In Glosten (1994), as well as in Viswanathan and Wang (2002) and Biais, Martimort and Rochet (2000), liquidity suppliers can only submit limit orders and liquidity demanders can only use market orders to hit the existing quotes; it follows that in these models agents are not allowed to choose between limit and market orders. In real markets, of course, at the very least the agents submitting orders to an LOB can choose between limit and market orders.
The choice between limit and market orders is a strategic element in any trading decision and depends on the relative probability of execution of the two orders, which in turn depends on a variety of factors, such as the asymmetry of the personal evaluations of the risky asset between the agents who submit the orders and those who hit the existing quotes, their degree of patience, their waiting costs and the state of the LOB. In the recent literature there are a few models for an LOB which embody the choice between market and limit orders; with the exception of Goettler, Parlour and Rajan (2008), in these early models there is no asymmetric information on the asset value.8 It is important, however, to understand the theory on the optimal traders’ submission strategies even when transaction costs are not due to informational asymmetries because there is evidence that non-informational frictions can be substantial; for example, Huang and Stoll (1997) show that on average they account for more than 80 per cent of the spread.
Firstly, let us note that the equilibrium bidding schedule is flatter in the limit order market (8.15) than in the uniform price market (8.17); this is because with price discrimination, competition for liquidity provision intensifies. Figure 8.1 plots the bid schedule under the discriminatory (8.16) and the uniform pricing rules (8.18) for different numbers of dealers: competition modifies only the slope of the uniform pricing schedule, but for the discriminatory schedule it also changes the intercept.
As mentioned, the model in Viswanathan andWang (2002) does not allow for asymmetric information among market participants. Biais, Martimort and Rochet (2000) introduce adverse selection in a model with the discriminatory pricing rule and show how imperfect competition among dealers within an LOB can be modelled as a game with multiple principals, where each dealer (principal) chooses his optimal trading strategy under the participation and incentive constraints of the investor (agent).
In the models of both Kyle (1985) and Grossman and Stiglitz (1980), the equilibrium auction pricing rule is uniform in the sense that it generates a single price at which all orders are executed; in Glosten and Milgrom (1985) each order is executed at a different price, which is determined by the conditional expectation rule; however, the customer pays the same marginal price for each unit in the same order. One of the peculiarities of the LOB, by contrast, is that an order can be satisfied at different prices, as limit sell (buy) orders can be executed at or above (below) their limit price. It follows that within an LOB each market order or marketable limit order larger than the quantity available at the inside spread can be filled at different prices, by absorbing the liquidity available at the best bid offer and then walking up (or down) the book. Because buy (sell) orders can be executed at increasing (decreasing) limit prices, when a liquidity supplier posts his price and quantity he will take into account that his price can be picked up not only by traders willing to trade the quantity he offers, as in Glosten and Milgrom, but also by agents willing to submit larger orders. Hence, if the order size is a proxy for the private information held by the customer submitting the order, the liquidity supplier will quote a price that is higher than the one he would post in a bilateral transaction as in Glosten and Milgrom.
The models presented in the previous chapters describe the price formation process in markets with different structures. As we saw in the previous article, among the markets with trade pricing rules, those governed by an order-driven execution system can be organized either as a continuous or as a call auction, while markets with a quote-driven system can be either a bilateral dealer market or a continuous auction that works as a limit order book.Within this outline, the Glosten and Milgrom (1985) model describes a bilateral quote-driven market in which dealers’ competition guarantees semi-strong efficiency; Kyle’s (1985) model proxies an order-driven call auction market where a specialist, or a number of market-makers, sets the market-clearing price after observing his, or their, customers’ aggregated order flow. Finally, the Grossman and Stiglitz (1980) model proxies an order-driven market where all participants can submit their demand schedules simultaneously.1 Since each demand function is a fairly accurate representation of a large number of small limit orders (Brown and Zhang, 1997), this market can be interpreted as a limit order book. As the next section shows, this interpretation has the advantage of considering all market participants as potential liquidity suppliers, i.e. of embodying the order-driven feature of a limit order book (LOB); it fails, however, to incorporate either the discriminatory pricing rule that characterizes an LOB or the agents’ strategic choices between limit orders and market orders. Section8.1 will introduce the reader to the discriminatory pricing rule and will sketch a basic model that embodies this rule; in this model, however, agents cannot choose the type of order to submit to the LOB, so section 8.2 presents models in which the choice between market and limit orders is endogenous.
As a consequence each of the mentioned types of bank capital represents its own risk class. Investors clearly have to be compensated to carry the additional risks compared with senior bank bonds. Figure 4.3 shows that on average the spread differentials between senior bonds and Lower Tier 2, Lower Tier 2 and Upper Tier 2, and Upper Tier 2 and Tier 1 tend to be roughly equal. But one should note that spread volatility also increases significantly when moving to more subordinated types of bank debt. Again, this can be explained by the Merton model. Since Tier 1 and Upper Tier 2 bonds are designed to absorb losses before holders of senior bonds and Lower Tier 2 suffer a loss, the strike price of their embedded short put option is closer at the money than that of senior and Lower Tier 2 bonds. Hence, in absolute terms the delta of the short put is higher, causing larger changes of the value of the option and consequently spreads, when fundamentals change.
A second method to slice the corporate bond universe, especially the financial sector, is by different degrees of subordination. We discuss the characteristics of different types of bank debt in detail. In summary, Tier 1 preferred, Upper Tier 2 and Lower Tier 2 differ from senior bank debt in two major dimensions: with respect to loss absorption and interest deferral features. Both Tier 1 and Upper Tier 2 capital are able to absorb losses. But while missed interest payments are canceled immediately for Tier 1 issues they are repaid at a later date for Upper Tier 2 bonds. On the other hand, Lower Tier 2 debt contains no loss absorption features.
BBB-rated corporate bonds obviously have a very high correlation to fluctuations of credit spreads in general. Although they made up on average only 25 percent of the Euro investment grade market, the influence of lower rated bonds on market spreads is substantial. Higher quality bonds, on the other hand, exhibit lower correlations to market spread changes. One reason is that their impact on the market direction is less pronounced because they are less volatile. But the second reason is probably more important. Euro corporate bonds are typically valued against swaps, that is the spread versus government bonds consists of two components: the swap spread and the spread over swaps. As a consequence changes of swap spreads have an influence on the spread of a corporate bond versus duration-matched treasuries. The higher the credit quality and the lower the spread of an issuer, the higher is the fraction of the benchmark spread that is due to the swap spread.
Investors require a premium for taking on credit risk. Not only does this premium, in other words the credit spread, have to increase with decreasing credit quality, but one also expects a higher sensitivity of spreads to changes of the fundamental environment for lower rated credits. As pointed out earlier, the assets of a company with a higher degree of leverage are nearer to the default threshold than those of a firm with a conservative balance sheet structure. In terms of the structural model the short put option on the assets of the issuer moves nearer at-the-money with decreasing credit quality, causing the delta to rise. Hence, a falling value of the assets, for example, in periods of a deteriorating economic environment and consequently declining equity markets, leads to a larger change in the credit spread the lower the credit quality of the issuer is.
While in a single name context ratings are often criticized for being lagging indicators of credit quality, classifying bonds by rating is one widely used method to reflect the behavior of different risk classes in credit markets.
Many market participants argue that spreads themselves and spread volatilities are more timely indicators of an issuer’s credit risk than ratings. They consequently prefer to split the universe in spread class buckets. The disadvantage of this method is that it leads to relatively unstable compositions of the individual buckets and is less convenient, because the major index providers do not calculate indices based on spread classes. Since the different rating buckets constitute the corporate bond market as a whole, there is clearly a correlation between overall market fluctuations and the spread changes of the different rating subportfolios.
The risk profile of a credit portfolio, in absolute terms as well as relative to a benchmark index, is largely determined by the weighting of different risk classes. Of course, the allocation of capital to riskier asset classes not only increases risk, but also offers ample opportunities for outperformance. From a top-down perspective there are various methods to split the corporate bond universe in different risk classes. Here the three most popular approaches are introduced: dividing the universe by rating classes, by degrees of subordination or by the degree of cyclicality of the different industries.
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