Do Investors Expect Mean Reversion in Asset Prices?

We investigate the existence and source of equilibrium mean reversion in UK non-financial and financial asset prices over the period 6 April, 1981, through 31 October, 1995. Our results indicate substantial expected transitory components in commodity and metals markets but report expected mean reversion for financial assets only at the near to maturity horizons. Implied cash flow yields appear to have a role in driving the mean reverting process particularly at short horizons while the role of interest rate movements varied across assets and across maturities. Our results reject the existence of a common risk premium across market term structures.     

Arbitrage and deflators in illiquid markets

This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with transaction costs or bid–ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. In the presence of nonlinearities, the classical notion of arbitrage turns out to have two equally meaningful generalizations, a marginal and a scalable one. We study their relations to state price deflators by analyzing two auxiliary market models describing the local and global behavior of the cost functions and constraints.     

The Determinants of Long‐Term Corporate Debt Issuances

A significant proportion of the debt issued by investment‐grade firms has maturities greater than 20 years. In this paper we provide evidence that gap‐filling behavior is an important determinant of these very long‐term issues. Using data on individual corporate debt issues between 1987 and 2009, we find that gap‐filling behavior is more prominent in the very long end of the maturity spectrum where the required risk capital makes arbitrage costly. In addition, changes in the supply of long‐term government bonds affect not just the choice of maturity but also the overall level of corporate borrowing.     

Asymmetric dynamics in correlations of treasury and swap markets: Evidence from the US market

Using the asymmetric dynamic conditional correlation (A-DCC) model developed by Cappiello et al. (2006), this paper empirically analyzes the conditional correlation between treasury and swap markets from February 9, 2006 to May 31, 2011, and makes two key contributions. First, the dynamics of the conditional correlation of only the 2-year maturity differs from those of other maturities. These patterns might be explained by the fact that a 2-year maturity is easily affected by market forecasts of monetary policy changes by the Federal Reserve Board. Second, the financial crisis dummies (ξ₁) are all negative in particular with significance at the 5% level for 7 year, 10 year, and 30 year maturities. This result indicates that arbitrage transactions between treasuries and swaps have not taken place on a sufficient scale during the financial crisis period. As Ito (2010) points out, market participants have been uncertain about the direction of the monetary policies of these financial institutions.     

Price Expectation and the Pricing of Stock Index Futures

Capital markets are not perfect or frictionless, and arbitrage mechanism cannot be complete, particularly for index arbitrage. This study constructs a theoretical foundation to explain why the price expectation of the underlying asset should be entered into the pricing formula of stock index futures. The price expectation and incompleteness of arbitrage then are taken into account to develop a pricing model of stock index futures in imperfect markets. This study also presents three approaches for estimating the model parameter. Finally, the concept of the degree of market imperfection is defined and the valuation model is provided.     

Arbitrage-free market models for option prices: the multi-strike case

This paper studies modeling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for constructing such models, we introduce the new concepts of local implied volatilities and price level. We show that these new quantities provide a natural and simple parametrization of all option price models satisfying the natural static arbitrage bounds across strikes. We next characterize absence of dynamic arbitrage for such models in terms of drift restrictions on the model coefficients. For the resulting infinite system of SDEs for the price level and all local implied volatilities, we then study the question of solvability and provide sufficient conditions for existence and uniqueness of a solution. We give explicit examples of volatility coefficients satisfying the required assumptions, and hence of arbitrage-free multi-strike market models of option prices.      

The fluctuating maturities of convertible bonds

The maturities of newly issued convertible bonds vary substantially over time. Firm-specific determinants of maturity from the straight debt literature are relevant for convertible bonds. However, the growth of the convertible arbitrage industry and the role of convertible arbitrage hedge funds have changed the importance of firm characteristics in the convertible bond market. Recently issued convertible bonds come with particularly short maturities that serve as substitutes for call provisions. This substitution implies that backdoor-equity and sequential-financing rationales for issuing callable convertible bonds are also applicable for non-callable convertibles with shorter maturities.     

Options Arbitrage in Imperfect Markets

Option valuation models are based on an arbitrage strategy—hedging the option against the underlying asset and rebalancing continuously until expiration—that is only possible in a frictionless market. This paper simulates the impact of market imperfections and other problems with the “standard” arbitrage trade, including uncertain volatility, transactions costs, indivisibilities, and rebalancing only at discrete intervals. We find that, in an actual market such as that for stock index options, the standard arbitrage is exposed to such large risk and transactions costs that it can only establish very wide bounds on equilibrium options prices. This has important implications for price determination in options markets, as well as for testing of valuation models.     

Asymptotic arbitrage and numéraire portfolios in large financial markets

This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind) introduced in Probab. Theory Appl. 39, 222–229 (1994) and in Finance Stoch. 2, 143–172 (1998). We show that the arbitrage properties of a large market are completely determined by the asymptotic behavior of the sequence of the numéraire portfolios related to small markets. The obtained criteria can be expressed in terms of contiguity, entire separation, and Hellinger integrals, provided that these notions are extended to sub-probability measures. As examples, we consider market models on finite probability spaces, semimartingale models, and diffusion models. We also examine a discrete-time infinite horizon market model with one log-normal stock. This work was supported by Southern Federal University, grant No. 26 “Mathematical Finance” and by RFBR, grant 07-01-00520.     

Gaussian models for Euro high grade government yields

This paper tests affine, quadratic and Black-type Gaussian models on Euro area triple A Government bond yields for maturities up to 30 years. Quadratic Gaussian models beat affine Gaussian models both in-sample and out-of-sample. A Black-type model best fits the shortest maturities and the extremely low yields since 2013, but worst fits the longest maturities. Even for quadratic models we can infer the latent factors from some yields observed without errors, which makes quasi-maximum likelihood (QML) estimation feasible. New specifications of quadratic models fit the longest maturities better than does the ‘classic’ specification of Ahn et al. [2002. ‘Quadratic Term Structure Models: Theory and Evidence.’ The Review of Financial Studies 15 (1): 243–288], but the opposite is true for the shortest maturities. These new specifications are more suitable to QML estimation. Overall quadratic models seem preferable to affine Gaussian models, because of superior empirical performance, and to Black-type models, because of superior tractability. This paper also proposes the vertical method of lines (MOL) to solve numerically partial differential equations (PDEs) for pricing bonds under multiple non-independent stochastic factors. ‘Splitting’ the PDE drastically reduces computations. Vertical MOL can be considerably faster and more accurate than finite difference methods.     

Ex post and ex ante returns and risks under different maturities of treasury bonds: evidence from developed and emerging markets

Based on asset pricing theory, reward/risk ratios vary positively with maturity of Treasury securities. We study the effect of increasing Treasury bonds' maturity on ex post and ex ante returns and risks in developed and emerging countries. As maturity increases, we show that ex post and ex ante returns are negative and they decrease while ex post and ex ante risks increase in developed countries, resulting in a sharp increase in the ex post and ex ante coefficient of variation. This indicates that investors are negatively rewarded for the risk they face for investing in Treasury bonds in developed markets. In emerging markets, as maturity increases, ex post and ex ante returns are positive for medium and long maturities and they increase while ex ante risk decreases with maturity. As maturity increases, the coefficient of variation in emerging and developed markets increases, indicating that reward to investors for facing extra risk decreases as maturity increases; however, investors are much better rewarded in emerging than developed markets.     

Permanent trading impacts and bond yields

We analyse four years of transaction data for euro-area sovereign bonds traded on the MTS electronic platforms. In order to measure the informational content of trading activity, we estimate the permanent price response to trades. We not only find strong evidence of information asymmetry in sovereign bond markets, but also show the relevance of information asymmetry in explaining the cross-sectional variations of bond yields across a wide range of bond maturities and countries. Our results confirm that trades of more recently issued bonds and longer maturity bonds have a greater permanent effect on prices. We compare the price impact of trades for bonds across different maturity categories and find that trades of French and German bonds have the highest long-term price impact in the short maturity class, whereas trades of German bonds have the highest permanent price impact in the long maturity class. More importantly, we study the cross-section of bond yields and find that after controlling for conventional factors, investors demand higher yields for bonds with larger permanent trading impact. Interestingly, when investors face increased market uncertainty, they require even higher compensation for information asymmetry.     

Flattening of Bond Yield Curves for Long Maturities

The paper presents a theoretical proof that flattening of yield curves for par bonds is inevitable for long maturities. This proof implies that behavioral explanations of flattening are unnecessary. The proof also implies that the use of yields to maturity of couponbearing bonds to estimate the true term structure (as well as forward rates) for long maturities has potentially infinite bias, suggesting that a greater effort should be made to directly estimate the true term structure in empirical work.     

Consistent price systems and arbitrage opportunities of?the?second kind in models with transaction costs

In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial endowments lying outside the solvency region but ending inside. Such a phenomenon was discovered by M. Rásonyi in the discrete-time framework. In this note, we consider a rather abstract continuous-time setting and prove necessary and sufficient conditions for a property which we call no free lunch of the second kind, NFL2. We provide a number of equivalent conditions elucidating, in particular, the financial meaning of the property B which appeared as an indispensable “technical” hypothesis in previous papers on hedging (superreplication) of contingent claims under transaction costs. We show that it is equivalent to another condition on the “richness” of the set of consistent price systems, close to the condition PCE introduced by Rásonyi. In the last section, we deduce the Rásonyi theorem from our general result by using specific features of discrete-time models.     

Global trends in real risk free rates

We examine real returns to government debt of the G7 countries, for both short and long maturities. Our focus is on returns to fixed income investing rather than contemporaneous yields. We find evidence that investments in the same maturity across countries may be modeled as a cointegrated process, in a vector error correction framework, with common trends separated into their permanent and transitory components for the system. Our findings are based on analysis of both short-term maturities and long-term maturities. However, the structure varies excessively across maturities and time frames, with recent data showing less integration.     

Reduced form modeling of limit order markets

This paper proposes a parametric approach for stochastic modeling of limit order markets. The models are obtained by augmenting classical perfectly liquid market models with a few additional risk factors that describe liquidity properties of the order book. The resulting models are easy to calibrate and to analyse using standard techniques for multivariate stochastic processes. Despite their simplicity, the models are able to capture several properties that have been found in microstructural analysis of limit order markets. Calibration of a continuous-time three-factor model to Copenhagen Stock Exchange data exhibits, for example, mean reversion in liquidity as well as the so-called crowding out effect, which influences subsequent mid-price moves. Our dynamic models are also well suited for analysing market resilience after liquidity shocks.     

Arbitrage and Viability in Insurance Markets

Insurance markets are subject to transaction costs and constraints on portfolio holdings. Therefore, unlike the frictionless asset markets case, viability is not equivalent to absence of arbitrage possibilities. We use the concept of unbounded arbitrage to characterize viable prices on a complete and an incomplete insurance market. In the complete market, there is an insurance contract for every possible event. In the incomplete market, risk can be insured through proportional and excess of loss like insurance contracts. We show how the the structure of viable prices is affected by the portfolio constraints, the transaction costs, and the structure of marketed contracts.