In: Finance
Theretical minimum price of European Put Option | |||
= (E / e^rt) - S | |||
Where, | |||
E = Exercise Price = $25 | |||
r = 4% = 0.04 | |||
t = 2 months = 2/12 | |||
S = Current Value of Stock = $18 | |||
Now, | |||
e^rt by excel formula = exp(0.04*2/12) = 1.0067 | |||
So, | |||
Theretical minimum price of European Put Option | |||
= (E / e^rt) - S | |||
= ($25 / 1.0067) - $18 | |||
= $24.83 - $18 | |||
= $6.83 | |||
The Market value of the Put option is $2 whereas the | |||
theretical minimum price is $6.83. Therefore the option | |||
is undervalued. | |||
Arbitrage Strategy - | |||
1) | Buy 1 Put Option at $2 | ||
2) | Buy 1 Stock @ $18 | ||
Value of Profits under arbitrage as follows - | |||
Cas Flow in Year 0 | |||
= Buying Price of Put Option and Stock | |||
= $2 + $18 | |||
= $20 | |||
Let us assume that there are 2 prices on expiry date, 1 below | |||
the strike price i.e. $20 and 1 above strike price i.e. $30 | |||
Cash Flow at the end of 6 months | |||
Particulars | Price = $20 | Price = $30 | |
Value of Put Option (Max((Strike Price-Price at end),0)) | $5 | 0 | |
Value of Stock | $20 | $30 | |
Total (Value of Put Option+Value of Stock) | $25 | $30 | |
Present Value Factor (1/e^rt) = (1/1.0067) | 0.9933 | 0.9933 | |
Present value of Total Value ($25*0.9933) & ($30*0.9933) | $24.83 | $29.80 | |
Cash Flow in Year 0 | $20.00 | $20.00 | |
Arbitrage Profit ($24.83-$20) & ($29.80-$20) | $4.83 | $9.80 | |