Question

In: Finance

A European put will expire in two months on a non-dividend paying stock. The strike price...

  1. A European put will expire in two months on a non-dividend paying stock. The strike price for the put is $25 and the price of the put option is currently $2.00. The current value of the stock underlying the put option is $18 and the risk-free rate (based on continuous compounding) is 4%. Using this information explain how an investor can take advantage of any arbitrage opportunity, assuming one exists. If arbitrage is possible, calculate the present value of any profits an investor can earn.

Solutions

Expert Solution

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

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