Consider the at-the-money call option on Roslin Robotics evaluated in Problem 11. Suppose the call option is not available for trade in the market. You would like to replicate a long position in 1000...

Consider the at-the-money call option on Roslin Robotics evaluated in Problem 11. Suppose the call option is not available for trade in the market. You would like to replicate a long position in 1000 call options.

a. What portfolio should you hold today?

b. Suppose you purchase the portfolio in part a. If Roslin stock goes up in value to $62 per share today, what is the value of this portfolio now? If the call option were available for trade, what would be the difference in value between the call option and the portfolio (expressed as percent of the value of the call)?

c. After the stock price change in part b, how should you adjust your portfolio to continue to replicate the options?

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11

Roslin Robotics stock has a volatility of 30% and a current stock price of $60 per share. Roslin pays no dividends. The risk-free interest is 5%. Determine the Black-Scholes value of a one year, at the money call option on Roslin stock.