in a one-period binomial model, assume that the current stock price is $100 and that it will rise by 10% with a probability of 45% or fall by 15% with a probability of 55% after one month. The annual risk-free rate of 2%. The call option price with an exercise price of $102 is equal to: O a $5.88 O b. $8.60 OC $5.33 Od $8.57
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- Consider the following data for a certain share. Current Price = S0 = Rs. 80 Exercise Price = E = Rs. 90 Standard deviation of continuously compounded annual return = \sigma = 0.5 Expiration period of the call option = 3 months Risk – free interest rate per annum = 6 percent a. What is the value of the call option? Use the normal distribution table. b. What is the value of a put option?Consider the following data for a certain share. Current Price = So = Rs. 80 Exercise Price = E = Rs. 90 Standard deviation of continuously compounded annual return = 0 = 0.5 Expiration period of the call option 3 months Risk – free interest rate per annum = 6 percent a. What is the value of the call option? Use the normal distribution table. b. What is the value of a put option?Using the binomial call option model to find the current value of a call option with a $25 exercise price on a stock currently priced at $26. Assume the option expires at the end of two periods, the riskless interest rate is ½ percent per period. What are the hedge ratios?
- 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 = .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 European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is 6 months. (a) Calculate u, d, and p for a two-step tree. (b) Value the option using a two-step tree.
- 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 .Suppose the current stock price of JuJube Inc is ¥100, the risk-free interest rate is 5%, the standard deviation is 25%, the time to maturity is 4 months, the strike price is ¥85, and the price of a call option is ¥25.20. Using the put-call parity relationship, the put option price is closest to A. ¥25.20 B. ¥16.40 C. ¥5.20 D. ¥8.80 E. None of the aboveAssume a stock price of $30.25, risk-free rate of 1 percent, standard deviation of 40 percent, N(d1) value of 0.7976, and an N(d2) value of 0.7089. What is the value of a six-month put with a strike price of $25 given the Black-Scholes option pricing model (rounded to the nearest cent)? $6.49 $0.83 $2.43 $1.12 None of the above are correct.
- Suppose a stock is currently (time t = 0) worth 100. Further, suppose the one year annually compounded interest rate is 2%, and the two year annually compounded rate is 3%. Find the following:a) The forward price for a forward contract on the stock with maturity year T1 = 1. b) The forward price for a forward contract on the stock with maturity year T2 = 2.c) The forward price for a forward contract with maturity T1 = 1 on a ZCB with maturity T2 = 2.d) The forward price for a forward contract with maturity T1 = 1 on a forward contract on the stock with maturity T2 = 2 and delivery price K = 101.What are the prices of a call option and a put option with the following characteristics? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Stock price Exercise price Risk-free rate = $70 = $65 = 4.2% per year, compounded continuously = 4 months Maturity Standard deviation = 60% per year Call price=? Put price=?Find the current price of a one-year, R110-strike American put option on a non- dividend-paying stock whose current price is S(0) = 100. Assume that the continuously compounded interest rate equals r = 0.06. Use a two-period Binomial tree with u = 1.23, and d = 0.86 to calculate the price VP(0) of the put option.