transaction time k_{2 }incur for both a purchase and a sale and are defined for a one way transaction in percentage terms. Furthermore, the forward price for a property derivative is

F_{t,T }

= S t e

r+p_{τ })τ

,

(2)

where p_{τ }is the property spread for a contract with a lifespan τ. If the investor buys a property derivative investment (PDI) instead of actual property, he gets

W_{PDI,T }

t = W e^{rτ }

+ (S_{T }

t = W e^{rτ }

+ S_{T }

F_{t,T })

S t e

r+p_{τ })τ

.

(3)

As a forward contract is unfunded, the initial wealth earns interest, captured by the first term in Eq. (3). For the no-arbitrage condition to hold, the expected wealth using a derivative investment must be equal or greater than the expected wealth using a actual property investment:

t

[ W A P I , T ] ≤

t

[ W P D I , T ] ,

(4)

or

( W t

( 1 + k 1 b + k 2 ) S t ) e r τ

+

(1

k_{1s }

k_{2})

t

[ S T ] ≤ W t e r τ

+

t

[S_{T }]

S t e

r+p)τ

,

(5)

where

[·] is the expected value under a martingale measure Q.

Following Bjoerk (1998) let the

m a r k e t c h o o s e t h i s m e a s u r e . W e a s s u m e t h a t S t f o l l o w s a g e o m e t r i c B r o w n i a n m o t i o n w i t h d r i f t µ , v a r i a n c e σ 2 a n d a W i e n e r p r o c e s s Z t . A s w e w i l l s e e i n t h e n e x t s e c t i o n , p r o p e r t y i n d e x e s o f t e n e hibit significant autocorrelation in the short term but the impact of autocorrelation on the expected value decreases exponentially and affects the expected values that are relevant in the context of arbi- trage free price bounds only marginally. We thus consider a geometric Brownian motion as reasonable x -

approximation that is analytically manageable. Let

X t = S t e

rτ

(6)

be the discounted index value. Then consider

t

## [X_{T }],

(7)

7