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- 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.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 the three calls from the previous problem expiring in T = 1 year. Suppose that the premium of the three options are $7, $3, $1 for A, B, and C, respectively, today (time 0). Suppose the price on the stock today is $14. Suppose the risk-free rate is constant at 5%. Graph the profit function for the butterfly strategy at time T taking into consideration the time value of the initial cost. By how much would the asset have to change over the year for your butterfly portfolio to be a loss?
- 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.This section asks you to calculate prices for various options. In all cases, consider a rate r = 7.97% per year. Estimate the volatility of returns using the estimator: 1 n-1 σ²≈ T-t i=0 Si+1 log. Sti 2 The term of each option will be T = 182/360 (half a year). Determine a reasonable strike K, which is at similar levels to the price series you have downloaded. An option is a derivative instrument that gives its holder the right to buy or sell an underlying asset at a pre-agreed price K at a future date T. If this right can only be exercised in time T, we say that the option is of the European type. If it can be exercised at T or at any time prior to T, then we say that the option is American. Likewise, if the option grants the right to buy, we say that the option is Call type, if it grants the right to sell then the option is Puttype. These types of options are the simplest and are known as European vanilla options. In this case, if T is the expiration date of the contract, and St is…Assume that the future stock price in T years is given by ST = S0 exp[(μ – 0.5σ2)T + (σ√T)ε], where the current stock price S0=105, expected return µ=0.15, volatility σ=0.80 and ϵ is a standard normal random variable. What is the price level in 6 months such that there is only a 1% chance of the actual value being higher? a. 360 b. 26 c. 105 d. 570
- 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?SECURITY MARKET LINE You are given the following historical data on market returns, r 8A-2 and the returns on Stocks A and B, r, and rp: M A Year M 1 29.00% 29.00% 20.00% 15.20 15.20 13.10 (10.00) (10.00) 0.50 4 3.30 3.30 7.15 23.00 23.00 17.00 6. 31.70 31.70 21.35
- Suppose the market premium is 12%, market volatility is 20% and the risk-free rate is 6%. Suppose a security has a beta of 0.8. Using the CAPM, what is its expected return? (Round off the final answer to one decimal place. Example of writing your answer 2.5%)(I want the answer in 60 minutes or within ) You have observed the following returns over time: Assume that the risk-free rate is 4% and the market risk premium is 2%. a. What are the betas of Stocks X and Y? Do not round intermediate calculations. Round your answers to two decimal places. Stock X: Stock Y: b.What are the required rates of return on Stocks X and Y? Do not round intermediate calculations. Round your answers to two decimal places. Stock X: % Stock Y: % c. What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y? Do not round intermediate calculations. Round your answer to two decimal places.Suppose an investor shorts a straddle (a call option + a put option with the same strike price) with the following parameter values: S = 200, K = 250, σ = 0.30, RF = 0.05, q = 0, T = 5 years, and the interest rate, volatility, and the dividend yield are all given as annual values. Assuming that average daily returns are approximately zero, what is the 5% daily Delta-Gamma VaR of the short straddle position in dollars? Use 3 decimal places for your answer. (If you need to round the Gamma in an intermediate step, please use at least *6 digits*.)