Problem 1. Gather the following information regarding Express Scripts:
- The current stock price.
- Ask price for a January 2011 call option with exercise price of $90
- Historical volatility
- Current risk-free interest rate
Problem 2. Based on risk-neutral pricing compute the probability that Express Scripts' price will be in between $75 and $105 in 333 days (expiration of January options).
Problem 3. Use BSM software to compute the value of a $90 put and $90 Call expiring in January. Without doing any calculations is current implied volatility greater than or less than actual volatility? Briefly explain.
Problem 4. What position in stocks would you need to take to hedge a short position in 100 calls? A short position in 100 puts?
Problem 5. For each of the positions (Stock/Call and Stock/Put) in #4 compute:
- Current value
- Value if stock price increases $1
- Value if stock price increases $5
Problem 6. Establish up a straddle with K = $90. What are the combined Delta, vega, and theta of your position? Explain intuitively the sign (positive or negative) on these Greeks.