Answer the following two questions with respect to the table below. A financial institution has the following portfolio of over-the-counter options on a stock: Vega of Option Туре Рosition Delta of Gamma of Option Option 0.50 Call -1,000 -500 2.2 1.8 Call 0.80 0.6 0.2 Put -2,000 -500 -0.40 1.3 0.7 Call 0.70 1.8 1.4 A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8. What position in this option and the underlying will make the portfolio delta and gamma neutral?

Answer the following two questions with respect to the table below. A financial institution has the following portfolio of over-the-counter options on a stock: Vega of Option Туре Рosition Delta of Gamma of Option Option 0.50 Call -1,000 -500 2.2 1.8 Call 0.80 0.6 0.2 Put -2,000 -500 -0.40 1.3 0.7 Call 0.70 1.8 1.4 A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8. What position in this option and the underlying will make the portfolio delta and gamma neutral?

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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5. Explain and give appropriate use of the following option trading strategies along with their Payoff.: a. Spreads b. Straddles c. Strangles d. Covered Call and Protective Put. State Put-Call Parity theorem for European options. European put and call options with a strike price of Rs. 24 and expiry in 6-months are trading at Rs. 5.09 and Rs. 7.78, respectively. The current stock price is Rs. 20.37 with a risk-free interest rate continuously compounding equal to 7.48%. Is there an arbitrage opportunity? How can it be exploited?
Use the binomal option pricing model to estimate the Call price. Stock price (S) $120.00 Stock price up (Su) $170.00 Stock price down (Sd) $50.00 Strike price (K) $120.00 rf 1.0% Call price up (Cu) Call price down (Cd) D PV(B) Call price (C)
am. 114.
Consider the following options on stock X: Option Delta Gamma Vega A 0.5 2.2 1.8 В 0.8 0.6 0.2 C -0.40 1.3 0.7 D 0.70 1.8 1.4 A bank is long 1000 units of Option A, short 200 units of Option B, short 2000 units of Option C, and short 500 units of Option D. The following two options are also available in the market: Option Delta Gamma Vega E 0.6 1.5 0.8 F 0.1 0.5 0.6 a) Design one strategy that would make the bank's portfolio delta neutral. b) Design one strategy that would make the bank's portfolio delta and gamma neutral. Explain why this strategy provides a better hedge with respect to changes in the price of stock X than the strategy you constructed in part (a). c) Design one strategy that would make the bank's portfolio delta, gamma, and vega neutral.
2. The following table shows the constituent stocks of a hypothetical index. Stock B splits two-for-one during the period. Stock A B C Beginning of Period Price ($) Shares 30 75 36 2,000 500 1,200 End of Period Price ($) 26 40 32 Shares 2,000 1,000 1,200 a. Calculate the returns on both the price-weighted index and the market value- weighted index of three stocks over the period. b. If you just buy 5,000 shares of stock C for $36, hold for 1 year, collect $8 dividend and sell it at $32. Calculate your total return.
Assume that you have been given the following information on Purcell Corporation's call options: Inputs Intermediate Calculations Current stock price = $12 d1 = 0.32863 Time to maturity of option = 9 months d2 = 0.05477 Variance of stock return = 0.10 N(d1) = 0.62878 Strike price of option = $12 N(d2) = 0.52184 Risk-free rate = 7% According to the Black-Scholes option pricing model, what is the option's value? Do not round intermediate calculations. Round your answer to the nearest cent. Use only the values provided in the problem statement for your calculations. $
3 You are given the following information on some company's stock, as well as the risk- free asset. Use it to calculate the price of the call option written on that stock, as well as the price of the put option. (HINT: You should use the Black-Scholes formula!) (Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16.) Today's stock - $77 price = Exercise price = $75 Risk-free rate = Option maturity = 5 months Standard deviation of annual stock returns Call price Put price $ $ 3.4% per year, compounded continuously = 59% per year 3.61 x 0.56 X 1
Consider the 1-period binomial model with a bond with A(0) = 60 and A(1) = 70 and a stock with S(0) = 4X and S^u(1) 6Y and S^d(1) = 3Z. = 1. What is the price (payoff) C(1) of a call option with strike price 28? 2. same... with strike price 45? 3. same... with strike price 72? 4. Set up a system of linear equations to determine a replicating portfolio for the call option from part 2 (strike price 45). 5. Solve it and determine the price C(O). 6. Compute, tabulate, and plot the price C(O) as you vary the strike price of the option from 28, 29, ..., 71, 72.
A call option on a stock trading at $58 has an exercise price of $47. The call option is _____ Check all that apply A. in the money B. out of the money C. at the money
A. An option is trading at $5.03. If it has a delta of -.56, what would the price of the option be if the underlying increases by $.75? What would the price of the option be if the underlying decreases by $.55? B. What type of option is this and how? C. With a delta of -.56, is this option ITM, ATM or OTM and how?
Vijay
Describe how a typical stock option plan works. What are someproblems with a typical stock option plan?

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