How Important Is Liquidity Risk for Sovereign Bond Risk Premia? Evidence from the London Stock Exchange

This paper uses the framework of arbitrage-pricing theory to study the relationship between liquidity risk and sovereign bond risk premia. The London Stock Exchange in the late 19th century is an ideal laboratory in which to test the proposition that liquidity risk affects the price of sovereign debt. This period was the last time that the debt of a heterogeneous set of countries was traded in a centralized location and that a sufficiently long time series of observable bond prices are available to conduct asset-pricing tests. Empirical analysis of these data establishes three new results. First, sovereign bonds with wide bid-ask spreads earn 3-4% more per year than bonds with narrow bid-ask spreads, and the difference is reflected in greater sensitivity to innovations in market liquidity. Second, small sovereign bonds, as measured by market value, earn 1.8-3.5% more per year than large sovereign bonds, and the difference is also reflected in their exposure to innovations in market liquidity. Third, market liquidity is a state variable important for pricing the cross-section of sovereign bonds. This paper thus provides estimates of the quantitative importance of liquidity risk as a determinant of the sovereign risk premium and underscores the significance of market liquidity as a nondiversifiable risk.Financial markets; International topics

The Zeeman Effect in Finance: Libor Spectroscopy and Basis Risk Management

Once upon a time there was a classical financial world in which all the Libors were equal. Standard textbooks taught that simple relations held, such that, for example, a 6 months Libor Deposit was replicable with a 3 months Libor Deposits plus a 3x6 months Forward Rate Agreement (FRA), and that Libor was a good proxy of the risk free rate required as basic building block of no-arbitrage pricing theory. Nowadays, in the modern financial world after the credit crunch, some Libors are more equal than others, depending on their rate tenor, and classical formulas are history. Banks are not anymore too "big to fail", Libors are fixed by panels of risky banks, and they are risky rates themselves. These simple empirical facts carry very important consequences in derivative's trading and risk management, such as, for example, basis risk, collateralization and regulatory pressure in favour of Central Counterparties. Something that should be carefully considered by anyone managing even a single plain vanilla Swap. In this qualitative note we review the problem trying to shed some light on this modern animal farm, recurring to an analogy with quantum physics, the Zeeman effect

A non-arbitrage liquidity model with observable parameters for derivatives

We develop a parameterised model for liquidity effects arising from the trading in an asset. Liquidity is defined via a combination of a trader's individual transaction cost and a price slippage impact, which is felt by all market participants. The chosen definition allows liquidity to be observable in a centralised order-book of an asset as is usually provided in most non-specialist exchanges. The discrete-time version of the model is based on the CRR binomial tree and in the appropriate continuous-time limits we derive various nonlinear partial differential equations. Both versions can be directly applied to the pricing and hedging of options; the nonlinear nature of liquidity leads to natural bid-ask spreads that are based on the liquidity of the market for the underlying and the existence of (super-)replication strategies. We test and calibrate our model set-up empirically with high-frequency data of German blue chips and discuss further extensions to the model, including stochastic liquidity

Information of Interest

A pricing formula for discount bonds, based on the consideration of the market perception of future liquidity risk, is established. An information-based model for liquidity is then introduced, which is used to obtain an expression for the bond price. Analysis of the bond price dynamics shows that the bond volatility is determined by prices of certain weighted perpetual annuities. Pricing formulae for interest rate derivatives are derived.Comment: 12 pages, 3 figure

On pricing kernels, information and risk

We discuss the finding that cross-sectional characteristic based models have yielded portfolios with higher excess monthly returns but lower risk than their arbitrage pricing theory counterparts in an analysis of equity returns of stocks listed on the JSE. Under the assumption of general no-arbitrage conditions, we argue that evidence in favour of characteristic based pricing implies that information is more likely assimilated by means of nonlinear pricing kernels for the markets considered.Comment: 20 pages, 3 figures, 1 tabl

Liquidity risks on power exchanges

Financial derivatives are important hedging tool for asset’s manager. Electricity is by its very nature the most volatile commodity, which creates big incentive to share the risk among the market participants through financial contracts. But, even if volume of derivatives contracts traded on Power Exchanges has been growing since the beginning of the restructuring of the sector, electricity markets continue to be considerably less liquid than other commodities. This paper tries to quantify the effect of this insufficient liquidity on power exchange, by introducing a pricing equilibrium model for power derivatives where agents can not hedge up to their desired level. Mathematically, the problem is a two stage stochastic Generalized Nash Equilibrium and its solution is not unique. Computing a large panel of solutions, we show how the risk premium and player’s profit are affected by the illiquidity.illiquidity, electricity, power exchange, artitrage, generalized Nash Equilibrium, equilibrium based model, coherent risk valuation

Implicit transaction costs and the fundamental theorems of asset pricing

This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Implicit transaction costs are composed of two terms, one is able to capture the bid-ask spread, and the second the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies having c\'adl\'ag (right-continuous with left limits) and c\'agl\'ad (left-continuous with right limits) paths of bounded quadratic variation and of finitely many jumps. That is, c\'adl\'ag and c\'agl\'ad predictable trading strategies of infinite variation, with finitely many jumps and of finite quadratic variation are allowed in our setting. Restricting ourselves to c\'agl\'ad predictable trading strategies, we show that the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also shown that the use of continuous and bounded variation trading strategies can improve the efficiency of hedging in a market with implicit transaction costs. To better understand how to apply the theory proposed we provide an example of an implicit transaction cost economy that is linear and non-linear in the order size.Comment: International Journal of Theoretical and Applied Finance, 20(04) 201