An instrument which mimics property performance and which can be sold short is clearly of value to a hedger as it replaces an actual sale. Also, as it is impossible to perform arbitrage from overvalued properties or to bet on a market downturn without property derivatives, speculators and arbitrageurs clearly value the possibility to do so using these new instruments.
In summary, the investor is willing to pay a premium to avoid transaction costs and transaction time. The investor does not engage in a hedge and hence does not need short sales. From the hedger’s perspective, avoiding transaction costs and transaction time is also valuable. In addition, the possibility of a short sale is necessary for the establishment of a hedge, hence the hedger is willing to pay a premium for this. The arbitrage free price bounds are defined by all three basic market frictions: transaction costs, transaction time and the short sale constraint. Due to the existence of frictions, the model provides only arbitrage free price bounds instead of a single arbitrage free price. To value these frictions, they are embedded in a no-arbitrage pricing model.
Arbitrage free price bounds
A property spread can be attributed to the frictions inherent in the market. Given the frictions, bounds of arbitrage free prices follow rather than one single arbitrage free price for property derivatives. The arbitrage free price bounds are a function of the price of the underlying instrument and of market frictions. Only if prices are outside these bounds can arbitrage be achieved using actual property.
We set the framework to derive analytical arbitrage free price bounds as follows. For any given property spread p, there is an upper arbitrage free price bound p and a lower arbitrage free price bound p. The upper bound is the maximum spread an investor is willing to pay for a derivative instead of buying actual property and is only affected by buyer and seller transaction costs k1b and k1s and by transaction time k2. If the property spread lies above the upper arbitrage free price bound, it is more attractive to buy actual property than to buy derivatives. Unlike the upper bound, the lower bound also reflects the value of the short sale constraint k3.
w For a given investment horizon T e a l t h W t h a s a t t i m e T a w e a l t h o f
t = τ, the actual property investor (API) initially endowed with
= ( W t
( 1 + k 1 b + k 2 ) S t ) e r τ
w h e r e S t i s t h e v a l u e o f a p r o p e r t y p o r t f o l i o o r p r o p e r t y i n d e x o n a t o t a l r e t u r n b a s i s i n t . F u r thermore, r represents the risk free interest rate. Transaction costs k1b or k1s as well as the cost of -