You are given the following information about a call option on a stock in the Black-Scholes framework:
• The annual continuously-compounded interest rate is 0.03.
• The annual price volatility is 0.03
• The current stock price is $56
• The option’s time to expiration is 2 years
• The price of the prepaid forward on the strike asset is $42
• d1 = 0.4
• The stock will pay a dividend in the amount of d dollars one year from today.
Find the size of the dividend.[$13.7252]
known
C(St , K, σ, r, T − t, δ) = Ste −δ(T −t)N(d1) − Ke−r(T −t)N(d2) where
d1 = [ln (St/K) + (r − δ + 0.5σ 2 )(T − t)]/ [σ √ T − t] and
d2 = [ln (St/K) + (r − δ − 0.5σ 2 )(T − t)]/ [σ √ T − t] = d1 − σ √ T − t.