Option pricing under short-lived arbitrage: theory and tests

Models in financial economics derived from no-arbitrage assumptions have found great favour among theoreticians and practitioners. We develop a model of option prices where arbitrage is short lived. The arbitrage process is Ornstein–Uhlenbeck with zero mean and rapid adjustment of deviations. We find that arbitrage correlated with the underlying can have sizeable impact on option prices. We use data from five large capitalization firms to test implications of the model. Consistent with the existence of arbitrage, we find that idiosyncratic factors significantly effect arbitrage model parameters.     

Arbitrage With Holding Costs: A Utility-Based Approach

Unit time costs, or holding costs, are incurred in many arbitrage contexts. Examples include losing the use of short sale proceeds and lending funds at below market rates in reverse repurchase agreements. This paper analyzes the investment problem of a risk averse arbitrageur who faces holding costs. The model allows prices to deviate from “fundamental” values without allowing for riskless arbitrage opportunities. After characterizing an arbitrageur's optimal strategy, the model is examined in the context of the Treasury market. The analysis reveals that holding costs are an important friction in this market and that they can significantly affect arbitrageur behavior.     

An investigation of price discovery in informationally-linked markets: equity trading in Malaysia and Singapore

Using transactions data for the Kuala Lumpur Stock Exchange and the Stock Exchange of Singapore (SES) for a major Malaysian conglomerate, Sime Darby Berhad, and intraday exchange rate data, we investigate whether and to what extent each exchange contributes to price discovery. Results indicate that the price series are cointegrated. The raw data appear to indicate the presence of arbitrage opportunities, but none exist after taking exchange rate changes into account. Using the common long-memory factors of Gonzalo and Granger (1995, Journal of Business and Economic Statistics 13, 1–9), we show that while the majority of the price discovery (approximately 70%) occurs in the home country (Malaysia), the 26–32% of the price discovery attributable to the SES is statistically significant and exceeds Singapore’s share of the trading volume. Further, we find evidence of strong error correction of Singapore prices to Malaysian prices, but only weak error correction of Malaysian prices to Singapore prices.     

Convertible bond arbitrage,liquidity externalities,and stock prices

In the context of convertible bond issuance, we examine the impact of arbitrage activity on underlying equity markets. In particular, we use changes in equity short interest following convertible bond issuance to identify convertible bond arbitrage activity and analyze its impact on stock market liquidity and prices for the period 1993 to 2006. There is considerable evidence of arbitrage-induced short selling resulting from issuance. Moreover, we find strong evidence that this activity is systematically related to liquidity improvements in the stock. These results are robust to controlling for the potential endogeneity of arbitrage activity.     

Mispricing of dual-class shares: Profit opportunities,arbitrage, and trading

This is the first paper to examine the microstructure of how mispricing is created and resolved. We study dual-class shares with equal cash flow rights and show that a simple trading strategy exploiting gaps between their prices appears to create abnormal profits after transactions costs. Trade and quote data show that investors shift their trading patterns to take advantage of gaps. Contrary to common perception, long–short arbitrage plays a minor part in eliminating gaps, and one-sided trades correct most of them. We also show that the more liquid share class is usually responsible for the price discrepancies.     

Short Interest and Frictions in the Flow of Information

This paper examines the correlation between short interest and price delay that parsimoniously measures the delay with which stock prices incorporate information. I find that price delay relates inversely to short interest indicating that short sellers reduce friction in the flow of information into stock prices. While price delay is shown to predict positive returns, this is mostly true in stocks with the least amount of short interest. Multivariate tests determine that the positive relationship between delay and future returns is decreasing in short interest. Results suggest that short sellers reduce delay and arbitrage the return premium commanded by delay.     

A Transactions Data Test of Stock Index Futures Market Efficiency and Index Arbitrage Profitability

This paper investigates the efficiency of the market for stock index futures and the profitability of index arbitrage for The Chicago Board of Trade's Major Market Index contracts. The spot value of the index is computed with transactions prices for the component shares of the index obtained from the Fitch database. The tests account for transaction costs, execution lags, and the uptick rule for short sales of stocks. Results indicate that the size and frequency of boundary violations are substantially smaller than those reported by earlier studies and have declined sharply with time.     

Taxes and the Pricing of Stock Index Futures

Stock index futures prices are generally below the level predicted by simple arbitrage models. This paper suggests that the discrepancy between the actual and predicted prices is caused by taxes. Capital gains and losses are not taxed until they are realized. As Constantinides demonstrates in a recent paper, this gives stockholders a valuable timing option. If the stock price drops, the investor can pass part of the loss on to the government by selling the stock. On the other hand, if the stock price rises, the investor can postpone the tax by not realizing the gain. Since this option is not available to stock index futures traders, the futures prices will be lower than standard no-tax models predict.     

Primes and Scores: An Essay on Market Imperfections

This paper investigates the reported relative mispricing of primes and scores to the underlying stock. Given transaction costs, we establish arbitrage-based bounds on prime and score prices. We then develop a new nonparametric statistical technique to test whether prime and score prices violate these bounds. We find that prime and score prices do exceed stock prices, and often by a considerable amount. We demonstrate that this increased value is most likely due to the score's ability to save on the costs of dynamic hedging. We also show how short sale and trust size constraints impede the ability to arbitrage price disparities.     

Tax Arbitrage and the Existence of Equilibrium Prices for Financial Assets

In models where both investors and securities are subject to differential taxation, there may be no set of prices that rule out infinite gains to trade, or “tax arbitrage.” This paper characterizes the joint restrictions on financial-asset returns and investors' tax schedules that preclude tax arbitrage in the absence of short-sale constraints. The authors show that, if there exists any configuration of marginal tax rates on investors' tax schedules that rule out infinite gains to trade, then “no-tax-arbitrage” prices will exist. They also show that the existence of “no-tax-arbitrage” prices ensures the existence of equilibrium prices.     

Exploring the transmission mechanism of speculative and inventory arbitrage activity to commodity price volatility. Novel evidence for the US economy

In the realm of monetary policy, we explore the transmission mechanism that relates speculative activity, inventory arbitrage activity, and commodity price volatility. In this direction, an ARMA-GARCH model is adopted to test this transmission effect on seven commodities using weekly U.S. data for the period 2008:12 to 2018:6. The results suggest that inventory arbitrage activities transmit monetary policy's effect onto commodities by strengthening the effect of the real interest rate on commodities' prices; in the case of palladium and crude oil's price conditional variances however the opposite effect is established. Speculative activities transmit monetary policy's effect mainly on commodities by increasing the positive effect of the real interest rate on metals and crude oil's prices, and on palladium and crude oil's price conditional variances. Our results show that inventory arbitrage activities are negatively related with commodities' prices, whilst speculative activities are positively related with commodities' prices. The two activities appear to exert mixed effects on commodities' price conditional volatilities. Additional evidence indicates that the relationship between the real interest rate and commodities' prices is positive and significant when unconventional monetary policy is considered, whilst we find that the real interest rate does not have any significant impact on most commodities' price conditional volatilities.     

American futures options arbitrage: evidence from the Nikkei 225 options market

Previous studies have examined the profitability of European index options arbitrage. This paper adds to the literature by investigating the arbitrage profitability of American index options—the Nikkei 225 index futures options traded on the Singapore Stock Exchange (SGX). Using the real-time bid–ask prices, we find evidence of profitable arbitrage opportunities, while the frequency of observations violating no-arbitrage bounds and the magnitude of arbitrage profits decrease with the level of transaction costs. Our results have implications for the analysis of American options market efficiency. Failure to use bid–ask prices may lead to biased conclusions.     

The principle of not feeling the boundary for the SABR model

The stochastic alpha–beta–rho (SABR) model is widely used in fixed income and foreign exchange markets as a benchmark. The underlying process may hit zero with a positive probability and therefore an absorbing boundary at zero should be specified to avoid arbitrage opportunities. However, a variety of numerical methods choose to ignore the boundary condition to maintain the tractability. This paper develops a new principle of not feeling the boundary to quantify the impact of this boundary condition on the distribution of underlying prices. It shows that the probability of the SABR hitting zero decays to 0 exponentially as the time horizon shrinks. Applying this principle, we further show that conditional on the volatility process, the distribution of the underlying process can be approximated by that of a time-changed Bessel process with an exponentially negligible error. This discovery provides a theoretical justification for many almost exact simulation algorithms for the SABR model in the literature. Numerical experiments are also presented to support our results.     

Index Options-Futures Arbitrage: A Comparative Study with Bid/Ask and Transaction Data

We can infer from bid/ask quotations and transaction prices that where options contracts are traded under a competitive open‐outcry market‐making system, the options and futures markets are dynamically efficient. Ex‐ante analysis shows that potential arbitrage opportunities disappear within five minutes. Transaction price data understate both the frequency and magnitude of arbitrage opportunities that are signaled by bid/ask quotes. Quotes stale fast, so opportunities are short‐lived and some of the arbitrage opportunities are deceptive. Nonetheless, the evidence suggests that bid/ask quotes provide valuable trading signals to arbitrageurs. Profitability from exploiting the quotes is negatively related to execution delay and execution risk.     

Short Sales Constraints and Momentum in Stock Returns

Abstract:   We show that stock characteristics identified by D'Avolio (2002) provide a reliable index of the mostly unobservable short sales constraints. Specifically, we find that this index is positively related to the level of short interest and to short selling costs implied by the disparity in prices in the options and stock markets, and is negatively related to future returns. Using this index, we show that the magnitude of momentum returns for the period 1984 to 2001 is positively related to short sales constraints, and loser stocks rather than winner stocks drive this result. We conclude that short sales constraints are important in preventing arbitrage of momentum in stock returns.     

价值性投资还是博彩性投机？——中国A股市场的MAX异象研究

本文利用1995—2017年中国A股上市公司公开数据实证检验了A股市场中的MAX异象,并从博彩性投机和有限套利视角深入探讨了异象的形成持续机制。结果显示:中国A股市场存在显著的MAX异象,个股当月MAX越小下月收益率就越高,构造多空组合可实现年化15.72%的收益。在投资者博彩性投机心理作用下,短期内MAX有惯性传递特征,投机性特征越强、内在价值越低的股票异象越显著。进一步实证分析发现:套利限制对MAX异象具有正向强化作用,套利限制越强异象越显著,多空策略组合获得的收益越高。本文的研究不仅有助于更好地理解中国股市中MAX异象,也对提升市场有效性、减小异象的影响有实践意义。     

Index futures arbitrage before and after the introduction of sixteenths on the NYSE

We find that market efficiency increased and the arbitrage link between index futures and the stock market strengthened after June 24, 1997, when the New York Stock Exchange reduced the minimum change for stock prices and quotes from an eighth to a sixteenth of a dollar. There has been a substantial increase in the number of arbitrage trades reported to the Securities and Exchange Commission (SEC) since the reduction in the minimum price increment. The average number of stocks traded and the average dollar amount underlying each arbitrage trade increases and decreases, respectively. The average index futures mispricing error (MPE) that triggers arbitrage is lower and reverts to zero more quickly.     

Index Options: The Early Evidence

Index options became the most important traded contracts during their first year of existence. Two contracts, namely those on the S&P100 and the Major Markets Index, have a trading volume which typically surpasses the trading volume in all individual stock option contracts. In this paper, we examine the pricing of the options on the S&P100 and the Major Markets Index. Using intra-day prices, we find the options frequently violate the arbitrage boundary, put/call parity, and are substantially mispriced relative to theoretical values. Our results suggest that tests of option pricing models may be more difficult than previously realized due to nonsynchronous prices, even using “real-time” data from the exchanges.     

Are performance based arbitrage effects detectable? Evidence from merger arbitrage

This paper examines the predictions of the performance based arbitrage hypothesis for the merger arbitrage market. Performance based arbitrage [Shleifer, A., Vishny, R.W., 1997. The limits of arbitrage. Journal of Finance, 52 (1), 35–55] is the notion that funds under management are withdrawn from arbitrageurs following trading losses, resulting in inefficient prices for securities subject to arbitrage trades. I examine general comovement in merger arbitrage spreads and the response of spreads to large arbitrage losses and substantial changes in deal flow. I find little evidence that merger arbitrage spreads exhibit systematic comovement or are substantially affected by important liquidity events in this market.     

Robust pricing and hedging under trading restrictions and the emergence of local martingale models

We pursue the robust approach to pricing and hedging in which no probability measure is fixed, but call or put options with different maturities and strikes can be traded initially at their market prices. We allow the inclusion of robust modelling assumptions by specifying a set of feasible paths on which (super)hedging arguments are required to work. In a discrete-time setup with no short selling, we characterise absence of arbitrage and show that if call options are traded, then the usual pricing–hedging duality is preserved. In contrast, if only put options are traded, a duality gap may appear. Embedding the results into a continuous-time framework, we show that the duality gap may be interpreted as a financial bubble and link it to strict local martingales. This provides an intrinsic justification of strict local martingales as models for financial bubbles arising from a combination of trading restrictions and current market prices.