ABC stock has price $71.40 at noon, and currently pays no dividend. Consider a six-month European-style call on ABC stock. The call has price = 4.55, delta = 0.45, theta = -6.00/year, gamma = .026. Suppose that the stock price is still $71.40 in 1.0 months. What should be the (new) price of the call option?

ABC stock has price $71.40 at noon, and currently pays no dividend. Consider a six-month European-style call on ABC stock. The call has price = 4.55, delta = 0.45, theta = -6.00/year, gamma = .026. Suppose that the stock price is still $71.40 in 1.0 months. What should be the (new) price of the call option?

Fundamentals of Financial Management (MindTap Course List)

14th Edition

ISBN:9781285867977

Author:Eugene F. Brigham, Joel F. Houston

Publisher:Eugene F. Brigham, Joel F. Houston

Chapter18: Derivatives And Risk Management

Section18.A: Valuation Of Put Options

Problem 2P

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Exercise 1.A stock is worth $50 on december, 1st 2021. This price increases by 4% ou decreases by 4% every 2 months. The flat continuous rate of interest is 5% and the continuous rate of dividend is 2%.a) What is the premium of an American call on this stock with a maturity of 6 months and a strike price of $48?b) What is the premium of a European put on the stock? Maturity and strike price remain unchanged.c) In option pricing theory, what does ‘risk neutral’ probability mean? What is the probability the European put gets exercised?
Exercise 1. A stock is worth $50 on december, 1st 2021. This price increases by 4% ou decreases by 4% every 2 months. The flat continuous rate of interest is 5% and the continuous rate of dividend is 2%. a) What is the premium of an American call on this stock with a maturity of 6 months and a strike price of $48? b) What is the premium of a European put on the stock? Maturity and strike price remain unchanged.
H2. Suppose that a stock price is currently 70 dollars, and it is known that at the end of each of the next two six-month periods, the price will be either 17 percent higher or 17 percent lower than at the beginning of the period. Find the value of an American put option on the stock that expires a year from now, and has a strike price of 76 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 11 percent. Answer = dollars. Please show proper step by step calculation
V3. Stock A is currently trading for $33 per share. The stock pays no dividends. A one-year European put option on the stock with a strike price of $35 is currently trading for $2.10. If the risk-free interest rate is 10% per year, what is the price of a one-year European call option on Stock A with a strike price of $35? (in dollars without the dollar sign, use two decimal places)
Aa.2 A stock price is currently $42. The risk-‐free interest rate is APR 4% with continuous compounding. What is the value of a six-‐month American put option with a strike price of $46 using two-‐step binomial option pricing model? Stock pricemove up by 5% or down by 7% for each three month. Less than $3.0. Larger than $3.0 but less than $3.7. Larger than $3.7 but less than $4.3. Larger than $4.3 but less than $5.0.
Mf1. The spot price of stock LD is 400$. The price of a call on LD that has a strike price of 371$ and expires in 8 months is 39.8$. Risk free Rate= 6% LD will pay a 10.82$ dividend in 2 months. What should the price of a put on LD that has the same strike price and maturity as the call be?
V3. Consider a European call option on Allana Inc. stock. The option matures in 8 months and its strike price is $50. Current stock price per Allana Inc.’s share is $50. Allana Inc. will pay $2 dividend per share in 2 month and $3 per share in 6 months and the risk free rate is 3% per annum with continuous compounding for all maturities. Assume that the standard deviation of Allana Inc.’s stock return is 30% per year. The Black-Scholes value of this call option is ______. $18.31 $15.17 $6.92 $5.24 $2.96
Question 4. A stock that pays no dividends has price today of 100. In one year’s time the stock is worth 110 with probability 0.75 and 85 with probability 0.25. The one-year annually compounded interest rate is 5%. a) Calculate the forward price of the stock for a forward contract with maturity one year. b) Calculate the price of a one-year European put option with strike 100. c) Suppose you observe that the put option in part (b) has a market price of 4. Determine an arbitrage portfolio and calculate how much profit is generated at time T = 1 by this portfolio.
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 σ = 20%, and the constant continuously compounded interest rate is r = 10%.
Question 6 In January 2024, Amazon shares are priced at $80 a share. You believe that theyare overvalued and are worth only $30 a share. June 2024 put options on a strike priceof $60 a share are currently valued at $5. Each put contract is based on 100 shares.(i) What is the intrinsic value of the put option per share? (ii) What is the time value of the put option per share? (iii) If we arrive at expiry in June and you are proved correct with Amazon shares sellingfor $30, what is your net dollar profit on a single put options contract in dollars bearing inmind the put option is based on a contract of 100 shares?(iv) What is your net dollar profit (+) or loss (-) as a holder of the put contract (based on a contract size of 100 shares) if we arrive at expiry in June and you are wrong and Amazon shares are selling for $100?
Question 6 In January 2024, Amazon shares were priced at $80 a share. You believe that they are overvalued and are worth only $30 a share. June 2024 put options on a strike price of $60 a share are currently valued at $5. Each put contract is based on 100 shares. (i) What is the intrinsic value of the put option per share? (ii) What is the time value of the put option per share? (iii) If we arrive at expiry in June and you are proved correct with Amazon shares selling for $30, what is your net dollar profit on a single put options contract in dollars bearing in mind the put option is based on a contract of 100 shares? (iv) What is your net dollar profit (+) or loss (-) as a holder of the put contract (based on a contract size of 100 shares) if we arrive at expiry in June and you are wrong and Amazon shares are selling for $100?