Question

Merck inc. is maintain the investment management cell and attempting to value call option and put option with maturity of 90 days with common exercise price of 40. The current price of stock in market in market is $38.75, which is also paying the dividend on quarterly basis that is $0.48 bi-monthly. Considering the risk fee rate of 4.6% and implied volatility of 30%. a. Based on the Black Scholes, Estimate the value of the call and put options. b. how the dividend paying effects the value of put and call value and Why this effect is substantial?

Answer 1

Answer) For part A please refer both the images. Divided payment is not assumed in black scholes model and therefore the same is excluded from the calculation.

Part B) Both the are affected by the dividend date. Put Option become more expensive as price will fall be the dividend amount. Call Options become cheap as anticipated fall in the price of the stock. It also assumes all other things being equal.

The reason being in put there is a contract where holder has a right to sell at exercise price whereas the writer has the obligation to buy. Therefore the seller collects the premium for taking the risk.

Whereas the call option loses value because here the buyer has a right to buy and since the price drops, the value of stock also drops.

This is substantial because it implies little changes in the option value over time. This is true with little payments, which is a negligible percentage of share price. High Dividend will have more impact in both the share and option prices.