This Demonstration illustrates the influence of the parameters

and

on the fair pricing of illiquid assets in a market-making approach.

The variable

is the discount rate of the next unit bought compared to the price of the preceding unit.

The variable

is the refinement rate (or the rate of subdivision) of the original assets. For example

means the original unit asset is split into 10 new unit assets.

and

represent the sensitivity of the average price with respect to

and

, respectively, computed as partial derivatives with respect to

and

.

We argue that the U.S. government would discover the real price of the Troubled Assets Relief Program's (TARP) troubled assets by becoming a market maker on those assets, if those assets were purchased at a sufficiently refined level of granularity (i.e., with

increasing).

The purple line represents the average price paid for each original unit of asset as the government keeps buying units of toxic assets, assuming no additional bargain hunters enter the market.

As the discount factor

increases, the unit price decreases very quickly. But it is not desirable for the market to have a very steep discount factor, as this steepness captures a relative lack of liquidity in the market. Instead, liquidity problems can be handled by refining the unit size of the assets, which contributes to a more effective price discovery process.

Furthermore, note that the sensitivity on

is structurally of a different order compared to the sensitivity on

. In this simplified model, the sensitivity on

is polynomial while the sensitivity on

is exponential.

The initial number of bad assets

is the total number of assets one must dispose of; it should preferably not be modified. Indeed we must always have

, because in the case

, there will be no assets to be disposed of and the point of the whole exercise becomes moot.