunity

Answer 1

The concept is based on Call Put parity aspect of option trading

C + PV(K) = P + S

C + K e^{-r t} = P+S

the above equation explain the implication of delta neutral portfolio , i.e. zero arbitrage in the situation. Any divergence between the value of calls and puts with the same strike price and expiration date will leads to an arbitrage opportunity for investors in market.

Using the data in above equation

3+30*2.72^(-0.1*0.25)= 2.25+31

=> 32.259 =33.25

As per the outcome above, the right hand side is higher than the left hand side of equation by (33.25 – 32.259) = 0.991.

To take advantage of the arbitrage opportunity in the condition , investor should buy the fiduciary call and at the same time sell the protective put.