(This equation can be interpreted as the producer surplus formula for the firm whose production technology for converting numeraire z into probability y of winning the object is defined by the auction and which resells the object at a fixed price t ).
12.
As a simple example to demonstrate the non-coherence of value-at-risk consider looking at the VaR of a portfolio at 95 % confidence over the next year of two default-able zero coupon bonds that mature in 1 years time denominated in our numeraire currency.
13.
By selecting as numeraire the time-" S " bond ( which corresponds to switching to the S-forward measure ), we have from the fundamental theorem of arbitrage-free pricing, the value at time 0 of a derivative which has payoff at time " S ".
14.
A direct extension, then, is the concept of a state price security ( also called an Arrow-Debreu security ), a contract that agrees to pay one unit of a numeraire ( a currency or a commodity ) if a particular state occurs ( " up " and " down " in the simplified example above ) at a particular time in the future and pays zero numeraire in all the other states.
15.
A direct extension, then, is the concept of a state price security ( also called an Arrow-Debreu security ), a contract that agrees to pay one unit of a numeraire ( a currency or a commodity ) if a particular state occurs ( " up " and " down " in the simplified example above ) at a particular time in the future and pays zero numeraire in all the other states.
