Consider a stock, the current price (So) 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: 30 Node Time: 0.0000 33.16 Payoff= 27.15 0.2500 36.64 30.00 24.56 0.5000 40.50 33.16 27.15 22.22 0.7500 44.75 即訂 36.64 [max(S₂, S.)-min(S₁,S₂) if S4 ≥ 30 max(S₁, S₂, S3)-S4 if S₁ < 30 30.00 24.56 20.11 1.0000 A European-style exotic derivative has been written on this stock. The derivative has one year to expiry. Denote by S₁, S2, S3 and S, the stock price after three, six, nine and twelve months respectively. The payoff to the derivative is specified as follows: 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 stock, the current price (So) 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: 30 Node Time: 0.0000 33.16 Payoff= 27.15 0.2500 36.64 30.00 24.56 0.5000 40.50 33.16 27.15 22.22 0.7500 44.75 即訂 36.64 [max(S₂, S.)-min(S₁,S₂) if S4 ≥ 30 max(S₁, S₂, S3)-S4 if S₁ < 30 30.00 24.56 20.11 1.0000 A European-style exotic derivative has been written on this stock. The derivative has one year to expiry. Denote by S₁, S2, S3 and S, the stock price after three, six, nine and twelve months respectively. The payoff to the derivative is specified as follows: 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.

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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(Expected rate of return using CAPM) a. Compute the expected rate of return for Acer common stock, which has a 1.8 beta. The risk-free rate is 5 percent and the market portfolio (composed of New York Stock Exchange stocks) has an expected return of 13 percent. b. Why is the rate you computed the expected rate? ... a. The expected rate of return for Acer common stock is %. (Round to one decimal place.)
2) Suppose that the price of a non-dividend-paying stock is $32, its volatility is 30%, and the risk-free rate for all maturities is 5% per annum. Provide a table showing the relationship between profit and final stock price for a bull spread using European put options with strike prices of $25 and S$30 and a maturity of one year. Ignore the impact of time value of money.
Consider the following information on a particular stock:Stock price = $88Exercise price = $84Risk-free rate = 5% per year, compounded continuouslyMaturity = 11 monthsStandard deviation =53% per year. What What is the delta of a put option?
You have been following a stock for 6 months and the following is its past return Year 1: -5% Year 2: -10% Year 3: 15% Year 4: 5% Year 5: 10% Year 6: 15% What is the expected return and standard deviation of the stock based on the historical data? Assume normal distribution, what is VaR at 5% for this stock? What is the Sharpe ratio of the stock based on historical data, risk free rate is 1%?
You have at hand the historical monthly excess returns of Strategy X over 12 months. In addition, you have the monthly excess returns to the market. The risk free rate is 2%. Excess returns (monthly) Strategy X Market 0.012 0.011 0.007 0.009 0.014 0.007 0.013 0.004 0.005 0.013 0.008 0.006 0.011 0.010 0.006 0.011 0.010 0.010 0.014 0.009 0.008 0.004 0.009 0.007 Required: Calculate the annualised CAPM alpha for Strategy X.
Indicate whether the following statements are true or false (circle one). Use 1 or 2 sentences to discuss why it is so. (a) If R, is simple 1-month return, then the annualized return is 12 x R, after assuming all R = R. True False Why? (b) Let and r GSA be continuously compounded 1 - month returns for Goldman Sachs Group (GS) and American International Group (AIG). If we construct a portfolio using the share ain[0, 1] for GS, the portfolio cc return is ľ AIG = 0x*y +(1-x)*r True False Why? (c) In 5. (b)., if 5% quantile of the portfolio cc return is given as AIG, GS, r 40.05 = -0.5, then 5% monthly Value-at-Risk for the $10,000 investment in this portfolio is $10,000 × (-0.5) = -$ 5,000. True False r
You expect the risk-free rate to be 4 percent and the market return to be 10 percent. You also have the following information about three stocks. Stock Beta Current Expected Expected Price Price Dividend U 1.5 $10 $11.50 $1.00 N 1.1 $27 $30 $0.00 Ο 0.8 $35 $36 $1.50 (Question 1 of 2) Based on the required rate of return estimated with the CAPM and your expected returns based on prices and dividends, select an investment strategy for each stock: Stock U Stock N [Choose ] [Choose ] Stock O [Choose ]
Consider the following information on a particular stock:Stock price = $88Exercise price = $84Risk-free rate = 5% per year, compounded continuouslyMaturity = 11 monthsStandard deviation =53% per year. What What is the delta of a call option?
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.
Stock A has a beta of 1.5, the risk-free rate is 4% and the return on the market is 9%. If inflation changes by -3%, by how much will the required return on Stock A change? (i.e. required return after change - required return before the change) answer format: show your answer in percent (without th
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 a certain butterfly spread on American International Group stock (AIG): this is a portfolio that is long one call at $50, long one call at $70, and short 2 calls at $60. Assume expiration of all options s at the same timet=T. (@) Graph the payoff of this portfolio at expiration T as a function of the stock price ST of AIG. (b) If today the calls cost $13.10, $5.00, and $1.00 for the strikes at 50, 60, and 70, respectively, what will be the profit or loss (PnL) from buying this spread if the stock turns out to be trading at S5 at time T2 at $35? Assume the risk-free rate is 0%,

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