RMSC2001_T8_BInomialTree.xlsx

	A	B	C	D	E	F	G	H	J
1	European Call
2	T	1
3	r	3%
4	K	11
5
6
7	t = 0			t = 1
8				S1u	14
9				c1u	3
10	S0	10		A1u	aS1 +be^rt
11	c0	?
12	A0	aS0 + b
13				S1d	8
14				c1d	0
15				A1d	aS1 +be^rt
16
17	Construct a replicating portfolio A by long a units of stock and b units of $1 risk-free bond, so that A1 = c1
18	14a+be^3% = 3			14	1.030454534	a	=	3
19	8a + be^3% = 0			8	1.030454534	b	=	0
20
21				=>		a	=	0.5	MMULT(MINVERSE(D22:E23),H22:H23)
22						b	=	-3.881782134
23
24	By no arbitrage, A0 = c0
25	c0 = aS0 + b =		1.118217866
26
27	Risk-neutral representation
28	u	1.4	=S1u/S0
29	d	0.8	=S1d/S0
30	qu	0.3840908899	=(e^(rT)-d)/(u-d)
31	qd	0.6159091101	=1-qu
32	c0	1.118217866	=e^(-rT)(quc1u + qdc1d)
33
34	European Put
35	T	1
36	r	3%
37	K	11
38
39
40	t = 0			t = 1
41				S1u	14
42				p1u	0
43	S0	10		A1u	aS1 +be^rt
44	p0	?
45	A0	aS0 + b
46				S1d	8
47				p1d	3
48				A1d	aS1 +be^rt
49
50	Construct a replicating portfolio A by long a units of stock and b units of $1 risk-free bond, so that A1 = c1
51	14a+be^3% = 3			14	1.030454534	a	=	0
52	8a + be^3% = 0			8	1.030454534	b	=	3
53
54				=>		a	=	-0.5	MMULT(MINVERSE(D22:E23),H22:H23)
55						b	=	6.793118735
56
57	By no arbitrage, A0 = c0
58	p0 = aS0 + b =		1.793118735
59
60	Risk-neutral representation
61	u	1.4	=S1u/S0
62	d	0.8	=S1d/S0
63	qu	0.3840908899	=(e^(rT)-d)/(u-d)
64	qd	0.6159091101	=1-qu
65	p0	1.793118735	=e^(-rT)(quc1u + qdc1d)
66
67	Put call parity
68	p0 = c0 + Ke^(-rT) - S0 =			1.793118735
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