Stock Price Formulation

What is the 'itayose' method?

Update : Jan. 04, 2010

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Answer :

As explained in 'How are stock prices determined?' above, the Itayose method is used to determine opening and closing prices, as well as the initial price after a trading halt and prices when special quotes or sequential trade quotes are indicated.

The order book prior to the start of the session is often complicated with offers (sell) at lower prices than bids (buy) and bids at higher prices than offer, as well as a mixture of market offers and bids. Under the Itayose method all orders reaching the order book are treated as simultaneous orders, in other words there is no time priority.
Bids and offers are matched at a single price according to the principle of price priority.
Orders are executed as follows:

  1. All market orders
  2. All limit orders to sell/buy at prices lower/higher than the execution price
  3. The entire amount of either all sell or all buy orders at the execution price:

The table below represents the order book. The centre column gives the prices, the second column from the left shows the volume of individual offers (sell), and the far left column shows the aggregate volume (working from the bottom (lowest price) of the order book) of offers. The right hand side of the table is a mirror image and represents the bid side (buy), with individual bids in the second column from the right and the aggregate volume (working from the top (highest price) of the order book) in the far right column.
Market orders on both sides are displayed at the very top.

We start by focusing on requirements (a) and (b) as set out above in order to determine the opening price. First, a price is determined by looking at the prices at which the amount of the aggregated bids and offers balance out. In this case these are 501 yen and 500 yen, so the opening price is likely to be one of these two prices.

Offer (sell) Offer (sell) Price Bid (buy) Bid (buy)
Aggregate Quantity   Quantity Aggregate
  600 Market orders 400  
4,400 800 502 100 500
3,600 2,000 501 700 1,200
1,600 400 500 1,000 2,200
1,200 200 499 800 3,000
1,000 400 498 3,000 6,000

Note: A trading unit is 100 shares. The same applies hereinafter.
So let's see what happens when we assume an opening price of 500 yen

Offer Price Bid First, according to requirement (a), the market orders of 400 shares to buy and 600 shares to sell are matched, leaving sell orders of 200 shares.
600 M.O. 400
800 502 100
2,000 501 700
400 500 1,000
200 499 800
400 498 3,000
Offer Price Bid Next, according to requirement (b), the market sell orders of 200 shares and sell orders of 600 shares at limit prices of 499 yen or less are matched with the buy orders of 800 shares at limit prices of 501 yen or more. Thus so far, 1,200 shares have been matched in total.
200 M.O.  
800 502 100
2,000 501 700
400 500 1,000
200 499 800
400 498 3,000
Offer Price Bid Finally, the sell orders of 400 shares at a limit price of 500 yen are matched with the buy orders of 1,000 shares at a limit price of 500 yen. Although this still leaves buy orders of 600 shares at 500 yen, this satisfies requirement (c).
  M.O.  
800 502  
2,000 501  
400 500 1,000
  499 800
  498 3,000
Offer Price Bid Thus the opening price is determined at 500 yen and transactions of 1,600 shares are completed at 500 yen.
  M.O.  
800 502  
2,000 501  
  500 600
  499 800
  498 3,000

Now, just as a precaution let's double-check by using 501 yen as the opening price.

Offer Price Bid According to requirement (a) and as explained above, the market orders are matched leaving sell orders of 200 shares.
600 M.O. 400
800 502 100
2,000 501 700
400 500 1,000
200 499 800
400 498 3,000
Offer Price Bid Then, assuming an opening price of 501 yen, the remaining market sell orders of 200 shares and sell orders of 1,000 shares at limit prices of 500 yen or less are matched with the buy orders of 100 shares at limit prices of 502 yen or more.

However, with only 100 shares on the bid side it is impossible to execute all the market sell orders. Thus meaning the Itayose requirements cannot be meet at 501 yen.
200 M.O.  
800 502 100
2,000 501 700
400 500 1,000
200 499 800
400 498 3,000

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