Friday, August 17, 2012

Pricing Put options Using Black-Scholes Model

This was part of an assignment assigned in "Derivatives Securities", I chose the put option "Credit Agricole" listed in the french stock exchange CAC 40

Characteristics of the selected derivatives:
-Derivatives : Turbo Put
-Underlying Asset: Credit Agricole S.A. share
-Strike Price (K): 3.5 euros
-Expiration Date: 21/09/2012
-Type: European Put option
-Risk Free Rate in France : R=0.152%
-Derivative's Identification Number: DE000CK52TT1
-Parity : 5 (5 put contracts give the right to sell one share of the underlying stock)

Step 1: Calculate the log return of the stock for the given period
Log Return= St/St-1

Step 2: Calculate Volatility of the stock 
 V=standard deviation(log return for the period of time)*Square root of 252
252 is the number of trading per year
 on excel =STDEV(Period of time)*SQRT(252)

Step 3: Calculate d1
d1 black-scholes model, option pricing

Step 4: Calculate d2

d2 black-scholes model, option pricing

 Step 5: Calculate the standard normal cumulative distribution function : N(d1) and N(d2)
On excel
N(d1)=NORMSDIST(d1) but for put option we look for N(-d1)=1- N(d1)
N(d2)=NORMSDIST(d2) for put option N(-d2)=1-N(d2)

Step 6: Calculate the price of the option

P= Ke^(-rt)*N(-d2) - St*N(-d1)

If you want to see the excel file for the pricing of the put option "Credit Agricole", go to this link to access it on google document:
Excel File for the pricing of the put option

 Once you calculate the option price using Black-scholes Model you can compare it to the actual price of the option and make conclusions.


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