F2 We will derive a two-state call option value in this problem. Data: So = $280; X = $290; 1 + r=1.10. The two possibilities for ST are $320and $200. The portfolio consists of 1 share of stock and 4 calls short.Required:a. The range of S is $120 while that of C is $30 across the two states. What is the hedge ratio of the call? (Round your answer to 2decimal places.)Hedge ratiob. Calculate the value of a call option on the stock with an exercise price of $290. (Do not use continuous compounding to calculatethe present value of X in this example, because the interest rate is quoted as an effective per-period rate.) (Do not round intermediatecalculations. Round your answer to 2 decimal places.)Call value

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Answered: We will derive a two-state call option…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.a. Show that the range of S is 50, whereas that of P is 30 across the two states. What is the hedge ratio of the put?b. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio?c. What is the present value of the portfolio?d. Given that the stock currently is selling at 100, solve for the value of the put.
Data: So=102; X = 115; 1 + r=1.1. The two possibilities for ST are 146 and 84. Required: a. The range of S is 62 while that of P is 31 across the two states. What is the hedge ratio of the put? b. Form a portfolio of one share of stock and two puts. What is the (nonrandom) payoff to this portfolio? c. What is the present value of the portfolio? d. Given that the stock currently is selling at 102, calculate the put value. × Answer is not complete. Complete this question by entering your answers in the tabs below. Required A Required B Required C Required D What is the present value of the portfolio? Note: Round your answer to 2 decimal places. Present value $ 146.00 x
Data: S0 = 102; X = 115; 1 + r = 1.1. The two possibilities for ST are 146 and 84. Required: The range of S is 62 while that of P is 31 across the two states. What is the hedge ratio of the put? Form a portfolio of one share of stock and two puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio? Given that the stock currently is selling at 102, calculate the put value.
Data: S0 = 120; X = 126; 1+r = 1.05. The two possibilities for ST are 150 and 102. (Round to 2 decimal places). The range of S is 48 while that of C is 24 across the two states. What is the hedge ratio of the call? Hedge ratio ? Calculate the value of a call option on the stock with an exercise price of 126. (Do not use continuous compounding to calculate the present value of X in this example because we are using a two-state model here; the assumed 5% interest rate is an effective rate per period.) Call value ?
You are evaluating a put option based on the following information: P = Ke-H•N(-d,) – S-N(-d,) Stock price, So Exercise price, k = RM 11 = RM 10 = 0.10 Maturity, T= 90 days = 0.25 Standard deviation, o = 0.5 Interest rate, r Calculate the fair value of the put based on Black-Scholes pricing model. Cumulative normal distribution table is provided at the back.
Data: S0 = 120; X = 126; 1 + r = 1.05. The two possibilities for ST are 150 and 102. Required: a-1. The range of S is 48 while that of C is 24 across the two states. What is the hedge ratio of the call? Note: Round your answer to 2 decimal places. a-2. Calculate the value of a call option on the stock with an exercise price of 126. (Do not use continuous compounding to calculate the present value of X in this example because we are using a two-state model here; the assumed 5% interest rate is an effective rate per period.) Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%.An individual asset i has an estimate of βi = 1.1 and σ2ei = 0.0225 using the single index modelRi = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi. (b) Calculate the optimal weight of combining asset i and the index portfolio M . (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combiningasset i and the index portfolio M .
Assume the APT equation for portfolios A and B with the following system of equations: E[rA] = λ0 + (λ1)3 + (λ2)0.2 = 11.0 E[rB] = λ0 + (λ1)2 + (λ2)1 = 13.0 Assume the following: . The risk free rate is λ0 = Rf = 5 . The expected return on the market portfolio is RM = 10 . Expected returns are consistent with the CAPM. . (hint: note that λ1 = E[RA] − Rf and λ2 = E[RB] − Rf ). Answer the following: (a) What are λ1 and λ2? (b) What is the CAPM β associated with the pure portfolio associated with factor 1? (c) What is the CAPM β associated with the pure portfolio associated with factor 2?
The model value of put option calculated by using binomial model is 10. Hedge ratio is 4/9. If market price of call is Rs 8, which of the following is required to take arbitrage benefit? Select one: O a. Buy 4 stock and 9 put options O b. Buy 4 stocks and sell short 9 stocks c. Write 4 puts and sell short 9 stocks O d. Buy 9 stocks and buy 4 puts
Let S = $100, K = $95, \sigma = 30%, r = 8%, T = 1, and \delta = 0. For simplicity, let u = 1.3, d = 0.8 and n = 2 (that is, 2 periods). When constructing the binomial tree for the European call option, what is A (Stock Share Purchased in the replicating portfolio) at the first node (Time 0)? Question 11 options: 0.1789 0.3886 1.0000 0.2550 0.6912
V3. By looking at the sensivities of your portfolio to δs = -$2 and δσ = -1%, you decide to hedge delta, gamma and Vega risk of your portfolio with the underlying stock and two different options on the same asset with below data. Calculate the units of stock you need to trade to hedge away all delta, gamma and Vega risks of your portfolio.(Note that here you have to calculate the units of stock, Option A and Option B, but you will only submit the units of stock.)
1. Consider a one period binomial model. Suppose So = 1 att = To; and Su = 2 and Sd = ½ at time T₁. If we assume the risk free rate R is 1.2, compute the current value of a European put with strike K = 1. Please round your answer to 2 decimals. Enter answer here 2. Compute the number of units of stock we need to short in order to replicate the option in the previous question. Please round your answer to 2 decimals. Enter answer here 3. Use Black-Scholes Formula to calculate the call price of a European call option with: So = 20, K = 20, r = 5%, c = 0,0 = 40%, T = 5; (round to two decimal digits).

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