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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- fill 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_forwardIn the Black-Scholes option pricing model, the value of a call is inversely related to: a. the risk-free interest stock b. the volatility of the stock c. its time to expiration date d. its stock price e. its strike pricearrow_forward6. Equilibrium pricing: Let the subscripts: j = 0 denote the risk-free asset, j = 1,...,n the set of available risky securities, and M the market portfolio. For the questions that follow, assume that CAPM provides an accurate description of reality. a. b. C. d. State the CAPM equation. (1) Use the CAPM equation to show that the following condition is true s; ≤ SM for any j. What is the significance of this condition when interpreted in the context of the capital market line? (5) Assume that B = 0.8, μM = 0.1 and r = 0.05. Using the CAPM, determine the expected return from holding one unit of asset j for one period. (2) Given your answer to c.), what could you conclude (from the perspective of the security market line) if a market survey indicated that the forecasted one- period return on asset j was 8 percent? Describe and motivate the rational trading response that is consistent with your conclusion. (4)arrow_forward
- Consider a forward contract on a stock that pays dividends at specific times ti, where 0 < t1 < t2 < ... < tn < T. Suppose that the dividend is a fixed amount: Di at fixed times ti. Show that in this case, the forward contract price is given byarrow_forwardWhat is the correct way to determine the value of a long forward position at expiration? The value is the price of the underlying ... ... multiplied by the forward price. ... divided by the forward price. ... plus the forward price. ... minus the forward price please need type answer not an imagearrow_forward4. Valuation of a Derivative Consider a derivative on a stock with the time to expiration T and the following payoff: 0 K₁ 0 if ST K₁. What is the present value of the derivative? Provide an analytic expression of the price using N(), the cumulative probability distribution function of a standard normal random variable.arrow_forward
- Question 1 (Mandatory) Which of the following equations calculates a put option's value? Os.et. N(d2) - K N(da) OK.ert. N(d2) - S. N(d) Os.e*t. N(-d2) - K N(-dg) OK.et.N(-d2)- S N(-d1) Question 2 (Mandatory) The forward price is determined at contract initiation but changes during the life of the forward contract. O True Falsearrow_forwardTick all those statements on options that are correct (and don't tick those statements that are incorrect). a. In general the equation S(T) + (K − S(T))† = (S(T) – K)† + K is valid. - b. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion. d. An American put option should never be exercised before the expiry time. e. If interest is compounded continuously then the put-call parity formula is P + S(0) = C + Ke¯r where T is the expiry time. C.arrow_forwardWhich of the following describes delta? O The ratio of the option price to the stock price None of these O The ratio of a change in the option price to the corresponding change in the stock price The ratio of a change in the stock price to the corresponding change in the option price O The ratio of the stock price to the option price ◄ Previous Next ▸arrow_forward
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