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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

15

• 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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