Answer and explanation:
The solution is determined using the explained formula below
C₀ + X × e - r × t = P₀ + S₀
S₀ = Stock price today
X = Strike price
C₀ = European call option premium
P₀ = European put option premium
T = Time to expiration
r = Risk-free rate of return
another thing which we have to take into consideration is the impact of dividend on put-call parity.
Since interest is a cost to an investor who borrows funds to purchase stock and benefit to the investor who shorts the stock or securities by investing the funds.
Here we will examine how the Put-Call parity equation would be adjusted if the stock pays a dividend. Also, we assume that dividend which is paid during the life of the option is known.
Here, the equation would be adjusted with the present value of the dividend. And along with the call option premium, the total amount to be invested by the investor is cash equivalent to the present value of a zero-coupon bond (which is equivalent to the strike price) and the present value of the dividend. Here, we are making an adjustment in the fiduciary call strategy. The adjusted equation would be
C₀ + (D + X * e - r * t) = P₀+ S₀ where,
D = Present value of dividends
We can adjust the dividends in another way also which will yield the same value. The only basic difference between these two ways is while in the first one we have added the amount of the dividend in strike price, in the other one we have adjusted the dividends amount directly from the stock.
P₀ = C₀ + X * e - r * t – S₀ - (S₀ * e - r * t),
