Question

(1) (2 pts.) Please use binomial option pricing model to derive the value of a one-year put option. The current share price is ?0=100 and exercise price ?=110. The T-bill rate is ?=10% per year and annual standard deviation is 20%.

Please show:

1. binomial tree

2. Probability of increase and decrease

3. U/D or % or increase for each case

Answer 1

S	100
E	110
u	1.2214
d	0.8187
p	0.71
(1-p)	0.29
r	1.11

Now we will calculate value of put at each node and discount it to period zero

P+ = [0.71*0 + 0.29*10] / 1.11 = 2.61

similarly P- and P have been calculated

Price of PUT = 6.3

Period 0			Period 1			Period 2
					uuS	149.18
					P++	0.00
		uS	122.14
		P+	2.61
100					uds	100.00
6.30					P+-	10.00
		dS	81.87
		P-	17.67
					ddS	67.03
					P--	42.97