Question

A non-dividend stock is trading at $30 and the stock price either moves up or down by 10% every three months. The risk-free interest rate is 5% p.a. (c.c.). Use the two-period binomial model to value a six-month European put option on the stock with an exercise price of $31

Answer 1

Soluition:-

First we need to Find Joint Probability-

Probabilty for upward Movement in first three Month =

Probabilty for upward Movement in first three Month =

Probabilty for upward Movement in first three Month = 0.5629

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

Probabilty for Downward Movement in first three Month =1 - 0.5629

Probabilty for Downward Movement in first three Month = 0.4371

Probabilty for upward Movement in Next three Month =

Probabilty for upward Movement in Next three Month =

Probabilty for upward Movement in Next three Month = 0.5629

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

Probabilty for Downward Movement in Next three Month =1 - 0.5629

Probabilty for Downward Movement in Next three Month = 0.4371

Value of Put option as on Today-

Option Price of Put 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
36.3	31	0	0.5629*0.5629	0.000
29.7	31	1.3	0.5629*0.4371	0.3199
29.7	31	1.3	0.4371*0.5629	0.3199
24.3	31	6.7	0.4371*0.4371	1.2801
				1.920

Value of PUT option as on Today =

Value of PUT option as on Today =

Value of PUT option as on Today = 1.92 * 0.9753

Value of PUT option as on Today = $1.873

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