Question

A stock price is currently priced at £110. Over each of the next two three-month periods it is expected to down by 7% or go up by 8%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of £105?

If possible, please provide a detailed step by step as I would like to fully comprehend it rather than just copying it. Thank you :)

Answer 1

Solution:-

First we need to Find Joint Probability-

Probabilty for Downward Movement in first three Month =

Probabilty for Downward Movement in first three Month =

Probabilty for Downward Movement in first three Month = 0.5505

Probabilty for upward Movement in first three Month =1 - Probabilty for downward Movement in first three Month

Probabilty for upward Movement in first three Month =1 - 0.5505

Probabilty for upward Movement in first three Month = 0.4495

Probabilty for Downward Movement in Next three Month =

Probabilty for Downward Movement in Next three Month =

Probabilty for Downward Movement in Next three Month = 0.5505

Probabilty for upward Movement in Next three Month =1 - Probabilty for downward Movement in Next three Month

Probabilty for upward Movement in Next three Month =1 - 0.5505

Probabilty for upward Movement in Next three Month = 0.4495

Option Price of call as on Today
		A	B	A*B
Current Market Price as on Expiry	Excersice Price	Option Price as on Expiry	Joint Probability	Expected Option price as on expiry
95.139	105	0	0.5505*0.5595	0.000
110.484	105	5.484	0.5505*0.4495	1.357014429
110.484	105	5.484	0.4495*0.5595	1.379199951
128.304	105	23.304	0.4495*0.4495	4.708579026
				7.445

Value of CALL option as on Today =

Value of CALL option as on Today =

Value of CALL option as on Today = 7.445 * 0.9753

Value of CALL option as on Today = $7.261

Value of six month european call option as on today is amounting to $7.261

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