CONNECT WITH LEARNSMART FOR BODIE: ESSE
11th Edition
ISBN: 9781265046392
Author: Bodie
Publisher: MCG
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Chapter 15, Problem 28C
Devise a portfolio using only call options and shares of stock with the following value (payoff) at the option expiration date. If the stock price currently
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Problem 6. Find a portfolio of vanilla options written on the same stock that produces the
following payoff at expiry date.
Profit
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100 105
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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.)
4. Consider a stock with a current price of S0 = $60. The value of the stock at time t = 1 can take one of two values: S1,u = $100, S1,d = $40. The price of a risk-free bond that pays out $1 in period t = 1 is $0.90.
(a) Using a one-step binomial tree, write down the possible payoffs of a put option on stock S with strike K = $60 and maturity t = 1.
(b) What is the price of this put option?
(c) What is the price of a call option with strike K = $60 and maturity t = 1? Please use put-call parity to find the call price.
Chapter 15 Solutions
CONNECT WITH LEARNSMART FOR BODIE: ESSE
Ch. 15.2 - Plot the rate of return to the call-plus-bills...Ch. 15.2 - Prob. 2EQCh. 15 - Prob. 1PSCh. 15 - Prob. 2PSCh. 15 - Prob. 3PSCh. 15 - Prob. 4PSCh. 15 - Prob. 5PSCh. 15 - Prob. 6PSCh. 15 - Prob. 7PSCh. 15 - The following diagram shows the value of a put...
Ch. 15 - You are a portfolio manager who uses Options...Ch. 15 - An investor purchases a stock for 38 and a put for...Ch. 15 - ll. Imagine that you are holding shares of stock,...Ch. 15 - Prob. 12PSCh. 15 - The common stock of the R.U.I.T. Corporation has...Ch. 15 - 14. The common stock of the C.A.L.L. Corporation...Ch. 15 - Prob. 15PSCh. 15 - Prob. 16PSCh. 15 - Prob. 17PSCh. 15 - Prob. 18PSCh. 15 - Prob. 19PSCh. 15 - In what ways is owning a corporate bond similar to...Ch. 15 - Prob. 21PSCh. 15 - Consider the following options portfolio: You...Ch. 15 - Consider the following portfolio. You write a put...Ch. 15 - A put option with strike price 300 on the Acme...Ch. 15 - You buy a share of stock, mite a one-year call...Ch. 15 - Joe Finance has just purchased a stock-index fund,...Ch. 15 - You write a call option with X=50 and buy a call...Ch. 15 - Devise a portfolio using only call options and...Ch. 15 - Prob. 29CCh. 15 - Prob. 1CPCh. 15 - Prob. 2CPCh. 15 - Prob. 3CPCh. 15 - Prob. 4CPCh. 15 - Prob. 5CPCh. 15 - Prob. 1WM
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Similar questions
- Question 2. At current time t a stock paying no income has price 45, the forward price with maturity T on the stock is 40, and the price of a zero coupon bond with maturity T is 0.95. Determine whether there is an arbitrage opportunity. If there is, find an arbitrage portfolio. Verify the portfolio you construct is an arbitrage portfolio.arrow_forwardSuppose that put options on a stock with strike prices $30 and $35 cost $4 and $7, respectively. What is the profit of a bull spread when stock price at maturity is above $35? Select one: a. -3 b. 0 C. 32 d. 2 e. 3 €arrow_forwardFinance (a) Consider a portfolio with a Delta of 100, a Gamma of -20, and a Vega of -10. There are two traded options available: Traded options 1 Traded options 2 Delta 0.2 -0.1 Gamma Vega 0.01 0.05 0.5 0.3 What position in the traded option and/or underlying stock would make the portfolio Gamma and Vega neutral? (Required: Show your work step by step)arrow_forward
- In follow an Ito process with >0, a stock is worth $80 today, if the price of an option that pays the holder $2 exactly the first time the stock price reaches $200, what is the price of an option? Show all calculation.arrow_forwardPlease step by step solutionsarrow_forwardData: So 101; X= 114; 1+r= 1.12. The two possibilities for sr are 143 and 85.arrow_forward
- You buy a share of stock, write a 1-year call option with X = $55, and buy a 1-year put option with X = $55. Your net outlay to establish the entire portfolio is $54. The stock pays no dividends. a. What is the payoff of your portfolio? Payoff b. What must be the risk-free interest rate? (Round your answer to 2 decimal places.) Risk-free rate %arrow_forwardQUESTION 2. Consider a stock valued So at time t = 0, and taking only two possible values S1 = S, or Si = S1 at time t = 1, with S, < I1. a) Compute the initial portfolio allocation (a, 3) of a portfolio made of a units of stock and $B in cash, hedging the call option with strike price K e [S,,3¡] and claim payoff Si – K if Si = 3ı C = (Si – K)* $0 if S = S1, at time t = 1. b) Show that the risky asset allocation a satisfies the condition a € [0, 1]. c) Compute the Superhedging Risk Measure SRMc' of the claim C = (S1 – K)+.arrow_forwardAn investor is considering to buy one of the following stocks: Stock Expected rate of return Risk W 15% 3.0% X 20% 5.0% Y 18% 3.6% Which stock he should buy? Select one: O a. Stock W or stock Y, both are indifference. O b. Stock W O c. Stock X O d. Stock Yarrow_forward
- Use the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.) Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value GA $ $ $ 48 60 0.07 0.04 0.50 0.26arrow_forwardData: 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.arrow_forward7arrow_forward
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