The Black-Scholes option pricing model (OPM) was developed in 1973. The creation of the Black-Scholes OPM played a significant role in the rapid growth of options trading. The derivation of the Black-Scholes Option Pricing Model rests on the concept of a According to the Black-Scholes Option Pricing Model, as the time to expiration, t, increases, the value of the call option Big Walnut Nut Company has a current stock price of $20.00. A call option on this stock has an exercise price of $20.00 and 0.36 year to maturity. The variance of the stock price is 0.04, and the risk-free rate is 5%. You calculate di to be 0.21 and N(0.21) to be 0.5832. Therefore, dy will be 0.09 and N(0.09) will be 0.5359. Using the Black-Scholes Option Pricing Model, what is the value of the option? (Note: Use 2.7183 as the approximate value of e.) $1.137 $0.966 $1.194 $1.080

The Black-Scholes option pricing model (OPM) was developed in 1973. The creation of the Black-Scholes OPM played a significant role in the rapid growth of options trading. The derivation of the Black-Scholes Option Pricing Model rests on the concept of a According to the Black-Scholes Option Pricing Model, as the time to expiration, t, increases, the value of the call option Big Walnut Nut Company has a current stock price of $20.00. A call option on this stock has an exercise price of $20.00 and 0.36 year to maturity. The variance of the stock price is 0.04, and the risk-free rate is 5%. You calculate di to be 0.21 and N(0.21) to be 0.5832. Therefore, dy will be 0.09 and N(0.09) will be 0.5359. Using the Black-Scholes Option Pricing Model, what is the value of the option? (Note: Use 2.7183 as the approximate value of e.) $1.137 $0.966 $1.194 $1.080

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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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. $
A speculative investor creates a portfolio of options written on the same underlying asset. He chooses to sell a put option with a strike of $100 and sell a call option also with a strike of $100. The two options have the same expiration. a. Sketch the payoff at maturity for a seller of a put option with a strike of $100. Carefully label the axes. b. Sketch the payoff at maturity for a seller of a call option with a strike of $100. Carefully label the axes. c. Sketch the payoff at maturity for the investor who sells both a call option and a put option each with a strike of $100. Carefully label the axes. The put option price is $14, and the price of the call option is $6. d. What is the profit at maturity for the speculative investor if the underlying asset at maturity is worth $100?
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
There are various ways to calculate the price of a call option using the Black-Scholes model. Below is a spreadsheet that breaks the required formulas into pieces to make it easy to work with. Column (1) shows the various inputs. The first five cells are the required inputs for a non-dividend paying stock. The remainder of the cells are the formula parts. Column (2) shows a solved problem for a stock selling for $50, with an exercise price of $45, an interest rate of 6 percent, 90 days (one-quarter of a year), and a standard deviation of .235. Column (3) shows how the cell values in Column (2) were calculated. Once you have this set up in the spreadsheet, you can calculate the price of any call option by substituting the correct values in the first five cells of column (2). Spreadsheet begins in row 2. Calculating a Call Price Using the Black-Scholes Model S 50 45 R 0.06 T 0.25 S 0.235 In(S/X) 0.105361 LN(B2/B3) r+0.50? 0.087613 B4+(,5)*(B6)^2 o(t)½ 0.1175 В6*((B5)^0.5) dl 1.083095…
Ningbo Industrial Concepts Incorporated Initial stock price $115.00 Exercise price $115.00 Call price $4.75 Put Price $4.50 Required: Using the information in the table above, please calculate dollar value of the following option strategies. Use this calculated dollar value to determine the profit of each strategy at various stock prices. (Use cells A3 to B6 from the given information to complete this question. Negative answer should be input and displayed as a negative value. All other answers should be input and displayed as positive values.) Ningbo Industrial Concepts Incorporated Dollar Value of Strategy as a Function of Current Stock Price Strategy $95.00 $105.00 $115.00 $125.00 $135.00 Straddle Strip Strap Ningbo Industrial Concepts Incorporated Rate of Return…
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.
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Assume the following inputs for a call option: (1) current stock price is $23, (2) strike price is $28, (3) time to expiration is 5 months, (4) annualized risk-free rate is 5%, and (5) variance of stock return is 0.3. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Use the Black-Scholes model to find the price for the call option. Do not round intermediate calculations. Round your answer to the nearest cent.
A stock has a price of $73, which can later be $77 or $69 with equal probabilities. The options with exercise price $77 are valued at $1.53 for the call and $1.73 for the put. a. Calculate the gains/losses/returns for the stock. b. Calculate the gain/losses/returns for a covered call and protective put portfolio.
(a) The table below gives information about European options with a maturity date of 6 months. Type Of option Strike Price Call 65 Call 58 Put 65 Premium 5 8 4 (i) Devise the payoff profile of the hedging strategy from the above for an investor betting on an increase in the stock price and calculate the payoff if the stock price increases to $66 after 6 months. (8 marks) (ii) Suppose that another investor expects a big stock price movement but is not sure of the direction. She however bets that the downward movement is more likely. Devise the corresponding trading strategy and calculate the payoff if the stock price is $55 after 6 months. (8 marks) (b) By analysing the pay off profiles of a protective put strategy and a straddle, discuss in what ways these strategies shield the investor from potential losses.
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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