Hi There

Can you please help in answering the below question :

Pick a company listed on a major Stock Exchange in Europe or the United States with the first letters of your first and last name in its name (e.g. Thomas Signer = Tyson Foods). If you have no company come to mind, look at the composition of an index such as S&P500 or the Eurostoxx50.

Now you think that this companys stock will either crash badly or go up a lot in the next 3 months; in short you expect anything but a steady development. To benefit from your expected big move either up or down you want to put on a Straddle. This means you buy a call option and you buy a put option on the stock with the same strike price. (see the sample payoff diagram in chapter 10). All calculations relate to 1 share.

a. Establish the annualized historical volatility of the stock over the last 4 months (show the calculations)

b. Calculate the value of a European call option that is ATM and show the results using the Black Scholes formula discussed in class (and used for a class exercise)

1. Set the strike price At-The-Money (rounded to the nearest dollar)

2. Determine the applicable risk free rate from the handouts (Bloomberg print BTMM USD);

3. Use an implied volatility calculated above

4. The time to maturity is 4 months

5. You may assume that your stock will pay no dividend over next 4 months

c. Calculate the value of a European put option with the same strike price as the call

1. Use same strike price as for call

2. Use same risk free rate

3. Use same implied volatility as for call

4. Same maturity

5. Assume there is no dividend over next 120 days

d. What is the total cost of buying the call and the put in USD or EUR (for 1 share)?

e. How much has the stock to move up or down for you to make a profit at expiration?

f. If you only knew the cost of the call, could you calculate the cost of the put without applying the Black-Scholes model? How? Show your calculation.

g. Delta: What is the delta of the call? what is the delta of the put? what is the net delta of the combined position?

h. What could the bank selling you the call and the put option do to hedge the two options sold to you? Be specific

i. Create a histogram of the returns of your chosen companys stock price over the last 90 days.

1. Do the returns of your stock fit the basic assumption of Black-Scholes?

2. What are the implications if not?

3. How could a trader adjust for a violation of the assumption? (To use the histogram function in excel, you may have to add a module to your excel spreadsheet: go to Menu time File, then to Options then to Add-ins, then add Analysis Tool pack; you will then find another item under data - google will help you further if my explanation isnt good enough!)

j. Can you find a call option traded on an exchange similar to the one you priced (same company, similar expiry, similar strike) add it as a print screen.

1. Are the prices you calculated and shown similar?

2. If not, what could explain the difference?