The share price of Heavy Metal (HM) changes only once a month: Either it goes up by 22% or it falls by 17.1%. Its price now is $42.5. The interest rate is 1.2% per month. What is the value of a one-month call option with an exercise price of $42.5? What is the option delta? The payoffs of the call option can be replicated by buying shares of stock and borrowing. What amount should be invested in stock and what amount must be borrowed? What is the value of a two-month call option with an exercise price of $42? What is the option delta of the two-month call over the first one-month period?
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- The stock price of Heavy Metal (HM) changes only once a month: either it goes up by 24% or it falls by 20.7%. Its price now is $48. The interest rate is 1.2% per month. What is the value of a one-month call option with an exercise price of $48? What is the option delta? The payoffs of the call option can be replicated by buying shares of stock and borrowing. What amount should be invested in stock and what amount must be borrowed? What is the value of a two-month call option with an exercise price of $49? What is the option delta of the two-month call over the first one-month period?The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. The current price of the stock is $100 per share, and the price of a 3-month call option at an exercise price of $100 is $10.a. If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $100? (The stock pays no dividends.)b. What would be a simple options strategy to exploit your conviction about the stock price’s future movements? How far would it have to move in either direction for you to make a profit on your initial investment?TreeOlivia's stock price is $180 and could halve or double in each six-month period. The interest rate is 12% a year. What is the value of a six-month call option on TreeOlivia with an exercise price of $120? What is the option delta for the six-month call with an exercise of $120? The payoffs of the six-month call option can be replicated by buying shares of stock and borrowing. What amount should be invested in stock and what amount must be borrowed? Assume the exercise price is $120. What is the value of the one-year call option on TreeOlivia with an exercise of $150? (Hint: use the two-step binominal tree) What is the value of the one-year put option on TreeOlivia with an exercise of $150?
- 1. The stock price of Heavy Metal (HM) changes only once a month: either it goes up by 20% or it falls by 16.7%. Its price now is $40. The interest rate is 12.7% per year, or about 1% per month. a. What is the value of a one-month call option with an exercise price of $40? b. What is the option delta? c. What is the option delta of the two-month call over the first one-month period? d. Show how the payoffs of this call option can be replicated by buying HM’s stock andborrowing. e. What is the value of a two-month call option with an exercise price of $40?The share price of Heavy Metal (HM) changes only once a month: Either it goes up by 22% or it falls by 18.5%. Its price now is $48.7. The interest rate is 0.9% per month. What is the value of a one-month call option with an exercise price of $48.7?The stock price of ABC changes only once a month: either it goes up by 20% or it falls by 16.7%. Its price now is £40. The interest rate is 12.7% per year, or about 1% per month. Required: i Suppose a one-month call option on this stock has an exercise price of £40, what is the option delta? ii Show how the payoffs of this call option can be replicated by buying ABC’s stock and borrowing. iii Using the risk-neutral method to calculate the value of a one-month call option with an exercise price of £40. iv Construct a two-month binomial tree. What is the value of a two-month call option with an exercise price of £40? v Use put-call parity, what is the price for a one-month put with the same exercise price? And a two-month put with the same exercise price?
- The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $50per share for months, and you believe it is going to stay in that range for the next 3 months. Theprice of a 3-month put option with an exercise price of $50 is $4.a. If the risk-free interest rate is 10% per year, what must be the price of a 3-month call optionon C.A.L.L. stock at an exercise price of $50 if it is at the money? (The stock pays nodividends.)b. What would be a simple options strategy using a put and a call to exploit your convictionabout the stock price’s future movement? What is the most money you can make on thisposition? How far can the stock price move in either direction before you lose money?c. How can you create a position involving a put, a call, and riskless lending that would havethe same payoff structure as the stock at expiration? What is the net cost of establishing thatposition now?The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $40 per share for months, and you believe it is going to stay in that range for the next 6 months. The price of a 6-month put option with an exercise price of $40 is $8.49. Required: If the semiannual risk-free interest rate is 3%, what must be the price of a 6-month call option on C.A.L.L. stock at an exercise price of $40 if it is at the money? (The stock pays no dividends.) What would be a simple options strategy using a put and a call to exploit your conviction about the stock price’s future movement? What is the most money you can make on this position? How far can the stock price move in either direction before you lose money? How can you create a position involving a put, a call, and riskless lending that would have the same payoff structure as the stock at expiration? What is the net cost of establishing that position now?The common stock of the CGI Inc. has been trading in a narrow range around $35 per share for months, and you believe it is going to stay in that range for the next three months. The price of a three-month put option with an exercise price of $35 is $2, and a call with the same expiration date and exercise price sells for $3. Suppose you write a strap ( = write 2 calls and write 1 put with the same strike price) and the stock price winds up to be $37 at contract expiration. What was your net profit on the strap? A. $200 B. $300 C. $400 D. $500 E. $700
- The current price of XL Corporation stock is $40. In each of the next two years, this stock price can either go up by $15.00 or go down by $15.00. XL stock pays no dividends. The one-year risk-free interest rate is 15% and will remain constant. Using the binomial pricing model, calculate the price of a two-year American put option on LC stock with a strike price of $40.ABC stock is currently trading at R70 per share. A dividend of R1 is expected after three monthsand another one of R1 after six months. A European call option on ABC stock has a strike priceof R65 and 8 months to maturity. Given that the risk-free rate is 10% and the volatility is 32%,compute the price of the option.You expect the price of a stock to increase by 20% in the following year, with a standard deviation of 30%. The stock currently trades at $50. You pursue a strategy of buying 100 shares of the stock on margin. The initial margin requirement is 50%. The annual interest on margin debt is 5% per year. (a) What is the expected return and standard deviation of your strategy? (assume there is no margin call.) (b) The maintenance margin is 30%. Six months after you establish your trade, you receive a margin call. What is the price of the stock when this happens?