Question

Merck inc. is mainta8n 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 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?

c. repeat part a and part b with the settings of American call option. Evaluate the difference between answer.

d. Based on technique of the pseudo-American call option, determine whether such technique effects the valuation of call option and put options.

e. With call and put which option has greater chance of early exercise and why. the answer should be calculative

Answer 1

A. Based on Black & Scholes.

Call option premium - $1.99 Call Option Delta - +0.477
Put option premium - $2.77 Put Option Delta - -0.523

B. Stocks generally fall by the amount of the dividend payment on the ex-dividend date (the first trading day where an upcoming dividend payment is not included in a stock's price). This movement impacts the pricing of options. Call options are less expensive leading up to the ex-dividend date because of the expected fall in the price of the underlying stock. At the same time, the price of put options increases due to the same expected drop. The mathematics of the pricing of options is important for investors to understand so they can make informed trading decisions.

C. American options are helpful since investors don't have to wait to exercise the option when the asset's price rises above the strike price. However, American style options carry a premium—an upfront cost—that investors pay and which must be factored into the overall profitability of the trade. if the price crosses the 40 mark before the maturity, the options buyer can exercise and make a profit.

D. I am not aware of the pseudo american call option.

E. Puts are at a greater risk of early assignment. In the case of puts, the game changes. When you exercise a put, you’re selling stock and receiving cash. So it can be tempting to get cash now as opposed to getting cash later. However, once again you must factor time value into the equation.

If you own a put and you want to sell the stock before expiration, it’s usually a good idea to sell the put first and then immediately sell the stock. That way, you’ll capture the time value for the put along with the value of the stock.

However, as expiration approaches and time value becomes negligible, it’s less of a deterrent against early exercise. That’s because by exercising you can accomplish your aim all in one simple transaction without any further hassles.

If you’ve sold a put, remember that the less time value there is in the price of the option as expiration approaches, the more you will be at risk of early assignment. So keep a close eye on the time value left in your short puts and have a plan in place in case you’re assigned early.