ABCDEFGHIJKLMNOPQRSTUVWXYZ
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European Call
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T1
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r3%
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K105
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S0100
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u1.1
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d0.9
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t = 1
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t = 0Su110
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Bu1.030454534
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Fu5
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S100Aua*Su + b*Bu
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B1
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F?Sd90
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Aa*S + b*BBd1.030454534
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Fd0
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Ada*Sd + b*Bd
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Construct a replicating portfolio A by long a units of stock and b units of $1 risk-free bond, so that A1 = c1
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Au = a*Su +b*Bu = Fu
1101.030454534a=5
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Ad = a*Sd +b*Bd = Fd
901.030454534b=0
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=>a=0.25
MMULT(MINVERSE(D22:E23),H22:H23)
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b=-21.8350245
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By no arbitrage
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F = A = a*S + b*B =
3.164975495
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Risk-neutral representation
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u1.1
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d0.9
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qu0.6522726698
=(e^(rT)-d)/(u-d)
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qd0.3477273302=1-qu
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c03.164975
=e^(-rT)(qu*c1u + qd*c1d)
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European put
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t = 1
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t = 0Su110
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Bu1.030454534
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Fu0
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S100Aua*Su + b*Bu
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B1
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F?Sd90
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Aa*S + b*BBd1.030454534
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Fd15
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Ada*Sd + b*Bd
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48
Construct a replicating portfolio A by long a units of stock and b units of $1 risk-free bond, so that A1 = c1
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Au = a*Su +b*Bu = Fu
1101.030454534a=0
110a + 1.03b = 0
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Ad = a*Sd +b*Bd = Fd
901.030454534b=15
90a + 1.03b = 15
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=>a=-0.75
MMULT(MINVERSE(D22:E23),H22:H23)
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b=80.06175652
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By no arbitrage
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F = A = a*S + b*B =
5.061756518
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Risk-neutral representation
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u1.1
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d0.9
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qu0.6522726698
=(e^(rT)-d)/(u-d)
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qd0.3477273302=1-qu
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F5.061757
=e^(-rT)(qu*c1u + qd*c1d)
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Put call parity
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p = c + Ke^(-rT) - S =
5.061757
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