Delta hedging.You own $35,000 shares of Saturn Ltd. common stock that is currently selling for $52. A call option on Saturn with astrike price of $52 is selling at $4.30 and has a delta of 0.54.a. Determine the number of call option contracts necessary to create a delta-neutral hedge (with sign!).Numbercontracts.Round your answer to closest integer.b. Calculate the total change in portfolio value for a $0.31 decrease in the price of Saturn stock, keeping in mindthat you can only trade option contracts, not the individual options.$ NumberRound your answer to the nearest cent.

a. Determine the number of call option contracts necessary to create a delta-neutral hedge.The…

Answered: Delta hedging. You own $35,000 shares…

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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You buy a share of stock, write a 1-year call option with X= $95, and buy a 1-year put option with X= $95. Your net outlay to establish the entire portfolio is $94. 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
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.
You buy a put and a call on a stock that expire at time T. They are European options. Both the put and the call have an exercise price of $50. Plot the cash flows at the time of expiry. This strategy has a name. What is it?
At time t=0 Mr. Anderson sets up a riskless portfolio by taking a position in an option and in the underlying asset. Explain what Mr. Anderson needs to do at time t=1 to keep his portfolio risk neutral and why. A stock price is currently $100 and at the end of four months it will be ST . A derivative written on this stock pays off expST1/3 in four months. Given that u = 1.15, d = 0.87, and that the risk-free interest rate is 10% p.a. (continuously compounded), answer the following questions using a one-period binomial model (show all the details of your calculations and display the results with four decimal places): Calculate the value of ∆ Calculate the current value of the derivative.
Suppose you are a seller . At time t = 0 you get £C from the buyer where C is the risk-neutral price of the option. You then have to design a hedging strategy which would allow you to meet your financial obligation in one year’s time. Your portfolio should consist of two investments: you are allowed to buy the underlying shares and to deposit money in the bank. The price of the share evolves according to a geometric Brownian motion. State the formulae you will need to compute the number of shares in the portfolio and the capital deposited in the bank at any time t, 0 ≤ t ≤ 1.
A stock price is $30. An investor buys one call option contract on the stock with a strike price of $28 and sells a call option contract on the stock with a strike price of $27. The market prices of the options are $2 and $1.7, respectively. The options have the same maturity date. Describe the investor’s position and the possible gain/loss he will get (taking into account the initial investment). Make a graph of your gain/loss.
By looking at the sensivities of your portfolio to ds = -$2 and So = -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.) Variable Option A Option B Delta (A) -0.5 0.2 Gamma (T) 0.2 0.1 Vega (v) 8
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.)
You buy a share of stock, write a 1-year call option with X = $85, and buy a 1-year put option with X = $85. Your net outlay to establish the entire portfolio is $83.3. Required: What is the payoff of your portfolio? What must be the risk-free interest rate? The stock pays no dividends. Note: Round your answer to 2 decimal places.
show this on a diagram please. An investor makes the following three investments: (i) the purchase of a stock for £38(ii) the purchase of a put option for £0.50 with a strike price of £35 and (iii) the sale ofa call option (ie. writing a call option) for £0.50 with a strike price of £40 . What is the maximum profit and loss for this position?
Suppose you construct a strategy based on options on a stock that is currently selling for $100. The strategy is as follows: Buy one call option having an exercise price of $95. Sell two calls having an exercise price of $100. Buy one call option having an exercise price of $105. All of the options are written on the same stock and all have the same expiration date. Compute the payoff (the dollars you receive) from this strategy at the expiration date for each of the following alternative stocks prices: $90, $95, $98, $100, $102, $105, and $110. What additional information would be required to determine whether your strategy had been profitable? What is the name of this strategy?
A call option on a stock has a delta of 0.3. A trader has sold 1,000 options. What position such as buy or sell and many shares should the trader take to hedge the position and why?

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