A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate values for u, d, and p when a 6-month time step is used. What is the value a 12-month American put option with a strike price of 1,480 given by a two-step binomial tree.
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A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate values for u, d, and p when a 6-month time step is used. What is the value a 12-month American put option with a strike price of 1,480 given by a two-step binomial tree.
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- A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate values for u, d, and p when a six-month time step is used. What is the value a 12-month American put option with a strike price of 1,480 given by a two-step binomial tree.The current spot price of a stock is $89.00, the expected rate of return is 9.8%, and the volatility of the stock is 18%. The risk-free rate is 3.3%. Assume the log-normal model. (a) Calculate the Delta A. and Vega v. of a European call with strike $94.00 expiring in 14 months. Enter your solution for A, to three decimal places. Enter your solution for v. as a dollar value to two decimal places. Ac = Vc = (b) Calculate the Delta A, and Vega v, of a European straddle with strike $94.00 expiring in 14 months. Enter your solution for As to three decimal places. Enter your solution for v, as a dollar value to two decimal places. As =A stock has a price of $37 and an annual return volatility of 59 percent. The risk-free rate is 3.13 percent. Perform calculations in Excel. a. Calculate the European call and European put option prices with a strike price of $38.00 and a 90-day expiration. (Use 365 days in a year. Do not round Intermediate calculations. Round your answers to 2 decimal places.) Call premium Put premium b. Calculate the deltas of the European call and European put. (Use 365 days In a year. A negative value should be Indicated by a minus sign. Do not round Intermediate calculations. Round your answers to 4 decimal places.) Call delta Put delta
- A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. The stock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compounded risk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.The current price of a non-dividend paying stock is $50. Use a two-step tree to value a European put option on the stock with a strike price of $50 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 50%. What is the value of the option according to the two-step binomial model. Please enter your answer rounded to two decimal places (and no dollar sign).Consider a two-period binomial tree model with u = 1.1 and d = 0.90. Suppose the current price of the stock is $50 and the nominal interest rate is 2%. What is the value of an American put with a strike price of $60 that will expire in 3 months? Use at least four decimal places for those questions that require a numerical answer.
- 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.Consider a stock, the current price (S.) of which is $30. We model stock-price evolution using a Binomial model. In every three-month period, u = 1.1052 and d = 0.9048. The risk free rate of interest is 5% per annum continuously compounded. The four-step Binomial tree is shown below: 44.75 40.50 36.64 36.64 33.16 33.16 30 30.00 30.00 27.15 27.15 24.56 24.56 22.22 20.11 Node Time: 0.0000 0.2500 0.5000 0.7500 1.0000 A European-style exotic derivative has been written on this stock. The derivative has one year to expiry. Denote by S;, S2, S; and S4 the stock price after three, six, nine and twelve months respectively. The payoff to the derivative is specified as follows: [max(S2,S,)–min(S,,S,) if S, 2 30 Рayoff 3D max(S,S,S,)-S, if S, < 30 Required: Using a four-step Binomial framework and the risk-neutral approach, calculate the current value of this exotic derivative. Use continuous compounding for all present value calculations. Show all working.You want to price an American Put option that is written on the stock of Shelby Ltd. The price of the stock is £20, the risk-free interest rate is 5%, the annualised volatility of the stock is 42% and the option expires in 5 months. Given that information, calculate the up-multiplier to be used in a nine-step binomial tree. Write your answer in decimal form with up to three decimal points Answer:
- Suppose the current value of a popular stock index is 653.50 and the dividend yield on the index is 2.8%. Also, the yield curve is flat at a continuously compounded rate of 5.5%. A.If you estimate the volatility factor for the index to be 16%, use the Black-Scholes model to calculate the value of an index call option with an exercise price of 670 and an expiration date in exactly three months. You may use Appendix D to answer the question. Do not round intermediate calculations. Round your answer to the nearest cent. $ B.If the actual market price of this option is $17.40, calculate the implied volatility coefficient. Do not round intermediate calculations. Round your answer to two decimal places. %Consider a stock with a current price of P = $27.Suppose that over the next 6 months the stockprice will either go up by a factor of 1.41 or downby a factor of 0.71. Consider a call option on thestock with a strike price of $25 that expires in6 months. The risk-free rate is 6%.(1) Using the binomial model, what are the endingvalues of the stock price? What are the payoffsof the call option?Suppose a stock, not paying any dividend, is currently trading at $50. The annual volatility of its price is 31.55%. This implies that in a one-period binomial tree model the stock price will either be $62.5 or $40 in six months. The annual interest rate is 5%. Consider a European call option with a strike price of $50 and maturity in six months. In the one-period binomial tree model, what's the fair value of the call?