Using the Black-Scholes formula find the price of a$50 strike price European call option expiring in 6months. The current price of the underlying stockis $45 and its return volatility is 20%. Thecontinuously compounding risk-free rate is 3%.Select one:O A. $0.91O B. $2.01O C. $1.25O D. None of the options are correctO E. $1.05

Call option is a derivative product that derives value from the underlying stock price and it gives…

Using the Black-Scholes formula find the price of a $50 strike price European call option expiring in 6 months. The current price of the underlying stock s $45 and its return volatility is 20%. The continuously compounding risk-free rate is 3%. Select one: O A. $0.91 OB. $2.01 OC. $1.25 OD. None of the options are correct O E. $1.05

Using the Black-Scholes formula find the price of a $50 strike price European call option expiring in 6 months. The current price of the underlying stock s $45 and its return volatility is 20%. The continuously compounding risk-free rate is 3%. Select one: O A. $0.91 OB. $2.01 OC. $1.25 OD. None of the options are correct O E. $1.05

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose the following for European options: Stock price $94 3-month call options with strike price $97 3-month put option with strike price $98 1-year risk-free rate is 3%. The put option is trading ot $5 and there is an identical call option that is trading for $4. The arbitrage gain that can be made is equal to: O a. $2.00 b. $0.27 Oc. $3.00 O d. $1.27 O e $227
Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.
*NoChatGPT answers please 6A) What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is 3 months? 6B) What is the assumption of the Black–Scholes–Merton stock option pricing model about the probability distribution of the stock price in one year? What is the assumption about the probability distribution of the continuously compounded rate of return on the stock during the year?
Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.
1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.77. and put option value is 1.99 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. explainc. What would be the extent of your profit in (a) depend on? explain
A call option with X = $55 on a stock priced at S = $60 is sells for $12. Using a volatility estimate of σ = 0.35, you find that N(d1) = 0.7163 and N(d2) = 0.6543. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than 0.35?
You are pricing options with the following characteristics: •Current stock price (St): $35.60 •Exercise price (X): $50 •Time to expiration (T-t): 9 months •Risk-free rate (rf): 3.25% •Volatility (0): 45% (a): What is the Black-Scholes value of call option? In your hand-written solution, provide the calculations of d1,d2, and the final call price. Use Excel or another spreadsheet program to compute the values of N(d1) and N(d2). See the notes for details. (b): Using put-call parity, what is the value of a put option? For this case, assume continuous compounding, which implies that PVt(X)=e-r(T-t).X.
Assume that the current price of a stock is S0 = 100. An investor holds long one European put option with a strike price of K = 100 and short one European call option with strike K = 105. Both options mature at the same time T. Assume that the stock price at maturity is ST = 102. What is the payoff to the investor? Select one: a. 2 b. 1 c. 0 d. -1 e. -2 f. None of the above
1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.7739. and put option value is 1.8101 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?
b) Suppose you are given the following information: Current market price of a share= R200 000 Option’s exercise price = R300 000 Time until the option expires= 5 yrs Risk free rate =4% Standard deviation of the returns on the share= 0.35 Required: i. Calculate d1 and d2 ii. Suppose N(d1) =0.7517 and N(d2) =0.4602; calculate the price of the call option on the share
Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is o = 20%, and the constant continuously compounded interest rate is r = 10%. (b) Repeat part (a) for a European put with strike 60 and maturity 18 months from now.
Consider an european call option on a stock that is not paying dividends with the following characteristics. (i) The stock price at t = 0 is S = $30. (ii) The stricke price is $31. (iii) The volatility of the stock is 20%. (iv) The free risk interest rate is 7%. Construct a 2 period recombining Binomial tree diagram and specty tne varue or the can optron at eacn node of the tree diagram.

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