The fundamental theorem of asset pricing under transaction costs

This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes. The robust no free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the existence of a strictly consistent price system (SCPS). This result relies on a new notion of admissibility, which reflects future liquidation opportunities. The RNFLVR condition implies that admissible strategies are predictable processes of finite variation. The Appendix develops an extension of the familiar Stieltjes integral for càdlàg integrands and finite-variation integrators, which is central to modelling transaction costs with discontinuous prices.     

The second fundamental theorem of asset pricing: a new approach

This article presents a new definition of market completenessthat is independent of the notions of no arbitrage and equivalentmartingale measures. Our definition has many advantages, allshown herein. First, it preserves the Second Fundamental Theoremof Asset Pricing, even in complex economies. Second, under ourdefinition, the market can be complete yet arbitrage opportunitiesexist. This is important in practice, and stands in contrastto the traditional definitions. Third, under the assumptionsof no arbitrage and when used in the standard models, our definitionis equivalent to the traditional one.     

Heterogeneous time varying transaction costs and asset pricing in international equity markets

In this paper, we examine the time variation in transaction costs relative to excess returns, in a panel consisting of 10 international equity indices over the time period 1984–2005. This is undertaken by extending the consumption CAPM (CCAPM) model proposed by Campbell and Shiller (Rev. Financ. Stud. 1:195–228, 1988) to incorporate time varying proportional transaction costs. We rigorously address both the cross-country heterogeneity in the estimated model and endogeneity. We find strong evidence that suggests transaction costs should be included as an additional explanatory variable in the CCAPM. This leads to the conclusion that transaction costs should be included in asset pricing models as their stochastic process impacts directly on private consumption expenditure.

An empirical analysis of intertemporal asset pricing models with transaction costs and habit persistence

In intertemporal asset pricing models, transaction costs are usually neglected. In this paper we explicitly incorporate transaction costs in these models and analyze to what extent this extension is helpful in explaining the cross-section of expected returns. An empirical analysis using CRSP data on size-based portfolios examines the role of the transaction costs and shows that incorporating such costs in the consumption-based model with power utility does not yield very satisfactory results. However, the introduction of habit persistence substantially improves the model. We find rather strong evidence of habit persistence in monthly consumption data. The plots of the models' pricing errors indicate that an intertemporal asset pricing model with transaction costs and habit persistence explains the cross-sectional variation in the portfolio returns quite accurately.     

A counter-example to an option pricing formula under transaction costs

In the paper by Melnikov and Petrachenko (Finance Stoch. 9: 141–149, 2005), a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial model with bid-ask spreads. We present a counter-example to show that the option pricing formula stated in that paper can in fact lead to arbitrage. This is related to the fact that under transaction costs a superreplicating strategy may be less expensive to set up than a strictly replicating one.     

Risk sensitive asset management with transaction costs

This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being functions of the factor levels. We develop methods of risk sensitive impulsive control theory in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter. The optimal trading strategy has a simple characterization in terms of the security prices and the factor levels. Moreover, it can be computed by solving a {\it risk sensitive quasi-variational inequality}. The Kelly criterion case is also studied, and the various results are related to the recent work by Morton and Pliska. Mansucript received: July 1998; final version received: January 1999     

Asymptotic replication with modified volatility under small transaction costs

We consider the dynamic hedging of a European option under a general local volatility model with small proportional transaction costs. Extending the approach of Leland, we introduce a class of continuous strategies of finite cost that asymptotically (super-)replicate the payoff. An associated central limit theorem for the hedging error is proved. We also obtain an explicit trading strategy minimizing the asymptotic error variance.     

Optimal tracking for asset allocation with fixed and proportional transaction costs

This paper studies the asset allocation problem of optimally tracking a target mix of asset categories when there are transaction costs. We consider the trading strategy for an investor who is trying to minimize both fixed and proportional transaction costs while simultaneously minimizing the tracking error with respect to a specified, target asset mix. We use imupulse control theory in a continuous-time, dynamic setting to deal with this problem in a general and analytical way, showing that the optimal trading strategy can be characterized in terms of a quasi-variational inequality. We derive an explicit solution for the two-asset case, and we use this to provide a sensitivity analysis, showing how the optimal strategy depends upon individual input parameters. We also use some theory for one-dimensional diffusion processes to derive analytical expressions for various measures of performance such as the average time between transactions.     

Asymptotic arbitrage with small transaction costs

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ _n on market n, in terms of contiguity properties of sequences of equivalent probability measures induced by λ _n -consistent price systems. These results are analogous to the frictionless case; compare (Kabanov and Kramkov in Finance Stoch. 2:143–172, 1998; Klein and Schachermayer in Theory Probab. Appl. 41:927–934, 1996). Our setting is simple, each market n contains two assets. The proofs use quantitative versions of the Halmos–Savage theorem (see Klein and Schachermayer in Ann. Probab. 24:867–881, 1996) and a monotone convergence result for nonnegative local martingales. Moreover, we study examples of models which admit a strong asymptotic arbitrage without transaction costs, but with transaction costs λ _n >0 on market n; there does not exist any form of asymptotic arbitrage. In one case, (λ _n ) can even converge to 0, but not too fast.     

On option pricing in binomial market with transaction costs

Option replication is studied in a discrete-time framework with proportional transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option-pricing model to cover the case of proportional transaction costs for one risky asset with different interest rates on bank credit and deposit. Contingent claims are supposed to be 2-dimensional random variables. Explicit formulas for self-financing strategies are obtained for this case.Received: March 2004, Mathematics Subject Classification (2000): 62P05JEL Classification: G11, G13The authors are grateful to an anonymous referee for numerous helpful comments and to Yulia Romaniuk for final corrections. The paper was partially supported by grant NSERC 264186.     

Cryptocurrency returns under empirical asset pricing

This study examines the predictability of cryptocurrency returns based on investors' risk premia. Prior studies that have examined the predictability of cryptocurrencies using various economic risk factors have reported mixed results. Our out-of-sample evidence identifies the existence of a significant return predictability of cryptocurrencies based on the cryptocurrency market risk premium. Consistent with capital asset pricing theory (CAPM), our results show that investors often require higher positive returns before taking on any additional risks, particularly in terms of riskier assets like cryptocurrencies. Tests involving the CAPM model demonstrates that the three largest cryptocurrencies have significant exposures to the proposed market factor with insignificant intercepts, demonstrating that the market factor explains average cryptocurrency returns very well.     

The dual optimizer for the growth-optimal portfolio under transaction costs

We consider the maximization of the long-term growth rate in the Black–Scholes model under proportional transaction costs as in Taksar et al. (Math. Oper. Res. 13:277–294, 1988). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341–1358, 2010) for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows one to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rate.     

Discrete versus continuous time models: Local martingales and singular processes in asset pricing theory

In economic theory, both discrete and continuous time models are commonly believed to be equivalent in the sense that one can always be used to approximate the other, or equivalently, any phenomena present in one is also present in the other. This common belief is misguided. Both (strict) local martingales and singular processes exist in continuous time, but not in discrete time models. More importantly, their existence reflects real economic phenomena related to arbitrage opportunities, large traders, asset price bubbles, and market efficiency. And as an approximation to trading opportunities in real markets, continuous trading provides a better fit and should be the preferred modeling approach for asset pricing theory.     

Optimal dividend policies for a class of growth-restricted diffusion processes under transaction costs and solvency constraints

In this paper, we consider a company whose surplus follows a rather general diffusion process and whose objective is to maximize expected discounted dividend payments. With each dividend payment, there are transaction costs and taxes, and it is shown in Paulsen (Adv. Appl. Probab. 39:669?C689, 2007) that under some reasonable assumptions, optimality is achieved by using a lump sum dividend barrier strategy, i.e., there is an upper barrier $\bar{u}^{*}$ and a lower barrier $\underline{u}^{*}$ so that whenever the surplus reaches $\bar{u}^{*}$ , it is reduced to $\underline{u}^{*}$ through a dividend payment. However, these optimal barriers may be unacceptably low from a solvency point of view. It is argued that, in that case, one should still look for a barrier strategy, but with barriers that satisfy a given constraint. We propose a solvency constraint similar to that in Paulsen (Finance Stoch. 4:457?C474, 2003); whenever dividends are paid out, the probability of ruin within a fixed time T and with the same strategy in the future should not exceed a predetermined level ??. It is shown how optimality can be achieved under this constraint, and numerical examples are given.     

Behavioral asset pricing under expected feedback mode

We develop an enhanced DSSW model of behavior asset pricing by introducing the expected feedback mode. Through numerical simulation, it has been theoretically proved that risky asset price is jointly determined by trend extrapolated effect of expected feedback traders and the creating space effect of noise traders, and that price fluctuation depends on the expected feedback coefficient. As expected feedback traders' expectation return has been realized and the above two effects are obviously imbalance, their confidence will deteriorate prior to price collapse, and eventually achieve self-fulfilling expectation of price reversal in the process of price momentum. This model sheds lights on financial anomalies of trade size clustering and the formation of stock bubble, besides it provides a new perspective for avoiding the “bewitching” trading and reducing market volatility.