Question

i) Stock ABC will pay an annual dividend yield (q) of 5%. The strike price of the European call is $20, volatility is 20%, stock price is $30 and yearly rfree =4%. The stock will pay dividends before the option expires. T=1. The following formulae are given: d1=ln[S/PV(X)]/(?T1/2)+[(?T1/2)/2] and d2=d1-?T1/2

ii) The current price of ABC stock is $25. Next year, this stock price will either go up 20% or go down by 20%. The stock pays no dividends. The one year risk free rate is 6% and will remain constant. The face value of the bond is $1. Using the binomial model calculate the price of a TWO PERIOD CALL option on ABC with a strike price of $25

Answer 1

Dear Student, As per the HOMEWORKLIB POLICY only one question per post is allowed. So I am solving the first one.

C SN(d1)- N(d2)Ke-r C- Call premium S = Current stock price Time until option exercise K Option striking price r-Risk-free interest rate N-Cumulative standard normal distribution e Exponential term St. Deviation In-NaturalLog

Stock price = $ 30

Strike Price = $20

Standard Deviation = sqrt(20%) = 44.72%

Risk Free rate = 4%

Dividend Yield = 5%

d1 = [ln(30/20) + (0.04 + 0.4472^2/2)*1]/[0.4472*sqrt(1)] = 1.2197

d2 = 1.2197-(0.4472*sqrt(1)) = 0.7725

N(d1) = 0.8887

N(d2) = 0.7801

Equity = Stock*Exp(-dividend yield*time)*N(d1) - Strike*exp(-risk free rate*time)*N(d2)

= $30*exp(-0.05*1)*(0.8887) - ($20*exp(-0.04*1))*(0.7801) = $ 10.371