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# Black-Scholes Model - Option Pricing

1. RED DOT currently sells for \$56, its volatility is 35% interest rates 2%. Use the Black and Scholes equations to compute the value of a call and a put. The strike price is \$55 and the options expire in 220 days.

2. Check the answer with the bsm calculator

3. Compute the . delta-theta-gamma approximation for a value of a call after 25 days for a stock price of \$60. Compare this to the actual call premium computed based on the new price and time to expiration. Does the approximation work? Shortly discuss.

4. You are a market maker who purchases one put contract (use info from #1) you would like to hedge your risk. Describe the portfolio you would establish to control stock. . Compute price risk.

5. Based on your answer to #4 compute your one-day holding profit if the new stock price is \$58. And If the stock price is \$52.

6. Based on the information from #1 set up a bear spread using calls with K = \$55 and \$65 (use software in the excel file attached to compute values). What are the combined Delta, vega, and Theta of your position? Then shortly explain the sign on each Greek.

Please see the attached files with the problems.

Text of the problems.doc - text of the problems