Please solve each question individually on Excel on a separate worksheet.
Homework 7 If you use Derivagem, you must include the Derivagem outputs. 1. Consider a European call option when the stock price is $18, the exercise price is $20, the time to maturity is 6 months, the volatility is 30% per annum, and the riskfree rate is 10% per annum. The stock is expected to pay $0.40 dividend in 2 months and another $0.40 dividend in 5 months. Find the BlackScholes call option price. 2. Currently, Apple stock is trading at $129.49. The 1month $130 Apple call option is trading at $2.95. The riskfree rate is 0.10%. Find the implied volatility. 3. What is VIX index and what is the current VIX? Compare it with the answer to Q2 and explain. 4. Consider a stock index currently standing at 2,100. The dividend yield on the index is 3% per annum and the riskfree rate is 1%. A 3month European call option on the index with a strike price of 2,000 is trading at $115.77. What is the value of a 3month 2,European put option with a strike price of 2,000? 319 rt fuIodel Valtt irtg S t o ck O pti otts : The Black- S ch ole s-!/Ierto 13.12. Assumethatanon-dividend-payingstockhasanexpectedreturnofpandavolatilityofo' that instiiution has just announced that it rvi1l trade a derivative An innovative {inancial pays off a dollar amount equal to 1,-rt\\ r'"\\sn/ at time time I. I. The variables Sg and and 51 denote the values of the stock price at time zero (a) Describe the payoff from this derivative' the price of the derivative at time zero' iUi U*r risk-.reurai valuation to calcuiate stock when the 13.i3. What is the price of a European call option on a non-dividend-paying per annum' the the risk-free interest tate is l2o/o stock price is $52, the strike irice is $50, volatiiity is 30%'per anl1um-, and the time to maturity is three months? stock when the i3.14. What is the price of a European put option on a non-dil'idend-paying per annum' the rate is 5a/o stock price is $6t, the strike price is S70, the risk-free interest six months? volatility is 35% per annum, and the time to maturity is has a market price of $2'50' The stock 13.15. A call option on a non-dividend-paying stock three months' and the riskprice is $15, the exelcise price is Si:, tt" time to maturity is freeinterestrateis5%petaEnum.Whatistheirnpliedvolatility? a call option gives a price that tends 13.16. Show that the Black-Scholes-Merton formula for to max(Ss - I(, 0) as T + 0' an American call option on a 13.17. Explain carefully why Black's approach to evaluating when only one dividend is dividend-paying stock may give an approximate answer even understate or oyerstate the true anticipated. Do"es the unr*.i given by-Black's approach oPtior value? ExPIain Your answer' stock price is $70' the time to maturity 13.18. Consider an American call option on a stock' The per annum, the exercise price is $65' is eight rnonths, the risk-ftee rate of interest is 10% after three months and again after and the ,or^t1iiyi, :2y". e airlo"nd of $1 is expected it can never be optimal to six rnonths. use the results in the appendix to show that use DerivaGem to calculate the exercise the option on either or tit" t*o dividead dates' ,mffi:ll;:i:t:llrr",r,iy $50 and ttre risk-rree interest rate is 5Yo. use the DerivaGem ["'"',{;r;;;;;-;^rrlate the following table of European call options on the stock inro a l\\-/'";'" prices consistent rvith ,r"t*ott.o volatilities, assuming no dividends. Are the option the assumptions underlying Black-Scholes-Merton? Muturity {months) 12 Strike price {$) 8.30 5.20 10.50 50 7.00 3.50 55 1.60 2.90 5.10 45 formulas 13.24. Shorv that the Black-Scholes-Merton 1.s0 for call and put options satisfy put-cali ParitY. *11i 13.21. Show rhat the probabitity that a European call option !" exercised in a risk-neutral chapter, N(d2). what is an expression for world is, ,,rith the notation introduced in this
