Assumption Of Arbitrage Research Articles

Extracting Implied Stock Returns from Options Prices

This paper proposes a new method for extracting the market’s expected return of a stock from options prices while also calculating option-specific risk discounts (calls) and premiums (puts). However, first, I revisit the variable μ (expected return of a stock) as it relates to stock prices in the Black-Scholes formula derivation. I postulate that μ is itself a function of time and therefore the partial derivative equation Black, Scholes, and Merton solved was incomplete. Importantly, this undermines the conclusion Black, Scholes, and Merton came to, that an option’s price is not a function of the expected return of the underlying stock. To extract the expected return from options prices, I begin by proposing formulas for call and put prices introducing variables for strike price specific discounts and premiums. Known qualities of options, required to satisfy the no arbitrage assumption, are then used to solve for these discounts and premiums as a function of the implied expected price of a stock and σ. Finally, implied expected price and σ are solved for using numerical analysis.

Detection of Arbitrage Opportunities and Forecasting in the Foreign Exchange Markets

In this paper, the existence of no arbitrage assumption over time and triangular arbitrage in a foreign exchange market is tested. Also, forecasting the exchange rates are studied. An optimal property of exchange rates returns to guarantee the no arbitrage assumption as well as for forecasting exchange rates is the martingale property. Some theoretical results under the risk neutral measure and their equivalents form in physical probability measure are given. Also, based on a real data set, it is seen that this assumption works well for forecasting purposes. Using the Doob maximal inequality, the accuracy of forecasts is surveyed. Then, a theoretical relation between beta market risks of exchange rates is surveyed. Finally, a conclusion section is also proposed.

Neural Network for Pricing and Universal Static Hedging of Contingent Claims

We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for interpretability of the model, a feature that is often desirable in the financial context. Specifically, the interpretation leads us to demonstrate that any contingent claim — possibly high dimensional and path-dependent — under Markovian and no- arbitrage assumptions, can be semi-statically hedged using a portfolio of short maturity options. We show how the method can be used to obtain an upper and lower bound to the true price, where the lower bound is obtained by following a sub-optimal policy, while the upper bound by exploiting the dual formulation. Unlike other duality based upper bounds where one typically has to resort to nested simulation for constructing super-martingales, the martingales in the current approach come at no extra cost, without the need for any sub-simulations. We demonstrate through numerical examples the simplicity and efficiency of the method for both pricing and semi-static hedging of path-dependent options.

A Time Series Model of Interest Rates With the Effective Lower Bound

Modeling interest rates over samples that include the Great Recession requires taking stock of the effective lower bound (ELB) on nominal interest rates. We propose a flexible time– series approach which includes a “shadow rate”—a notional rate that is less than the ELB during the period in which the bound is binding—without imposing no–arbitrage assumptions. The approach allows us to estimate the behavior of trend real rates as well as expected future interest rates in recent years.

Is the January effect rational? Insights from the accounting valuation model

Abstract Employing a permanent earnings valuation model and a novel sample partition, we find evidence that the January effect “anomaly” is consistent with rational economic market behavior. Investors in firms which experience January effect return premiums appear to discount first quarter earnings performance but reward permanent earnings and expectations of future improvements. Our evidence also supports a tax-loss selling explanation for the January effect. We find that the January effect is experienced by relatively few firms in the sample overall, but a substantial percentage of January effect firms are identified as potential tax-loss sellers. Our results complement prior research suggesting that the January effect is neither a result of irrational noise traders nor consistent with systemic risk factor explanations. Our study reconciles the assumption of arbitrage inherent in trading studies with a fundamental accounting valuation approach and offers some further insights into the nature of this market phenomenon.

Pricing American options when there is short-lived arbitrage

Models in financial economics derived from no–arbitrage assumptions are standard fare among theoreticians and practitioners. However, several authors have investigated the impact of short lived arbitrage on European options using models borrowed from disequilibria in physics. In this paper, we extend that research by assessing the impact of arbitrage on American options. We use an Ornstein–Uhlenbeck Bridge as a model for the arbitrage process and calculate American option prices using a bivariate lattice with density matched probabilities. We find that arbitrage correlated with the underlying has an economically meaningful sizeable impact on option prices. Short lived arbitrage has essentially virtually no economic impact on option prices when the arbitrage is uncorrelated with underlying asset returns.

Herd behaviour in stock markets: an international perspective

In this paper, we study the behavioral finance as a theory that seeks to combine cognitive and psychological components with economic and financial aspects to explain irrationality of financial decisions. It is a paradigm where financial markets are studied using models that are less tight than those based on expected utility theory of Neumann Morgenstern and on arbitrage assumptions. Behavioral finance has two main parts: cognitive psychology and the limits to arbitrage.Cognitive refers to how people think. There is a large literature in psychology that claims people make asymmetric errors in thinking. Limits to arbitration refer to prediction data where forces of arbitrage circumstances will be effective or not Our empirical validation focused on one of the cognitive components: herding. Indeed, we examined herd behaviour in an international context (the United States (DJU), Argentina (MERV), and France (CAC20)) using the model of Chang et al (2000). Our results led us to conclude that there is no herd behaviour.

Herd behaviour in stock markets: an international perspective

In this paper, we study the behavioral finance as a theory that seeks to combine cognitive and psychological components with economic and financial aspects to explain irrationality of financial decisions. It is a paradigm where financial markets are studied using models that are less tight than those based on expected utility theory of Neumann Morgenstern and on arbitrage assumptions. Behavioral finance has two main parts: cognitive psychology and the limits to arbitrage.Cognitive refers to how people think. There is a large literature in psychology that claims people make asymmetric errors in thinking. Limits to arbitration refer to prediction data where forces of arbitrage circumstances will be effective or not. Our empirical validation focused on one of the cognitive components: herding. Indeed, we examined herd behaviour in an international context (the United States (DJU), Argentina (MERV), and France (CAC20)) using the model of Chang et al (2000). Our results led us to conclude that there is no herd behaviour.

A Generalized Multiple-Factor Asset Pricing Model

This paper derives a generalized multiple-factor asset pricing model using only the assumption of no arbitrage. This generalization differs from the standard multiple-factor pricing models in two ways. First, similar to standard models, a traded asset's expected return is linear in a finite number of traded risk-factor returns. Different from standard models, however, this model allows an infinite number of distinct risk-factors in the economy, where any asset's return depends on only a finite number of these. Different assets will, in general, depend on a different finite set of risk-factors. Second, positive alphas imply arbitrage opportunities and not just abnormal expected returns. This model can potentially explain many of the observed differences between existing multiple-factor asset pricing model implications and the empirical evidence.

Is the KOSPI 200 Options Market Efficient? A Nonparametric Tests of the Martingale Restriction

A number of studies on the S&P 500 index options market claim that the no arbitrage assumption cannot be rejected for this market because either the martingale restriction defined in Longstaff (1995) cannot be rejected by the data, or, even when it is rejected, a large proportion of the violation can be explained by market friction factors. The present study singles out the effect of market inefficiency from market friction by testing the martingale restriction for the KOSPI200 index options market, which is the most liquid and active options market in the world. Not only using the parametric methods adopted in previous studies but also using the nonparametric methods which enable us to avoid the model misspecification problem, we empirically present clear evidence of a violation of the martingale restriction. In addition, in contrast to the S&P 500 options market, regression analyses and robustness tests indicate that market friction factors can explain only a small portion of the percentage differences between option-implied and market-observed index prices. Overall, the results do not support the basic no-arbitrage assumption or the market efficiency in the KOSPI200 options market.

Incentive incompatibilities and arbitrage opportunities

PurposeThe paper aims to examine the practical importance of the finding of Mayers and Smith, that underinvestment is a problem when debt exposed to bankruptcy is part of the financial structure.Design/methodology/approachThe paper examines critically the assumptions underlying the Mayers and Smith paper.FindingsThe necessary assumption of deterministic arbitrage in the market for productive properties used by Mayers and Smith in their model is found to be unrealistic. Even if that assumption were valid, however, the result of Mayers and Smith establishes that raising exposed debt is a negative net present value project for the investor and hence that form of financing would not be found in practice.Practical implicationsThe existence of exposed debt does not explain the demand or commercial insurance.Originality/valueThe paper challenges the results of Mayers and Smith that have been used to examine the effect of debt on insurance demand for almost 20 years with mixed results.

The role of credit constraints and government subsidies in farmland valuations in the US: an options pricing model approach

The Modigliani–Miller (M–M) theorem of financial asset theory concludes that asset values are independent of financing. In other words, debt-solvency (credit constraints) does not affect asset values. Therefore, using the M–M theorem one can argue that credit constraints in the farm sector (where land is the most important asset) do not affect the value of farmland. However, this proof relies on several arbitrage assumptions that are violated in the case of agricultural assets. This paper examines the effect of debt-solvency and government payments on changes in annual farmland values by state in the United States. Using panel cointergration method, results indicate that farmland values are significantly affected by both solvency and government payments. In addition, the results imply that government payments may affect agricultural asset values beyond the direct effect hypothesized in the literature.

The space-time pattern of price waves

We investigate the way price fluctuations are transmitted between spatially separated markets. More specifically we show that the correlation patterns of wheat prices exhibit definite regularities some of which appear to be at variance with intuitive reasoning. Such patterns can be explained in the framework of a wave propagation model based on the so-called spatial arbitrage assumption. In 19th century France the velocity of price waves was of the order of 100 km/month. The economic implications of such an order of magnitude are discussed. In the concluding section we emphasize that what gives this problem its importance is its relative “simplicity”, a word for which we propose an operational definition.

Implementing Residual Income Valuation With Linear Information Dynamics

Residual income (RI) valuation is a method of estimating firm value based on expected future accounting numbers. This study documents the necessity of using linear information models (LIMs) of the time series of accounting numbers in valuation. I find that recent studies that make ad hoc modifications to the LIMs contain internal inconsistencies and violate the no arbitrage assumption. I outline a method for modifying the LIMs while preserving internal consistency. I also find that when estimated as a time series, the LIMs of Ohlson (1995), and Feltham and Ohlson (1995) provide value estimates no better than book value alone. By comparing the implied price coefficients to coefficients from a price level regression, I find that the models imply inefficient weightings on the accounting numbers. Furthermore, the median conservatism parameter of Feltham and Ohlson (1995) is significantly negative, contrary to the model's prediction, for even the most conservative firms. To explain these failures, I estimate a LIM from a more carefully modeled accounting system that provides two parameters of conservatism (the income parameter and the book value parameter). However, this model also fails to capture the true stochastic relationship among accounting variables. More complex models tend to provide noisier estimates of firm value than more parsimonious models.

No Arbitrage Between Economies and Correlation Risk Management

The first goal of this paper is to clarify the implications of the no arbitrage assumption in the context of several countries and extend to a general setting of continuous-time finance and stochastic interest rates results which were more or less present in classical finance models such as the international APT (see Solnik (1983)). In particular, the remarkable relationship between the risk premia in two different countries and the sole volatility of the exchange rate is easily derived. Secondly, we examine the pricing and hedging of cross-currencies options when interest rates are stochastic in all countries. The dependence of risk neutrality arguments on the reference numeraire as developed in Geman (1989) becomes particularly clear in the case of several currencies.

Measuring Marginal Effective Tax Rates: Theory and Application to Canada

This paper summarizes the various methodologies for estimat ing marginal effective tax rates applying to investment decisions. The conceptual framework is developed for several types of investment decisions, including depreci able capital, inventories, and depletable assets. The analysis involves incorporating personal and corporate taxes into the neo-classical theory of the firm. Some of the theoretical issues are discussed including the treatment of adjustment costs, non price-taking behaviour, and the implications of an open economy. The problems involved with implementing effective tax rates empirically are discussed. These include the arbitrage assumption, the treatment of risk, the treatment of firms temporarily in a non-taxable position, and data problems, including problems of aggregation. A number of illustrative calculations are presented using Canadian data.

The Gibson Paradox and the Monetary Standard

This paper analyzes the Gibson paradox, a strong positive correlation between prices and interest rates over the past 250 years. The phenomenon of Gibson's paradox is significant in Britain but not significant in the United States. However, there is a significant correlation between British interest rates and U.S. price levels. The price movements show a strong characteristic of random walk under the gold standard, but appear not to be random walk under the non-gold standard. Based on (a) the price random walk assumption and (b) the real return arbitrage assumption, this paper constructs a simple model to explain the above interesting empirical results.

The sensitivity of effective marginal tax rate calculations to alternative arbitrage assumptions

This paper reports some estimates of effective marginal tax rates under alternative assumptions regarding arbitrage and the relationship between inflation and market interest rates. It is shown that the pattern of tax rates is similar whatever assumptions are used.

Purchasing power parity theory and the monetary approach to the balance of payments

In this article the monetary approach to the balance of payments is discussed as a theory and as a guide to balance of payments policy. It is argued that the monetary approach to the balance of payments is strongly connected with the assumption of complete arbitrage in commodities and financial assets. Recent research leads to the conclusion that no such complete arbitrage generally exist. Therefore, the monetary approach gives only an incomplete theory of the balance of payments. The other existing theories have to be used also, especially as guides to balance of payments policies.

Some Implications of the Elimination of Intertemporal Arbitrage Opportunities for Interest Rate Changes

One of the implications of the efficient markets hypothesis stated in terms of expected returns is that intertemporal arbitrage opportunities will be eliminated.' The time paths of prices of assets or commodities cannot give rise to known or expected extra-normal profit (or loss) opportunities, because private agents would buy (or sell) causing current prices to rise (or fall) until the profit opportunities were eliminated. Thus, the assumption of no intertemporal arbitrage opportunities restricts the time paths of prices which are admissible in a model and eliminates the possibility of setting the rate of change of prices as an exogenous parameter. This paper examines the way in which the no intertemporal arbitrage assumption restricts the implications of a model, using the standard aggregate supply-aggregate demand model as an illustration. Elimination of intertemporal arbitrage opportunities in such a model will involve the elimination of persistent unexploited profit opportunities due to systematic biases in the generally-held expectations of prices. Such systematic biases in price expectations could be profitably exploited by an agent with additional information.2 We eliminate the possibility of such intertemporal arbitrage opportunities from the model through the assumption of rational expectations. In the first section of the paper we find that the time path of bond prices in this model is completely specified by the structure of the economy, the monetary policy rule being followed, and current and past random errors. Consequently, the rate of change of bond prices cannot be introduced as an additional exogenous parameter. In the second section we examine the effects of anticipated and unanticipated changes in the money supply on nominal interest rates. Here we find that an anticipated increase in the rate of growth of the money supply will lead to an immediate increase in the nominal