Question

J Corp. common stock is priced at $36.50 per share. The company just paid its $0.50 quarterly dividend. Interest rates are 6.0%. A $35.00 strike European call, maturing in 6 months, sells for $3.20. What is the price of a 6-month, $35.00 strike put option

Answer 1

Answer:

Explanation:

The time (T) = 6 months = 6/12 years  = 0.5 years

Interest rate (r) = 6% = 0.06

The stock is priced [S(0)] = $36.50

The price the stock sells at 6 months ($V_c$) = $3.20

European call (K) = $35

The price (P) is given by:

$P=V_c+K.e^{-rT}-S(0)+Dividends\\But, Dividends = 0.5*e^{-0.25*0.06}+ 0.5*e^{-0.5*0.06}\\Therefore, P=V_c+K.e^{-rT}-S(0)+0.5*e^{-0.25*0.06}+ 0.5*e^{-0.5*0.06}\\Substituting:\\P=3.2+35*e^{-0.06*0.5}-36.5+0.5*e^{-0.25*0.06}+ 0.5*e^{-0.5*0.06}\\P=3.2+33.9656-36.5+0.4926+0.4852\\P=1.64$

The price of a 6-month, $35.00 strike put option is $1.65