Use the information below to calculate today's European put price. [round to two decimal places] The stock's price S is $52. After three months, it either goes up and gets multiplied by the factor U = 1.2, or it goes down and gets multiplied by the factor D = 1/U. Options mature after T = 0.5 year and have a strike price of K = $51. The continuously compounded risk-free interest rate r is 2.8 percent per year
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- Use the information below to calculate today's European call price in a two-step binomial tree. [round to two decimal places] The stock's price S is $53. After three months, it either goes up and gets multiplied by the factor U = 1.15, or it goes down and gets multiplied by the factor D = 1/U. Options mature after T = 0.5 year and have a strike price of K = $50. The continuously compounded risk-free interest rate r is 1.9 percent per yearSuppose 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 spot price of a non-dividend paying stock is recorded as ₺100 at the close of the day. You estimate that this price is equally likely to go up by 11.1% or go down by 10% every two months and observe that the continuously compounded annual risk-free rate is 20% per year across all maturities. Use a multistep binomial tree together with the risk-neutral valuation approach to compute the theoretical price of a European put option written on this stock with a strike price of ₺80 and exactly six months until expiration
- Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. (a) What is the evolution of the prices of the underlying asset in time? Show it on a binomial tree.A power option pays off [max(S₁ - X),01² at time T where ST is the stock price at time T and X is the strike price. Consider the situation where X = 26 and T is one year. The stock price is currently $24 and at the end of one year it will either $30 or $18. The risk-free interest rate is 5% per annum, compounded continuously. What is the risk- neutral probability of the stock rising to $30? 0.500 0.603 0.450 None of the aboveUse the following data for a fictitiously named company OPPS to answer the questions that follow: — The current stock price S is $23. — The time to maturity T is six months. — The continuously compounded, risk-free interest rate r is 5 percent per year. — European option prices are given in the following table: Strike Price Call Price Put Price K1 = $17.5 6.00 0.10 K2 = 20 4.00 0.50 K3 = 22.5 2.00 1.00 K4 = 25 1.00 2.50 You buy a call option with strike price K2 = 20 and sell a call option with strike price of K3 = 22.5. Then which of the following statements is INCORRECT? The derivative has zero-profit when the stock price at expiration is $21.5. You have set up a call spread. You have set up a bullish spread. The maximum loss is –$2 for a stock price at expiration less than or equal to $20. The maximum profit is $0.5 for a stock price at expiration greater than or equal to $22.5.
- The stock price is currently $30. Each month for the next two months it is expected to increase by 8% or reduce by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off [max(30 — St; 0)]2, where St is the stock price in two months? If the derivative is American-style, should it be exercised early?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.Consider a 3-month European call option on a non-dividend-paying stock. The current stock price is $20, the risk-free rate is 6% per annum, and the strike price is $20. Assume a risk-neutral world. You calculate the following values using the Black-Scholes-Merton model: d1 = 0.2000 N(d1) = 0.5793 d2 = 0.1000 N(d2) = 0.5398 a) What is the probability that the call option will be exercised? b) What is the expected stock price at the option’s expiration in 3 months? Assume that all values of the stock price less than $20 are counted as zero. c) What is the expected payoff on the option at expiration (in 3 months)? d) Calculate the PV of the expected payoff from part c).
- 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?Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. What is the value of the option. Provide all necessary calculations.Give typing answer with explanation and conclusion J&J stock price is currently trading at $100. Over each of the next two three-month periods it is expected to go up by 8% or down by 7%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of the first 3-month if it is expected to down by 7% European call option with a strike price of $95? Compute the current price if use American call option with a strike price of $95. (draw the tree figure for stock movement).