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Table 10.1: Building the Binomial Tree Forward from the Current Stock Price

Table 10.1: Building the Binomial Tree Forward from the Current Stock Price

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Step 2: Compute the Option Pay-off at

Maturity



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• From the tree, we have three hypothetical stock price values at

maturity and we can easily compute the hypothetical call option at

each one.

• The value of an option at maturity is just the payoff stated in the

option contract

• The payoff function for a call option is



• For the three terminal points in the tree in Table 10.1,



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Step 2: Compute the Option Pay-off

at Maturity



16



• For the put option we have the payoff function



• and so in this case we get



• Table 10.2 shows the three terminal values of the call and

put option in the right side of the tree.

• The call option values are shown in green font and the put

option values are shown in red font.

Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



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Table 10.2: Computing the Hypothetical Option

Payoffs at Maturity

Market Variables



D



St =



1000



1528.47



Annual r =



0.05



628.47

0.00



Contract Terms

X=



900



B



T=



0.25



1236.31



Parameters

Annual Vol=



0.6



tree steps =



2



A



E



1000.00



1000.00



dt=



0.125



u=



1.236311



100.00



d=



0.808858



0.00

C



Stock is black



808.86



Call is green

Put is red

F

654.25

0.00

245.75



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



Step 3:Work Backwards in the Tree to

Get the Current Option Value













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Stock price at B = $1,236.31 and at C = $808.86

We need to compute a option value at B and C

Going forward from B the stock can only move to either D or E

We know the stock price and option price at D and E

We also need the return on a risk-free bond with 1.5 months to

maturity

• The term structure of government debt can be used to obtain this

information

• Let us assume that the term structure of interest rates is flat at 5%

per year



Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen



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Table 10.1: Building the Binomial Tree Forward from the Current Stock Price

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