Microsoft PowerPoint - PoF.ppt

Arbitrage free forward priceƒ 137

Underlying = dividend-paying security

ƒ

... no arbitrage condition

Z

... present value of the dividends during

T

ƒ

Suppose

Ä

arbitrage strategy

ƒ

t=t0

• Long forward:

0

• Sell security short:

+S

t0

-Invest

Z

at

r :

-Z

-Invest

St0

-Z

at

r

:

-(S

-Z)t0

-Sum:

0

ƒ

t=T

• Fulfill forward:

-F

t0,T

• Receive from investment:

+(

St0

-Z)e

rT

• Sum = Arbitrage profit:

(S

-Z)et0

rT

-F

t0,T

(

)

rT

t

T

t

e

Z

S

F

−

=

0

, 0

()

rT

t

T

t

e

Z

S

F

−

<

0

, 0

Derivative securities: Forwards - Pricing