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where k3 is the cost of the short sale constraint and eproceeds from the sale over the hedging time τ.

reflects the interest earned on the cash

I f , f o r a g i v e n h e d g e h o r i z o n , t h e h e d g e r h o l d s o n t o t h e p o r t f o l i o S t a n d s e l l s a p r o p e r t y d e r i v a t i v (PDH) instead of the physical properties, he gets e

WPDH,T

= ST + (Ft,T

ST )

= S T + S t e

r+pτ )τ

ST

(14)

= S t e

r+pτ )τ

For the no-arbitrage condition, the expected wealth using the derivative hedge must be equal to or greater than the expected wealth after a actual sale:

[ W A P H , T ]

[ W P D H , T ] ,

(15)

or

(1

k1s

k2

k 3 ) S t e r τ

(k1b + k2)

[ S T ] S t e

r+pτ )τ

(16)

It follows that the lower bound of the property spread p is

pτ =

ln[(1

k1s

k2

k3)e

τ

(k1b + k2)e

r+

)τ ]

r.

(17)

Empirical results

Empirically observed derivative prices allow us to quantify the cost of the frictions in our arbitrage free price bound framework.

In July 2008, three year notes on the Halifax HPI were traded at a discount such that the breakeven on the notes corresponds to a 45% decline in UK house prices. In contrast, the biggest peak to trough move in the history of the Halifax HPI was -14.7%, from July 1989 to February 1993.

It is obvious that market participants had a negative view on property prices and were ready to pay a significant premium to sell a property index derivative short. Hedge funds were strong sellers of property derivatives as they bought distressed subprime credit portfolios and hedged their collateral risk by selling property derivatives short. Property derivatives still offer the only way to hedge this property

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