BSM model. Mars Corp. common shares aretrading at $46 on the market. Currently, thecontinuously compounded risk - free rate is 9% peryear and the annual standard deviation of thecontinuously compounded rate of return on Marsshares is 16%. There are put and call options onMars common shares with an exercise price of $48and a 180-day expiry date? Using the Black-Scholes option pricing model, calculate thefollowing: Notes: 1. The cumulative standardnormal table is available on Moodle. 2. Use fullaccuracy in all the calculations excep for finding N(d1,2) These values are supposed to come fromthe table, which has 2 decimals accuracy. Thus, ifyou are using Excel you must round the argumentsof d1,2 to 2 decimals, and N(d1, 2) to 4 decimals. a.What is the value of d1 ? Number Round youranswer to two decimal places. b. What is the valueof call delta? Number Round your answer to fourdecimal places. c. What is the value of the calloption? $ Number Round your answer to twodecimal places. d. What is the value of the putoption?

Black-Scholes Model Calculations for Mars Corp. Options (with approximations)Given:Stock Price (S) =…

Answered: BSM model. Mars Corp. common shares are…

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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uppose an American put is trading for $16.50and an American call is trading for $15, whereboth options have identical terms. The underlying stock price is $99, and the exercise price is$100. The annual risk - free interest rate is 5 per cent, and the time to expiration for both optionsis one year. Assuming that the stock pays no dividends, identify the appropriate arbitrage trading strategy
You are given the following information about the stock of Company ABC: Share price $80 risk free rate of interest is 6%, time to expiration is 6 months, annualised standard deviationis 0.5 and exercise price is $85. Calculate the appropriate call value of the stock according to the Black-Scholes option pricing formula. (Show your workings in full) Calculate an appropriate put premium. (Show your workings in full)
The current price of a non - dividend paying stock is $38.52. Use a two-step tree to value a European call option on the stock with a strike price $32.3 that expires in 12 months. The risk free rate is 9.9% per annum, and the volatility is 28.1%. What is the option price?
Suppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1-year eective annual interest rate is 10%. (a) Graph the payo and prot diagrams for a forward contract on XYZ stock with a forward price of $55. (b) Is there any advantage to investing in the stock or the forward contract? Why? (c) Suppose XYZ paid a dividend of $2 per year and everything else stayed the same. Now is there any advantage to investing in the stock or the forward contract? Why?
Give typing answer with explanation and conclusion The stock of Nugent Nougats currently sells for $46 and has an annual standard deviation of 47 percent. The stock has a dividend yield of 5.6 percent and the risk-free rate is 5.6 percent. What is the value of a call option on the stock with a strike price of $42 and 44 days to expiration?
If a particular stock does not pay dividends and is currently priced at $24 per share, what should be the price of a call option with a maturity of one year and a strike price of $24.5 if put options with the same features currently cost $2? Assume a risk free rate of 2%. (use 5 decimal places)
Shopify, Inc common stock currently sells for $1,229.91 per share, and the standard deviation of returns is 58.67%. A call option with a strike price of $1,100 is currently trading on the market. The option expires in 0.15 years, and the risk-free rate of return is 0.9%. Shopify does not pay a dividend. What is rho (ρ) for this call option assuming a continuous model such as the Black-Scholes model? A) 104.1327 B) 107.2895 C) 57.7772 D) 107.0002
A stock is currently priced at $40. The risk-free rate of interest is 8% p.a. compounded continuously and an 18-month maturity forward contract on the stock is currently traded in the market at $38. You suspect an arbitrage opportunity exists. Which one of the following transactions do you need to undertake at time t = 0 to arbitrage based on the given information? Long the forward, short-sell the share and invest at risk-free rate Long the forward, borrow money and buy the share Short the forward, borrow money and buy the share Short the forward, short-sell the share and invest at risk-free rate
Optival’s stock is currently trading at $60 per share with a historical volatility of 20%. The risk-free rate is 4%. Consider a European call and put option on Optival’s stock with an exercise price of $55 that expires in 2 years. Use excel or a similar program to determine the option price using the Black-Scholes formula. (a): What is the value the European call and put option on Optival’s stock with a strike price of $60? (b): To the nearest cent, how much does the option value change for the following adjustments to the input values: ∆ in Call Value ∆ in Put Value ↑ stock price by $1 to $61 ↑ strike price by $1 to $56 ↑ the rF by 1% to 5% ↑ volatility by 1% to 21% ↑ time to maturity by 1 yr (c): Why does the value of the call increase by less than $1 when the stock price increases by $1? (d): To the nearest percent and holding all else constant, how high would the risk-free rate need to be for a 1 year increase in time to maturity to have a negative impact on the value of…
Assume the price of an non-dividend stock is $40, the annual volatility of the stock is 20%, and the continuous compound risk-free interest rate is 5%. What's the price of a European put option on this stock with delivery price of $40 with 1-year expiration? (The standard normal distribution table is in the attachment or you can use excel function NORMSDIST, and please keep the results with 3 decimal places.) (BS Model-Option Pricing)
Consider a XYZ stock index spot price is 69 and 7-months forward price is 70. The continuously compounded dividend yield and risk-free interest rate are 3% and 5% respectively. Market maker could take arbitrage opportunity by (long/short) forward contract and (long/short) synthetic forward contract which includes (buying/selling) stock and (borrowing / lending ) money. So the profit at expiration time will be . (Please round your answer to 4 decimal places)
Give typing answer with explanation and conclusion to all parts A call option on a non-dividend-paying stock has a market price of +212. The stock price is $15, the exercise price is $13, the time to maturity is 3 months, and the risk-free interest rate is 5% per annum. What is the implied volatility? Please do all work?

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