Suppose you hold LLL employee stock options representing options to buy 11,600 s

Question

Suppose you hold LLL employee stock options representing options to buy 11,600 shares of LLL stock. LLL accountants estimated the value of these options using the Black-Scholes-Merton formula and the following assumptions:

You wish to hedge your position by buying put options with three-month expirations and a $25 strike price. How many put option contracts are required? (Note that such a trade may not be permitted by the covenants of many ESO plans. Even if the trade were permitted, it could be considered unethical.) (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Suppose you hold LLL employee stock options representing options to buy 11,600 shares of LLL stock. LLL accountants estimated the value of these options using the Black-Scholes-Merton formula and the following assumptions:

Explanation / Answer

Call delta current StockPrice S0 21.99 annual return volatility sigma 22.00% effective annual risk-free rate r 4.60% Exercise Price X 22.5 Time to Maturity(yrs) T 3.5 Dividend Yield q 0.00% d1 d1=[ln(So/X)+(r-q+.5*sigma^2)*T]/[sigma*sqrt(T)] 0.5413 d2 d2=[ln(So/X)+(r-q-.5*sigma^2)*T]/[sigma*sqrt(T)] 0.1297 delta of call=N(d1) N(d1)=NORM.S.DIST(d1,TRUE) 0.705835 d1=[ln(21.99/22.5)+(0.046-0+.5*0.22^2)*3.5]/[0.22*sqrt(3.5)] d2=[ln(21.99/22.5)+(0.046-0-.5*0.22^2)*3.5]/[0.22*sqrt(3.5)] Put delta current StockPrice S0 21.99 annual return volatility sigma 22.00% effective annual risk-free rate r 4.60% Exercise Price X 25 Time to Maturity(yrs) T 0.25 Dividend Yield q 0.00% d1 d1=[ln(So/X)+(r-q+.5*sigma^2)*T]/[sigma*sqrt(T)] -1.0067 d2 d2=[ln(So/X)+(r-q-.5*sigma^2)*T]/[sigma*sqrt(T)] -1.1167 delta of put=N(-d1) N(-d1)=NORM.S.DIST(-d1,TRUE) 0.842963 d1=[ln(21.99/25)+(0.046-0+.5*0.22^2)*.25]/[0.22*sqrt(.25)] d2=[ln(21.99/25)+(0.046-0-.5*0.22^2)*.25]/[0.22*sqrt(.25)] For hedging calls with put, delta of put=delta of call =>11,600*delta of call=Np*delta of put (=>>> Np=(11,600*delta of call)/delta of put=9713 Number of put option contracts (=Np) 9713

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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