Understanding Financial Risk Management by Corelli Angelo

Author:Corelli, Angelo
Language: eng
Format: epub
ISBN: 978-1-317-75382-7
Publisher: Taylor & Francis (CAM)

8.1.2 Price formation

Order driven markets are the focus of recent attention from practitioners. In recent years in fact, most markets in the world have set new rules for handling orders, due to the development of electronic limit order book trading platforms in virtually all of the market centres in the world.

Combining orders on the two sides of the market is not easy. High-valuation investors are willing to buy from the low-valuation shareholders, in order to gain from the price difference. That causes a problem to low-valuation shareholders, since they make no gain from it. The same holds for low-valuation investors trying to buy from low-valuation shareholders.

A popular model of price formation in stocks markets is the Foucault model, which is based on several assumptions. Trading is continuous with a single risky asset in the market, and investors trade one share of it sequentially through market or limit order.

Two groups of investors populate the market, one putting a high value Vh on the asset and the other with a low value Vi < Vh. High-value and low-value investors populate the market with proportions h and l respectively.

Investors are risk-neutral and maximized their expected utility. For a buy order processed at price b it is given by

E(u) = η(Vi − b), i = h, l

where

η is the probability of execution of the order.

Similarly, the expected utility from a sell order at a specified price is

E(u) = η(b − Vi), i = h, l

In the absence of a trade, the utility is normalized to zero.

A proportion δ of the investor has access to private information about innovation of asset value, which is worth H+ or H− with 50% probability each.

Consider a set of mutual strategies, where each trader has an optimal strategy, given the strategies of the other traders. Each trader must choose a type of order (market vs limit) and (for limit orders) the bid or ask order placement price.

Equilibrium is defined as optimal bid and offer prices b* and a*, such that a counterparty in the next period is induced to trade at these prices via a market order.

The expected utility of a limit buy order placed at bid price b can then be rewritten as

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