Friday, June 29, 2012

Derivatives: Find if an option has an arbitrage opportunity (example with a european put option)

In order to find this out if an option has an arbitrage opportunity you must check  if the Option price is withing the upper and lower bounds.

Characteristics of the selected derivative:

Turbo Put
Underlying Asset:
Credit Agricole SA  shares
Strike Price (K):
3.5 euros
Expiration Date:
European Put option
Risk free rate in France:
r= 0.152%
Derivative's Identification
Parity :
5 (5 Puts give the right to sell one share of the underlying stock)

Choice of Risk Free Rate: I chose the interest rate of BTFs financial instrument which is a short term government debt issued in France with a maturity of 3 to 6months, as the Put option will expire in in more than 3 months, I chose a risk-free rate that match the length.

Parity: This Put option has a parity of 5 which means that 5 put contracts give the right to sell one share of the underlying asset: “Credit Agricole SA”, as we use the stock price and strike price to calculate the lower and upper bounds it is needed to multiply the put price by 5 to check whether the price is within the bounds.

The following terms are used:
I will use the following terms:           
K=Strike Price
r=risk free rate          
t=time to maturity (accounting basis D/365)
St: Price of the underlying asset: Credit agricole SA.'s stock           
p: Put price    

The Put option is a European Style option, therefore we will calculate the bounds according to the put-call parity: c + Ke^-rt=So + p

For a euro-put: Lower Bound: p Ke^-rt –So
                         Upper Bound: p Ke^-rt

and we get the following table(if you want me to send you the excel file, give me your email):

We can see clearly that the option price is between the Upper and lower bounds, therefore there was no arbitrage opportunity on this put option during the last 30 trading days


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