Question

we have an European put option on a security (CCC) that pays dividends. Current price is $65, and the exercise price is at $55, the risk-free interest rate is 6% per annum, the volatility is 25% per annum., and 3 months is the time to maturity.  the CCC stock’s ex-dividend is in two months. The anticipated dividend is $0.85.

What is the European put option's current value? ( calculate)  If the dividend would have been $1.00 would the value of the put been higher or lower? (explain)

Answer 1

For a discrete dividend, the present value of the dividend is subtracted from the current price of the underlying.

PV of dividend = q*exp^(-r*T) where q = 0.85; r = 6%; T (time till dividend is paid) = 2/12

PV of dividend = 0.85*exp(-6%*2/12) = 0.8415

Adjusted current price = 65 - 0.8415 = 64.16

Using Black Scholes, we have:

Formulas:

Values:

Put option price = $0.2996

For a put option, as dividend value increases, the option premium will also increase because the stock price is expected to reduce by the dividend amount. This will lead to an increase in the put option value.