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# Black-Scholes Model

### Option Pricing using Black-Scholes, Warrants, Leasing, Understanding Option Quotes

1) Black-Scholes: What are the prices of a call option and a put option with the following characteristics? Stock price = \$38 Exercise price = \$35 Risk -free rate = \$6% per yr compounded continuously Maturity = 3 months Standard deviation = 54% per year 2) Warrant Value: A warrant gives its owner the right to purcha

### Black and Scholes, Binomial Model, hedge ratios, arbitrage opportunity

Question 1) Panera's (PNR) stock price is \$45. Its standard deviation is 35%. Interest rates are 3%. You are interested in an 8-month call. u and d are computed based on the formulas: 1. Draw the two-period binomial tree for PNR call options with exercise price = \$40. . 2. Compute the hedge ratios at time 0 and after 4 mont

### Determine the price of a call option. What is the price sensitivity of the option to changes to the price of the stock?

Determine the price of a call option assuming that the exercise price is \$45, the value of the stock is \$43, risk -free rate is 3%, standard deviation of 35%, and 6 months to maturity. What is the price sensitivity of the option to changes to the price of the stock? Would the sensitivity be different if the exercise price wa

### Use the Black and Scholes equations to compute the value of a call and a put. Check the answer with the bsm calculator. Compute the . delta-theta-gamma approximation for a value of a call. What are the combined Delta, vega, and Theta of your position?

1. RED DOT currently sells for \$56, its volatility is 35% interest rates 2%. Use the Black and Scholes equations to compute the value of a call and a put. The strike price is \$55 and the options expire in 220 days. 2. Check the answer with the bsm calculator 3. Compute the . delta-theta-gamma approximation for a value of

### Options, risk-neutral probability, standard deviation, logarithm of a stock

1) A stock price is currently \$100. Over each of the next two three-month periods it is expected to increase by 12% or fall by 12%. Consider a six-month European call option with a strike price of \$105. The risk-free rate is 3%. What is the risk-neutral probability of a 12% rise in both quarters? 2) A stock price is currentl

### Option Pricing Models- Black-Scholes option-pricing model, Two-Period Binomial Model

1. A stock currently sells for \$60 and pays no dividends. There is a call option (striking price = \$65) on this security that expires in 41 days. At present U.S. Treasury bills are yielding 1 percent per year. You estimate the past volatility of the stock returns to be 39 percent (i.e., standard deviation). Using Black-Scholes o

### 1) An investor is speculating with a long call position what is the most likely preference of the investor relative to a change of the rho? 2) The binomial price will theoretically equal the Black and Scholes price under which of the following condition? 3) What will happen when the volatility is 0 in the Black and Scholes model ? 4) To construct a riskless hedge, the number of puts per 100 shares purchased is 5) Which of the following statements about the delta is not true?

1) An investor is speculating with a long call position what is the most likely preference of the investor relative to a change of the rho? A - Increase B - Stay constant C - Indifferent 2) The binomial price will theoretically equal the Black and Scholes price under which of the following condition? 1. when th

### Textbook: Essentials of Investments. Chapter 16 (1, 2, 5, 6, 7 & 12). Problems on call and put options. We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? In each of the following questions, you are asked to compare two options with parameters as given. What is the hedge ratio of the put? Verify that the put-call parity relationship is satisfied by your answers. Use the Black-Scholes formula to find the value of a call option on the following stock. All else being equal, is a put option on a high beta stock worth more than one on a low beta stock? The firms have identical firm-specific risk.

1.We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity relationship as well as a numerical example to prove your answer. 2.In each of the following questions, you are asked to compare two options with parameters as giv

### Veblen: Black-Scholes option pricing model; Mr Herman's currency risk reductions plan

Veblen International would like you to demonstrate your knowledge of the Black-Scholes option pricing model by finding the call price of a U.S. call option with the following characteristics. Show and submit all work completed: * stock price = \$60 * exercise price = \$60 * risk-free rate = 10% * volatility (

### Johnson 9-3 Technology

Here is the following information about the Johnson 9-3 Technology: Current stock price: 15 Time to maturity of option: 6 months Variance of stock return=0.12 d2=0.00000 N(d2)= 0.50000 Strike price of option: 15 Risk-free rate: 6% d1:0.24495 N(d1)=0.59675 Using the Black -Scholes Option Model, what would be the v

### Which event is likely to increase the market value of a call option on common stock

Which of the following events are likely to increase the market value of a call option on a common stock. Explain. a) An increase in the stock's price. b) An increase in the volatility of the stock price. c) An increase in the risk-free rate. d)A decrease in the time until the option expires.

### Price of a Call Option Using the 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 \$30 (2) Exercise price is \$35 (3) time to expiration is 4 months, (4) annualized risk-free rate of 5%, and (5) variance of stock return is .25

### Purcell Industries: Black Scholes Option Pricing Model

Assume you have been given the following information on Purcell Industries Current Stock Price= \$15 Exercise Price Option=\$15 Time to maturity of option=6 months Risk-free rate=6% d2=.00000 d1=.24495 N(d2)=.50000 N(d1)=.59675 Using the Black-Scholes Option Pri

### Question about Value of Call Option using Black-Scholes model

An analyst is interested in using the Black-Scholes model to value call options on the stock of Ledbetter Inc. The analyst has accumulated the following information: · The price of the stock is \$40. · The strike price is \$40. · The option matures in 3 months (t = 0.25). · The standard

### OJournalizing Stock transactions using the fair value method

Prepare the necessary entries from 1/1/07-2/1/09 for each of the following events using the fair value method. If no entry is needed for an event, write "No Entry Necessary." [Hint: Remember, there are five different dates involved] a) On 1/1/07, the stockholders adopted a stock option plan for top executives whereby ea

### Derivatives- option pricing

Need answers with calculations in Excel spreadsheet. 1. A stock currently sells for \$50 and pays no dividends. There is a call option (striking price = \$55) on this security that expires in 61 days. At present U.S. Treasury bills are yielding 3.3 percent per year. You estimate the past volatility of the stock returns to be 39

### Black-Scholes Valuation Model: Call Option

A) Consider an option on a non-dividend-paying stock when the stock price is \$40, the exercise price is \$40, the risk-free interest rate is 9%, the volatility is 30% per annum, and the time to maturity is 12 months. Using the Black-Scholes valuation model, what is the price of a European-style call option under these conditions?

### Value of an option

You are considering the purchase of a call option on Priceless Packing Inc. Priceless has a current stock price of \$40.00 per share with an annual volatility of 45 percent. The exercise price of the option is \$38.00 and the riskless rate of interest is 6 percent. If this stock pays no dividends and the option matures in six mont

### The exercise price on one of Flanagan Company's options is \$15

Dear OTA, Please solve Problems 9-2 ,9-3 , 9-4 and 13-1. Thanks

### Future contracts : margin account, theoretical future price for the contract, hedging price risk using futures, future contract to reduce beta of an investment. Options- put, theoretical value, Black model to compute the value of the call option

1. The CBOT offers a mini Dow Jones future contract. The multiplier on the contract is 10. The initial margin is \$6,000; maintenance margin is \$2,500. As of the close of trading Monday, February 18 the June contract was priced at 12358. You can find quotes at the Wall Street Journal's Market Data Center. Assume that on Monday

### Derivative problems: Option Pricing

Please see the attached file. 1) Option pricing principles are now often used in corporate finance applications. It is common to look at equity in a corporation as an option. What type of option is equity similar to? Discuss what factors would affect the price of equity and in what direction based on this option pricing view.

### Black Scholes Option Pricing Model and Assumptions

Explain the Black Scholes Option Pricing Model including the underlying assumptions.

### ESO Plan

Incorporate an ESO plan into a company's valuation. For your company (Dell, Inc), incorporate the effect of the Employee Stock Option (ESO) plan into the common equity valuation. Be sure to consider both the forecasted ESO grants and outstanding ESOs. Perform your valuation in Excel; use appropriate formulas/equations.

### Value option with Black-Scholes Option Pricing Model

Assume you have been given the following information on Purcell Industries: Current stock price = \$15 Strike price of option = \$15 Time to maturity of option = 6 months Risk-free rate = 6% Variance of stock return = 0.12 d1 = 0.24495 d2 = 0.00 N(d1) = 0.59675 N(d2) = 0.5000 Using

### Equity and Debt Worth

Fethe Inc. is a custom manufacturer of guitars, mandolins, and other stringed instruments located near Knoxville, Tennessee. Fethe's current value of operations, which is also its value of debt plus equity, is estimated to be \$5 million. Fethe has \$2 million face-value zero coupon debt that is due in 2 years. The risk-free rate

### Financial Options and Applications

An analyst wants to use the Black-Scholes model to value call options on the stock of Ledbetter Inc. based on the following data: ? The price of the stock is \$40. ? The strike price of the option is \$40. ? The option matures in 3 months (t = 0.25). ? The standard deviation of the stock's returns is 0.40, and the variance i

### Black-Scholes Option Pricing Model.

What is the value of a 9-month call with a strike price of \$45 given the Black-Scholes Option Pricing Model and the following information? Stock price: \$48 Exercise price: \$45 Time to expiration: .75 Risk-free rate : .05 N(d1): .718891 N(d2): .641713 A. \$2.03 B. \$4.86 C. \$6.69 D. \$8.81 E. \$9.27

### Derivatives: Call option, Put option, Put-call parity

P15-16. Explain the following paradox. A put option is a highly volatile security. If the underlying stock has a positive beta, then a put option on that stock will have a negative beta (because the put and the stock move in opposite directions). According to the CAPM, an asset with a negative beta, such as the put option, has

### Currency Derivatives

1. On Monday morning, an investor takes a long position in pound futures contract that matures on Wednesday afternoon. The agreed-upon price is \$1.78 for 62,500 pound sterling. At the close of trading on Monday, the futures price has risen to \$1.79. At Tuesday close the price rises further to \$1.80. At Wednesday close, the