please answer question 7

A stock has two possible ending prices six months from now: $120 or $90. A call option written on this stock has an exercise price of $110. The option expires in six months. The risk-free rate is 6% per year. The current price of the stock is $100. a. Show how you can create a hedge portfolio using a combination of the stock and call option on this stock. b. What is the equilibrium price of the call option on this stock? 2 3. A stock has two possible ending prices six months from now: $ 45 or $60. A call option written on this stock has an exercise price of $48. The option expires in six months. The risk-free rate is 4 % per year . The current price of the stock is $50. What is the equilibrium price of the call option on this stock? Suppose you find this call option trading at $3.00, describe an arbitrage strategy you can use to take advantage of the mispricing and calculate your arbitrage profit per share used in the strategy. 4. Assume the following information for a stock and a call option written on the stock: Exercise price $45 Current stock price $30 a2-0.25 Time to expiration, t 0.25 Risk-free rate, r-0.05 Black-Scholes OPM C-sIN(di)-Xe" IN(d)) di-InS/X)+(r 1/2at at d-di at a. Use the Black-Scholes formula to determine the value of the call option. b. What is the value of the corresponding put option on the same stock with the same exercise price and time to maturity? c. Repeat a and b when the time to expiration is 0.5. d. Repeat a and b when the exercise price $35 5. In using the Black-Scholes call option formula, what would be the effect on the call option a. if o rises, other things remaining the same? b. if T falls, other things remaining the same? c. if the current stock price rises, other things remaining the same? 6. Consider the Black-Scholes call option formula and suppose the price of the underlying stock gets very large relative to the option's exercise price. As the stock price gets larger, what value would the option be approaching? 7. A non-dividend-paying stock has a current price of S30 and a volatility of 20 percent per year. The risk-free rate is 7 % per year a. Use the Black-Scholes equation to value a European call option on the stock with an exercise price of $28 and time to maturity of three months. b. Calculate the price of the put option on this stock with the same exercise price and time to maturity c. Without performing the calculations, state whether the price would be higher if the call were American. Why? 8. Suppose a put and a call exist on the same stock, each having an exercise price of $75 and each having the same expiration date. The current price of the stock is $68. The put's current price is $6.50 higher than the call's price. A riskless investment over the time until expiration will yield 3 percent. Given this information, are there any riskless profit opportunities available? Are the put and call priced in an equilibrium relationship with one another? 9. Combine the Black-Scholes equation for a European call option with the put-call parity condition to derive the Black-Scholes equation for European puts. 10. The current price of an American call option with one year to expiration is $10. The stock on which the call is written is selling at $65 and the exercise price of the option is $55. The risk-free rate is 89% per year. What would you rather do: i. sell the option now and invest the proceeds in the risk-free asset, or ii, sell the stock short, invest the proceeds in the risk-free asset and wait till expiration to exercise the option? Show the end of year cash flows to justify your choice