Microsoft PowerPoint - PoF.ppt

Arbitrage free forward priceƒ 139

Underlying = commodity that is an investment asset, e.g. gold

ƒ

... no arbitrage condition

L

... present value of the storage costs incurred during

T

ƒ

Suppose

Ä

arbitrage strategy

ƒ

t=t0

• Long forward:

0

• Sell security short:

+S

t0

-Invest

St0

+L

at

r

:

-(S

+L)t0

-Sum:

0

ƒ

t=T

• Fulfill forward:

-F

t0,T

• Receive from investment:

+(

St0

+L)e

rT

• Sum = Arbitrage profit:

(S

+L)et0

rT-F

t0,T

(

)

rT

t

T

t

e

L

S

F

+

=

0

, 0

()

rT

t

T

t

e

L

S

F

+

<

0

, 0

Derivative securities: Forwards - Pricing