Question

The current price of Gringotts Bank Corporation is $50. The price will increase by 40% or fall by 35% during each of the next two years. The company will pay a $9 dividend at the end of the first year if the stock price has risen, and will pay a $4 dividend if the price has fallen. It will not pay any dividends at the end of second year. The annualized, continuously compounded interest rate is 5%. What is the value of a 2-year European call option with a $45 strike price? What if it’s an American call option?

Answer 1

American call option is the type of option contract that can be exercised at any time on or before maturity

whereas european option can be exercised only on maturity.

Here we need to calculate value of 2-year call option i.s FAIR OP(option price)

Fair OP in case of european option i.e Fair OP on Expiry =Max of(CMP on expiry-Excercise price,0)

Dividend at yr end 2 =Dividend at yr end1*e^.05 =Dividend at yr end1*1.0513

Possibility	CMP as on expiry(A)	Dividend receive at year end 1	Dividend at yr end 2(B)=Div*1.0513	Adjusted CMP=A-B	EP	FAIR OP of Call as on epiry
1	98	9	9.4617	88.5383	45	43.5383
2	45.5	9	9.4617	36.0383	45	0(Will not excercise)
3	45.5	4	4.2052	41.2948	45	0(Will not excercise)
4	21.125	4	4.2052	16.9198	45	0(Will not excercise)

For American call option:

Fair OP would be =Max of (CMP as on today-EP as on today,0)

Possibility	CMP as onToday (A)	Dividend receive at year end 1	Dividend at yr end 0(B)=Div*.9512	Adjusted CMP=A-B	EP as on Expiry=C	EP as on today=C*.9048	FAIR OP of Call as on today
1	50	9	8.5608	41.4392	45	40.716	0.7232
2	50	9	8.5608	41.4392	45	40.716	0.7232
3	50	4	3.8048	46.1952	45	40.716	5.4792
4	50	4	3.8048	46.1952	45	40.716	5.4792