Vince,

Over the weekend, I fomulated the idea using option pricing for the EOL 
price seeting rules. The initial results look interesting.  I will write it up for
your inputs.

Also attach is the program SnagIt, for printing window.

Zimin

 

-------------------- main idea ------------------------------

A market maker fulfills the obligation to provide liquidity,
therefore he should be compensated for his service. In the option
langauge, the market maker sells options to the traders, for a
market order to buy, the market maker has to sell at the ask price
and for a market order to sell, the market maker has to buy at the
bid price. When the ask price is hit the trader exercised a call
option against the market maker, when the bid price is lifted, the
trader exercised a put. The option premium that the traders paid
to the market maker is implicitly embedded in the bid-ask spread.

There is a capital requirement for the market making. In a rising
(falling) market, the market maker will accumulate a net short
(long) position. There are two kind of costs. The first is
associated to carry the market-to-market(MTM) value to the next
period. The market maker needs to charge a risk-free interest for
the carrying the inventory to the next period. The second is the
charge for the risk capital. If the ask (bid) were hit (lifted) in
a rising (falling) market, the market maker would realized a loss
reflecting the MTM change. Thus, the risk capital that the market
maker laid aside is the amount of money that he is prepared to
lose, in exchange for some return. The risk adjusted return on
capital or RAROC rate reflects the risk attitude of the market
maker in providing the liquid to the market participants.

In balance, the market maker sells options to compensate his costs
in provide market liquidity. From this train of thoughts, I derive
a formula for the bid and ask prices as function of the last
executed price, inventory level, price volatility, trade size,
order arrival rate, risk-free interest rate and RAROC rate. The
limit orders are not considered here, since there are very few
limit orders traded on EnronOnLine (EOL).