Black–Scholes and Dividends [LO2] 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 are 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 $94 per share, the standard deviation of its return is 50 percent per year, and the risk-free rate is 4 percent per year, compounded continuously. What is the price of a call option with a strike price of $90 and a maturity of six months if the stock has a dividend yield of 2 percent per year?
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- V You buy a straddle, which means you purchase a put and a call with the same strike price. The put price is $2.80 and the call price is $4.20. Assume the strike price is $75. What is the cost of this strategy? 2. What are the break-even stock pricesarrow_forward1. Given that the Asian option is an option where the strike price is equal to the average prices of the underlying stock, what is the strike price if you have the following stock prices? 7.822, 3.026, 9.206, 7.211 2. The asian option is an option where you can exercise the option at any time (True or False) 3. floors can be used to limit the losses for your credit portfolio if you are invested in variable rate bonds (True or False)arrow_forwardH5. What is the payoff to the trading strategy if the stock price at expiration is equal to $0 (i.e., the stock price is zero)? What is the payoff to the trading strategy if the stock price at expiration is equal to $50? What portfolio of calls (maturity T, any strike) and/or bonds (Zero Coupon Bond paying $1 at time T) will give you the desired payoff? Group of answer choices Sell $30 zero-coupon bonds, buy a call option with a strike price of $20, sell two call options with a strike of $40, and sell a call option with a strike price of $80 Buy $30 zero-coupon bonds, sell two call option with a strike price of $30, buy 2 call options with a strike of $40, and sell a call with a strike price of $80 It is not possible to construct this payoff with only calls and bonds Sell $50 zero-coupon bonds, buy two call with the strike price of $80, buy two calls with a strike price of $40, and sell a call with a strike of $20 Buy $30 zero-coupon bonds, sell a call option with a strike…arrow_forward
- A call option with a strike price of $100 costs $5. A put option with a strike price of $85 costs $4. Explain how a strangle can be created from these two options. What is the cost of this strategy? When should I exercise my options? For what range of future stock prices would the strategy lead to a gain and what is the maximum gain you can receive? Prove your answer by providing an example. 5 For what range of future stock prices would the strategy lead to a loss and what is the maximum loss you could sustain? Prove it by giving an example.arrow_forwardQ7. In a market that is efficient, investors are only compensated for bearing Group of answer choices 1. diversifiable risk 2. unique risk 3. total risk 4. non-diversifiable riskarrow_forwardProblem 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_forward
- 1. 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_forwardData: S0 = 120; X = 126; 1+r = 1.05. The two possibilities for ST are 150 and 102. (Round to 2 decimal places). The range of S is 48 while that of C is 24 across the two states. What is the hedge ratio of the call? Hedge ratio ? Calculate the value of a call option on the stock with an exercise price of 126. (Do not use continuous compounding to calculate the present value of X in this example because we are using a two-state model here; the assumed 5% interest rate is an effective rate per period.) Call value ?arrow_forward3) The return on a stock, in a factor model, in a given period will be related to A) firm-specific events. B) macroeconomic events. C) the error term. D) both firm-specific events and macroeconomic events. E) neither firm-specific events nor macroeconomic events. 4) Assume the index model is valid, what inputs will be required to determine covariance between two assets? A) βk B) βL C) σM D) all of the options E) None of the options are correct.Choose the correct answer with justification.arrow_forward
- 2. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, = 0.5a. What is correct of the call options using Black-Scholes model? b. Compute the put options price using Black-Scholes model. 3Suppose a European put options has a price higher than that dictated by the putcall parity.a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless.Note: Use the call and put options prices you have computed in the previous question 2 above.b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?arrow_forward6. Explain why an option’s time value is greatest when the stock price is near the exercise price and why it nearly disappears when the option is deep in- or out-of-the- money.arrow_forward2. In the context of binomial option pricing model, a decrease in the stock price volatility will reduce the current option value True or falsearrow_forward
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