The option premiums below are for three-month European options on a non-dividend-paying stockwith a current spot price of 65.Strike PriceCallPut588.910.98654.403.35683.064.96The continuously compounded rate of interest is 6.5%.A 58-65-68 asymmetric butterfly spread is constructed using a total of 20 three-month call options.Let X1 and X2 be the spot prices of the underlying stock at expiration for which the spread wouldhave a profit of 0, and such that X2 > X1. Calculate X2 - X1.O 7.83O 7.99O 8.478.15O 8.31

An asymmetric butterfly spread involves buying the lowest and highest price calls and selling the…

A 58-65-68 asymmetric butterfly spread is constructed using a total of 20 three-month call options. Let X1 and X2 be the spot prices of the underlying stock at expiration for which the spread would have a profit of 0, and such that X2 > X1. Calculate X2 - X1.

A 58-65-68 asymmetric butterfly spread is constructed using a total of 20 three-month call options. Let X1 and X2 be the spot prices of the underlying stock at expiration for which the spread would have a profit of 0, and such that X2 > X1. Calculate X2 - X1.

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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4. Option pricing - Multiperiod binomial approach Aa Aa The value of an option can be calculated by using a step-by-step approach in the case of single periods or by using sophisticated formulas that can be easily created through a spreadsheet. In the real world, two possible outcomes for a stock price in six months is an assumption. The stock markets are volatile, and stocks move up and down based on market- and firm-specific factors. Use the following formula to calculate the value of any call option within the same time period. To use the formula for different call options, you can solve this formula with algebra or program it into a spreadsheet. Cu{[1 + (rrF / 365)365/(t/n) – d]} Ca{u - [1 + (rrF / 365)365/(t/n)]} + u - d u - d Vc = [1 + (TRF / 365)]365/(t/n) Based on your understanding of the binomial option pricing model, is the following statement true or false? Tu is the price of an option that will return $1 if the price of the underlying stock goes up and $0 if the price of…
Consider shorting a call option c on a stock S where S = 24 is the value of the stock, K = 30 is the strike price, T = ½ is the expiration date, r = 0.04 is the continuously compounded interest rate per year, and  = 0.3 is the volatility of the price of the stock. Determine the delta ratio Δ .
Only typing. .... . A strip is a variation of a straddle involving two puts and one call. Construct a short strip using the August 170 options. The price of the call option is $8.10 and the price of the put option is $6.75. Hold the position until the options expire. Determine the profits and graph the results. Identify the breakeven stock prices at expiration and the minimum profit.
Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. What would the price of the call option ‘c’ need to be for put-call parity to hold?
Assume the stock's future prices of stock A and stock B as following distribution State Future Price Stock A Future price Stock B $10 $7 $8 $9 If the time 1 price of stock A is $6, and the time 1 price of stock B is $5. And C and C2 represents the time 1 price of ciaim on state 1, C, represents the time 1 prices of unit claims on states 1 and 2. Use the information about stock prices and payoffs to • Find the time 1 prices C, and C2. • Find the risk - free rate of return, obtained in this market
3. A stock sells for $110. A call option on the stock has an exercise price of $105 and expires in 43 days. If the interest rate is 0.11 and the standard deviation of the stock’s return is 0.25. a) Calculate the call using the Black-Scholes model b) What would be the price of a put with an exercise price of $140 and the same time until expiration? c) How does an increase in the volatility and interest rate changes affect the underlying stock’s return on an option’s value? Explain.
Consider an American put option (K=$100) expiring in one year on a stock trading for $84. The return volatility on the stock is 27.3% and the riskless rate is 5%. Find the price of the option using a Binomial Model with two steps. (Respond with two decimal places, such as "-12.34") 26.59 Correct Answer: 18.28
A butterfly spread is a position in three options on the same underlying stock with different strikes. An investor buys one call with a strike K1 = 22, sells two calls with a strike K2 = 24 and buys one call with a strike K3 = 26. What is the payoff of the butterfly spread, if the stock price equals $26 at maturity?
Black-Scholes Model Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $32, (2) strike price is $37, (3) time to expiration is 3 months, (4) annualized risk-free rate is 7%, and (5) variance of stock return is 0.16. Do not round intermediate calculations. Round your answer to the nearest cent.
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.
Assume that after one time period, the value of a stock of 80 would be either 120 Or 60. Suppose that, for any y, at a cost of Cy, one can purchase at a time-0 the option to buy y shares of the stock at time-1 at a price of 90 per share. For what values of C, no-arbitrage will be possible? Using the arbitrage theorem, find the value of C for the data given for your group in the above question Derive the first order partial derivative of the Black-Scholes option cost C with respect to r. (FOCUS ONLY OM THE LAST TWO )
A stock price is currently $23. A butterfly spread (ie. options are bought with strike prices of K₁ and K3, and two options with the middle strike price K₂ are sold) is created from call options with strike prices of $20, $25, and $30. Which of the following is TRUE? Select one alternative: O It is incorrect to assume that there is always a gain when the stock price is greater than $30 or less than $20. O The loss when the stock price is greater than $30 is the same as the loss when the stock price is less than $20. The gain when the stock price is greater than $30 is greater than the gain when the stock price is less than $20. O The gain when the stock price is greater than $30 is less than the gain when the stock price is less than $20.

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