Black-Scholes and Dividends In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black-Scholes option pricing model with dividends is:
All of the variables arc the same as the Black-Scholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the stock.
- a. What effect do you think the dividend yield will have on the price of a call option? Explain.
- b. A stock is currently priced at $113 per share, the standard deviation of its return is 50 percent per year, and the risk-free rate is 5 percent per year, compounded continuously. What is the price of a call option with a strike price of $110 and a maturity of six months if the stock has a dividend yield of 2 percent per year?
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- Both call and put options are affected by the following five factors: the exercise price, the underlying stock price, the time to expiration, the stock’s standard deviation, and the risk-free rate. However, the direction of the effects on call and put options could be different. Use the following table to identify whether each statement describes put options or call options. Statement Put Option Call Option 1. When the exercise price increases, option prices increase. 2. An option is more valuable the longer the maturity. 3. The effect of the time to maturity on the option prices is indeterminate. 4. As the risk-free rate increases, the value of the option increases.arrow_forwardfill the missing words: a. For ( ) options, when the spot price is ( ) than(or equal to)the exercise price, then profit/loss equals the premium. b. For ( ) options, when the spot price is ( ) than (or equal to) the exercise price, then the profit/loss will be equal to the option premium.arrow_forwardThe below question is of the course "Financial Derivatives and Risk Management". 1. Explain the call-put parity relation and how it is justified. 2. Describe the five variables like Stock Price, Exercise Price, Risk-Free Rate, Volatility or Standard Deviation, and Time to Expiration that the Black-Scholes-Merton Formula uses to calculate the price of call and put options. 3. Explain how the change in these variables like Stock Price, Exercise Price, Risk-Free Rate, Volatility or Standard Deviation, and Time to Expiration affect the price of the option. 4. Explain how these variables like Stock Price, Exercise Price, Risk-Free Rate, Volatility or Standard Deviation, and Time to Expiration are grouped to show the put-call parity relationship and suggest the condition in which there is an arbitrage opportunityarrow_forward
- Select all that are true with respect to the Black Scholes Option Pricing Model (BSOPM) Group of answer choices When using BSOPM to value a stock option, the BSOPM assumes that stock prices follow a normal distribution. When using BSOPM to value a stock option, the BSOPM assumes that stock returns follow a normal distribution. Half of the observations in a normal distribution are above the mean and half are below the mean. Fisher Black and Myron Scholes were awarded the Nobel Prize in 1997 for their work in Option Pricing.arrow_forwardUnder which of the following circumstances would you want to buy a stock? Select one: a. The HPR is greater than zero. b. A stock's holding period return is greater than the CAPM return c. A stock's CAPM return is greater than its holding period return d. The stock's price is higher than its valuearrow_forwarddiscussed that equity can be thought of as an option on the firm. If this is true, answer the following four questions: a) What type of option is it (i.e., the term that indicates what the option holder has the right to do)? b) Who sells (i.e., writes) the option? c) Who buys (i.e., holds) the option? d) What is the strike/exercise price?arrow_forward
- Both call and put options are affected by the following five factors: the exercise price, the underlying stock price, the time to expiration, the stock’s standard deviation, and the risk-free rate. However, the direction of the effects on call and put options could be different. Use the following table to identify whether each statement describes put options or call options. Statement Put Option Call Option 1. An option is more valuable the longer the maturity. 2. A longer maturity in-the-money option on a risky stock is more valuable than the same shorter maturity option. 3. When the exercise price increases, option prices increase. 4. As the risk-free rate increases, the value of the option increases.arrow_forwardDescribe the effect of a change in each of the following factorson the value of a call option: (1) stock price, (2) exercise price,(3) option life, (4) risk-free rate, and (5) stock return standarddeviation (i.e., risk of stock).arrow_forward1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.arrow_forward
- Problem 4d: State whether the following statements are true or false. In each case, provide a brief explanation. d. In a binomial world, if a stock is more likely to go up in price than to go down, an increase in volatility would increase the price of a call option and reduce the price of a put option. Note that a static position is a position that is chosen initially and not rebalanced through time.arrow_forwardBelow is a chart with profit/loss on the vertical axis, and the $/£ exchange rate on the horizontal axis. The solid line shows the profit/loss schedule for a: Question 8 options: put option in isolation (e.g. used for speculating that the pound will depreciate) None of the above covered call option (a call option is used as a hedge) covered put option (a put option is used as a hedge)arrow_forwardAssume the stock’s future prices of stock A and stock B as the following distribution State Future Price Stock A Future price Stock B 1 $10 $7 2 $8 $9 If the time 1 price of stock A is $6, and the time 1 price of stock B is $5. And C1 represents the time 1 price of claim on state 1, C2 represents the time 1 price of claim on state 2 Use the information about stock prices and payoffs to Find the time 1 price C1 and C2. Find the risk–free rate of return, obtained in this market.arrow_forward
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