Pick a company listed on a major Stock Exchange in Europe or the United States. 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 company's 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. 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.
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?