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- 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 £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. =
- Consider a call option on one share of BP with a strike price of $70 and exercise time 1 quarter (3 months). Suppose the current stock price for BP is S(0) = $65 per share. Suppose further that A(0) = $100, A(1) = $102 and two possible prices for S(1) are S $74 with probability 0.5, S(1) = $66 with probability 0.5. Evaluate the expected returns E(Ks) and E(Kc) for the stock and the option.The price of a share follows the geometric Brownian motion with parameters µ = 0.2 and σ = 0.18. Presently, the share’s price is £38. Consider a call option having one year until its expiration time and having a strike price of £40. The continuously compounded interest rate is 5%. (a) What is the risk-neutral price C of this call option?Suppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1-year eective annual interest rate is 10%. (a) Graph the payo and prot diagrams for a forward contract on XYZ stock with a forward price of $55. (b) Is there any advantage to investing in the stock or the forward contract? Why? (c) Suppose XYZ paid a dividend of $2 per year and everything else stayed the same. Now is there any advantage to investing in the stock or the forward contract? Why?
- A European call that will expire in one year is currently trading for $3. Assume the risk-free rate (based on continuous compounding) is 5%, the underlying stock price is $60 and the strike price is $55. a. Is there an arbitrage opportunity? b. Describe exactly what a trader should do to take advantage of the arbitrage opportunity assuming it exists. c. Determine the present value of the profit that the trader can earn assuming you identify an arbitrage opportunity. Use at least four decimal places for those questions that require a numerical answer.Consider a stock with a current price of $15 that will be worth either $10 or $25 1 year from now. Assume rf = 0% (annual compounding). You have invented a new derivative security called an "inverse", whose payoff in 1 year is 100 divided by the stock price, i.e., payoff =100/S1 . If the beta of the stock is 1.2, what is the beta of this new derivative?Using the Black-Scholes model find the premium on a call option with an exercise price of $50 on a share currently priced at $40. Assume the riskless rate of 1% per annum and the option has two years to expiration. The risk of the stock is measured by a σ value of 0.15. Decompose the premium into intrinsic value and time value? By how much is the call option priced above minimum value? Repeat the exercise for a current share price of $60.
- The current price of a non-dividend paying stock is $30. Use a two -step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when the volatility is 20%? (Hint: Calculate u and d using the CRR approach.) A. $1.48 B. $1.08 C. $1.68 D. $1.28A non-dividend-paying stock, currently priced at GH¢125 per share, can either go up by GH¢25or down GH¢25 in a year. Consider a one-year European call option with a strike price ofGH¢135. The continuously-compounded risk-free interest rate is 8%. Use a one-period binomialmodel to determine the current price of the call option.Suppose that the current price of Roblox Corporation common stock is (RBLX) is $100. If the price of RBLX will be either $150 or $50 one year from now, what is the price of a call option with a strike price of $120 expiring one year from now? Assume that the current risk free rate is 1%. What is the risk neutral probability of the stock being $150 one year from now?