25.23 In addition to the five factord discussed in the chapter, dividends also a

Question

25.23

In addition to the five factord discussed in the chapter, dividends also affect the price of an option. The Black-Scholes option pricing model with dividends is:

C= S x e-dt x N(d1)- E x e -Rt xN (d2)

d1 ={1n(S/E)+(R-d+variance/2)xt} / (standard deviation x square root t)

d2=d1- std deviation x square root t

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 %per year, and the risk-free rate is 4% per year, compounded continuously. What is the price of a call option with stricke price of $90 and a maturity of six months if the stock has a dividend yield of 2%per year?

Explanation / Answer

a.   Effect of Dividend Yeild on Call Option Pricing

Options are usually priced with the assumption that they are only exercised on expiration date. Since whoever owns the stock as of the ex-dividend date receives the cash dividend, sellers of call options on dividend paying stocks are assumed to receive the dividends and hence the call options can get discounted by as much as the dividend amount.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.