Suppose that call options on a stock with strike prices $100 and $106 cost $8 and 55, respectively. How can the options be (the profits from option positions and the total profit).
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- In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49Suppose that put options on a stock with strike prices $18 and $20 cost $2 and $3.50, respectively. How can the options be used to create a bull spread? Construct atable that shows the profit and payoff for the spread.Assume a stock is selling for GH¢48.50 with options available at 40, 50, and 60 strike prices.The 50 call option price is at 2.75.a. What is the intrinsic value of the 50 call?b. Is the 50 call in the money?c. Are the 40 and 60 call options in the money?
- Suppose that both a call option and a put option have been written on a stock with an exerciseprice of $40. The current stock price is $42, and the call and put premiums are $3 and $0.75,respectively. Calculate the profit to positions of both the short call and the long put with an expiration day stock price of $43.Whats the profit of the "Straddle" when stock price is $15, $20, $25, $30, $35, $40, $45, $50, $55, and $60 respectively? Given: - Stock price = $35.00 - Call option price = $3.00 - Put option price = $2.00 - Exercise Price = $35.00Describe the effect on a call option’s price that results from an increasein each of the following factors: (1) stock price, (2) strike price, (3) time toexpiration, (4) risk-free rate, and (5) standard deviation of stock return.
- Suppose that both a call option and a put option have been written on a stock with an exerciseprice of $40. The current stock price is $42, and the call and put premiums are $3 and $0.75,respectively. Draw fully labelled profit diagrams of a long call and a short put.You use the Black-Scholes-Merton model for a put option on a stock. You calculate N(d1) = 0.60 and N(d2) = 0.56. a) What is the delta of the put option? b) You short 100 put options. How would you hedge your delta exposure using the underlying stock? How many shares would you need to buy or sell?Assume that you have been given the following information on Purcell Industries' call options: Current stock price = $14 Strike price of option = $13 Time to maturity of option = 9 months Risk-free rate = 6% Variance of stock return = 0.16 d1 = 0.51704 N(d1) = 0.69744 d2 = 0.17063 N(d2) = 0.56774 According to the Black-Scholes option pricing model, what is the option's value?
- A non – dividend – paying stock with a current price of $52, the strike price is $50, the risk free interest rate is 12% pa, the volatility is 30% pa, and the time to maturity is 3 months? a) Calculate the price of a call option on this stock b) What is the price of a put option price on this stock? c) Is the put-call parity of these options hold?A stock has a price of $73, which can later be $77 or $69 with equal probabilities. The options with exercise price $77 are valued at $1.53 for the call and $1.73 for the put. Calculate the gains/losses/returns for the stock. Calculate the gain/losses/returns for a covered call and protective put portfolio.You use the Black-Scholes-Merton model for a put option on a stock. You calculate N(d1) = 0.60 and N(d2) = 0.56. a) What is the delta of the put option? Solution for A = -0.40 b) You short 100 put options. How would you hedge your delta exposure using the underlying stock? How many shares would you need to buy or sell?
