Let S = $100, K = $95, r = 8%, σ = 0.3, 6 = 0, T = 1 year. The stock price is modeled by a 3-period binomial forward tree and the length of each period is 4 months. Determine the premium of 95-strike American put with 1 year to expiration.
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- 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 deltaHEJO company has the current stock price of $20 today. Use a 1 step binomial tree to estimate the price of a oneyear call on thisstock. Assume the price can increase or decrease by 10% in in the next year with equal likelihood. Risk free rate is 2%, the strike is $21. A. Find the hedge ratio(H), (make sure have the correct sign, this will be written out as a decimal Answer: 0.25 B) Find the call's value or price today Answer: .58 C) Using the above information to price a put using call parity. Answer: 1.17 Please explain without using excel.a) If the dividend yield is 1.40% annualized, the interest rate is -0.10% annualized, and the index is trading at 28, 144 today, what is the expected price of a 6-month forward? 28, 144e(-0.001 -0.0140)*0.50 = 27,961.66 b ) The 6-month forward is currently quoted at 28,000. Using the information above and the grid below, show how you would arbitrage this index profitably. Be sure to indicate whether each transaction is long or short ( buy or sell) and to include (+) and (-) signs on your cash flows. Use 0 decimals (whole numbers only) in your answers. Transaction Time 0 cash flows Time t cash flows Totals:
- Suppose you are attempting to value a 1-year expiration option on a stock with volatility (i.e., annualized standard deviation) of σ = .40. What would be the appropriate values for u and d if your binomial model is set up using:a. 1 period of 1 year.b. 4 subperiods, each 3 months.c. 12 subperiods, each 1 month.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 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 you are attempting to value a 1-year expiration option on a stock with volatility (i.e., annualized standard deviation) of σ = 0.34. What would be the appropriate values for u and d if your binomial model is set up using: 1 period of 1 year. 4 subperiods, each 3 months. 12 subperiods, each 1 month.Consider shorting a call option c on a stock S where S = 24 is the value of the stock, K = 30 is the strike price, T = ½ is the expiration date, r = 0.04 is the continuously compounded interest rate per year, and = 0.3 is the volatility of the price of the stock. Determine the delta ratio Δ .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.
- Consider a two-period binomial tree model with u = 1.05 and d = 0.90. Suppose the current price of the stock is $100 and the nominal interest rate is 2%. What is the value of an American put with a strike price of $95 that will expire in 146 days?The following two-step binomial tree depicts the quarterly price path of an underlying share for an American call option. Each step represents a quarter of a year. The strike price of this option is $40 and the risk free rate is 5% pa. a) Calculate the payoff of the option at point (b). Give your answer in dollars and cents to the nearest cent. Payoff at point (b) = $ Binomial Share Prices a) b) c) d) e) f) $41.00 $43.87 $38.13 $46.94 $40.80 $35.46 a) b) Calculate the value of the option at point (b). Give your answer in dollars and cents to the nearest cent. Value of the option at point (b) = $ b) c) -d) e) f)1. HEJO company has the current stock price of $20 today. Use a 1 step binomial tree to estimate the price of a oneyear call on thisstock. Assume the price can increase or decrease by 10% in in the next year with equal likelihood. Risk free rate is 2%, the strike is $21. A. Find the hedge ratio(H), (make sure have the correct sign, this will be written out as a decimal B) Find the call's value or price today Note: Show the calculation without using excel.