Question

Consider an option on a non-dividend paying stock when the stock price is $67, the exercise price is $61, the risk-free rate is 0.5%, the market volatility is 30% and the time to maturity is 6 months. Using the Black-Scholes Model when necessary (i) Compute the price of the option if it is a European Call. (ii) Compute the price of the option if it is an American Call. (iii) Compute the price of the option if it is a European Put. (iv) Assuming two dividend payments $1.75 and $2.75, two months and five months from now, compute the price of the option if it is a European Call. (v) Refer to the dividend information provided in (iv) above. Compute the price of the option if it is an American Call. Provide a graphical illustration to demonstrate how the price of this American Call and the payoff from the same change with respect to changes in the stock price. (vi) PUT ALL IN EXCEL ATTACHMENT SHOWING FORMULAS

Answer 1

As per concept of Black Scholes model , the valuation of European style of option , as

Answer 1 and III)  

Answer 2) American style by use of binomial method,

Strike price = 61
Discount factor per step = 0.9988
Time step, dt = 0.2500 years, 91.25 days
Growth factor per step, a = 1.0013
Probability of up move, p = 0.4667
Up step size, u = 1.1618
Down step size, d = 0.8607

Value of option 9.376309.

kindly re-post the remaining question as