Question

5) A three-month European put option is written on a stock that provides a continuous dividend yield of 2%; the strike price is $95, the risk-free rate is 2% and the stock's volatility is 40%. Assume that the stock is currently selling for $90. What is the price of the put?

Answer 1

Price of Put = $10.08

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

A B C 다 1 Stock Price Strike Price Maturity Risk free rate Volatility Dividend yield $90.00 $95.00 0.25 2.00% 40% 2% 2. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 d1 d2 N(D1) N(02) N(-d1) N(-d2) N(d1): PDF -0.1703 -0.3703 0.4324 0.3556 0.5676 0.6444 0.3932 Put $10.08 00 Price 19 20 21

Cell reference -

A B C 1 2 3 st Stock Price Strike Price Maturity Risk free rate Volatility Dividend yield 90 95 =3/12 0.02 0.4 0.02 5 6 7 8 9 10 11 12 d1 d2 N(D1) N(D2) N(-d1) N(-d2) N(dl): PDF =(LN(C2/C3)+C4* (C5-C7+C6^2/2))/(C6*SQRT(C4)) =C9-C6*SQRT(C4) =NORMSDIST(09) =NORMSDIST(C10) =NORMSDIST(-09) =NORMSDIST(-10) =NORM.S.DIST(C9,FALSE) 13 14 15 16 17 Put 18 Price =C3*EXP(-C5*C4)*C14-C2*EXP(-C7*C4)*C13 19 20 71

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.