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 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?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 current price of a non-dividend paying stock is $30. Use a two-step tree to value a put option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, and in each step the stock price either moves up by 10% or moves down by 10%. Suppose that the risk free rate is 8% per annum with continuous compounding. 1) What should be the EUROPEAN put option price today? 2) If the option was an AMERICAN put option, what should be the price today? 3) If the volatility was given as 30%, how would the AMERICAN put option price change? Volatility is 30%,The share price of your favourite company is currently traded at a price of £60 and interest is compounded continuously at rate 3.7% per year. Assume that the share evolves according to a discrete time LogNormal process with time measured in years, drift μ= 0.15 and volatility o = 0.24. You decide to buy a European call option with a strike price of £63 and an expiration date of two years from now. What is the no- arbitrage price for this option? State your answer to the nearest pence. Do not enter the pound sign.
- The share price of your favourite company is currently traded at a price of £60 and interest is compounded continuously at rate 3.7% per year. Assume that the share evolves according to a discrete time LogNormal process with time measured in years, drift µ = 0.15 and volatility o = 0.24. You decide to buy a European call option with a strike price of £63 and an expiration date of two years from now. What is the no-arbitrage price for this option? State your answer to the nearest pence. Do not enter the pound sign.Suppose that shares of FC Inc. are trading at $100. Consider an American put option withstrike price 110. The option matures two periods from now and it pays no dividends. The price can go upby 15% or down by 10% in each period. What is the price of the option today? The risk-free rate is 7%.The share price of your favourite company is currently traded at a price of £40 and interest is compounded continuously at rate 3.7% per year. Assume that the share evolves according to a discrete time LogNormal process with time measured in years, drift ?=0.15 and volatility ?=0.24. You decide to buy a European call option with a strike price of £42 and an expiration date of two years from now. What is the no-arbitrage price for this option?
- The share price of your favourite company is currently traded at a price of £80 and interest is compounded continuously at rate 3.7% per year. Assume that the share evolves according to a discrete time LogNormal process with time measured in years, 0.15 and volatility o = 0.24 drift µ . You decide to buy a European call option with a strike price of £84 and an expiration date of two years from now. What is the no-arbitrage price for this option? State your answer to the nearest pence. Do not enter the pound sign. =Suppose that a stock price is currently 35 dollars, and it is known that four months from now, the price will be either 51 dollars or 29 dollars. Find the value of a European call option on the stock that expires four months from now, and has a strike price of 39 dollars. Assume that no arbitrage opportunities exist and a risk-free interest rate of 10 percent.Answer =dollars.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?