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.     

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.     

Implied Foreign Exchange Risk Premia

This paper uses implied volatilities from foreign exchange option prices and the results of no‐arbitrage theory to estimate foreign exchange risk premia. In particular, under the assumption of no‐arbitrage, the foreign exchange risk premium is driven by the difference between investors’ market prices of risk in the two currencies. In an international economy with three currencies, sterling, US dollar and Deutschemark, we can use the information on implied volatilities of the three cross rates to derive estimates of implied or ex ante market prices of risk and of foreign exchange risk premia. The foreign exchange risk premia estimates are then compared to survey‐based risk premia.     

Asset pricing theory for two price economies

We show that nonlinearly discounted nonlinear martingales are related to no arbitrage in two price economies as linearly discounted martingales were related to no arbitrage in economies satisfying the law of one price. Furthermore, assuming risk acceptability requires a positive physical expectation, we demonstrate that expected rates of return on ask prices should be dominated by expected rates of return on bid prices. A preliminary investigation conducted here, supports this hypothesis. In general we observe that asset pricing theory in two price economies leads to asset pricing inequalities. A model incorporating both nonlinear discounting and nonlinear martingales is developed for the valuation of contingent claims in two price economies. Examples illustrate the interactions present between the severity of measure changes and their associated discount rates. As a consequence arbitrage free two price economies can involve unique discount curves and measure changes that are however specific to both the product being priced and the trade direction. Furthermore the developed valuation operators call into question the current practice of Debt Valuation Adjustments.     

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.      

Transactions data tests of efficiency of the Chicago board options exchange

This paper performs lower boundary condition tests based on rational pricing of call options and an implied standard deviation test based on the bid/ask prices of options. These efficiency tests attempt to closely approximate conditions in the option markets to avoid the pitfalls indicated by Phillips and Smith (1980). The tests use transactions data and account for the effects of stock and option bid/ask prices, simultaneity of stock and option prices, depth of market, execution lag and transaction costs. The small and relatively infrequent profits due to market mispricing disappear in the lower boundary tests when transaction costs are taken into account. Frequent violations of the tighter boundary conditions in the implied standard deviation test are reported, but the estimated profits cannot be unambiguously attributed to option market inefficiency.     

Stochastic Volatilities and Correlations of Bond Yields

I develop an interest rate model with separate factors driving innovations in bond yields and their covariances. It features a flexible and tractable affine structure for bond covariances. Maximum likelihood estimation of the model with panel data on swaptions and discount bonds implies pricing errors for swaptions that are almost always lower than half of the bid–ask spread. Furthermore, market prices of interest rate caps do not deviate significantly from their no‐arbitrage values implied by the swaptions under the model. These findings support the conjectures of Collin‐Dufresne and Goldstein (2003) , Dai and Singleton (2003) , and Jagnnathan, Kaplin, and Sun (2003) .     

Implied liquidity: Model sensitivity

The concept of implied liquidity originates from the conic finance theory and more precisely from the law of two prices where market participants buy from the market at the ask price and sell to the market at the lower bid price. The implied liquidity λ of any financial instrument is determined such that both model prices fit as well as possible the bid and ask market quotes. It reflects the liquidity of the financial instrument: the lower the λ, the higher the liquidity. The aim of this paper is to study the evolution of the implied liquidity pre- and post-crisis under a wide range of models and to study implied liquidity time series which could give an insight for future stochastic liquidity modeling. In particular, we perform a maximum likelihood estimation of the CIR, Vasicek and CEV mean-reverting processes applied to liquidity and volatility time series. The results show that implied liquidity is far less persistent than implied volatility as the liquidity process reverts much faster to its long-run mean. Moreover, a comparison of the parameter estimates between the pre- and post-credit crisis periods indicates that liquidity tends to decrease and increase for long and short term options, respectively, during troubled periods.     

Valuation of Risky Assets in Arbitrage Free Economies with Frictions

This paper derives a framework for arbitrage models in markets with frictions. It generalizes the existence of a valuation operator to such markets. As in perfect markets, the valuation operator is a linear operator and its existence is implied by the no-arbitrage condition. In imperfect markets the valuation operator is individual-specific and depends on the agent's position in the market. The methodology employed in the paper is duality in convex programming.     

International high-frequency arbitrage for cross-listed stocks

We explore high-frequency arbitrage activities on international cross-listed stocks and develop a methodology to study the effect of information latency in high-frequency trading. We derive statistical arbitrage bounds for a mean-reverting synthetic instrument engineered from cross-listed stock prices, and we propose a new strategy that takes advantage of price deviations outside these bounds. Market frictions such as trade costs, inventory control, and arbitrage risks are considered. The strategy is tested with cross-listed stocks involving three exchanges in Canada and the United States in 2019. The annual net profit with the limit order strategy is around US$6 million, whereas the market order version is not profitable because of the great interconnectedness between exchanges in our data.     

A multiple-curve Lévy forward rate model in a two-price economy

An advanced Heath–Jarrow–Morton forward rate model driven by time-inhomogeneous Lévy processes is presented which is able to handle the recent development to multiple curves and negative interest rates. It is also able to exploit bid and ask price data. In this approach in order to model spreads between curves for different tenors, credit as well as liquidity risk is taken into account. Deterministic conditions are derived to ensure the positivity of spreads and thus the monotonicity of the curves for the various tenors. Valuation formulas for standard interest rate derivatives such as caps, floors, swaptions and digital options are established. These formulas can be evaluated numerically very fast using Fourier-based valuation methods. In order to exploit bid and ask prices we develop this approach in the context of a two-price economy. Explicit formulas for bid as well as ask prices of the derivatives are stated. A specific model framework based on normal inverse Gaussian and Gamma processes is proposed which allows for calibration to market data. Calibration results are presented based on multiple-curve bootstrapping and cap market quotes. We use data from September 2013 as well as September 2016. The latter is of particular interest since rates were deep in negative territory at that time.     

Valuation of risky assets in arbitrage-free economies with transactions costs

This paper analyzes the equilibrium valuation of risky assets in the case where transactions costs are present. The methodology involves applying ‘theorems of the alternative’ (Farkas' Lemma) as a consequence of arbitrage-free markets. Under relevant assumptions, it is found that the price of an asset having transactions costs is the corresponding price that would obtain in a perfect market, plus a ‘fudge factor’. This latter factor is provided explicit bounds.     

Liquidity risk in derivatives valuation: an improved credit proxy method

The models used to calculate post-crisis valuation adjustments, market risk and capital measures for derivatives are subject to liquidity risk due to severe lack of available information to obtain market implied model parameters. The European Banking Authority has proposed an intersection methodology to calculate a proxy CDS or Bond spread. Due to practical issues of this method, Chourdakis et al. introduce a cross-section approach. In this paper, we extend the cross-section methodology using equity returns, and show that our methodology is significantly more accurate compared to both existing methodologies, and produces more reliable, stable and robust market risk and capital measures, and credit valuation adjustment.     

Modelling the shape of the limit order book

This article develops a parsimonious way to use the shape of the limit order book to produce an estimate of the asset price. The posited model captures and describes the evolution of the distribution of limit orders on the bid and ask sides of the LOB during the trading session and provides estimates of the execution asset price over time. The performance of the model is evaluated against some existing standards from the market microstructure literature during the trading session. Empirical evidence on listed companies confirm a strong contribution of our methodology to the innovation in asset prices, according to the information share coefficients. We also document a significant improvement relative to the Hasbrouck [J. Finance, 1991, 46, 179–207] model when our model estimates are included as regressors.     

Arbitrage-Free Valuation of Exhaustible Resource Firms

We provide an arbitrage-free valuation of exhaustible resource firms through extending the Gibson and Schwartz (1990) model and also the Jamshidian and Fein (1990) solution to valuing an entire petroleum firm based on quoted oil futures. Our solutions are compared to accounting, traditional finance and to stockmarket valuations on a daily basis. An alternative expression of the valuations relative to stockmarket prices is in terms of the time varying implied 'market price' of convenience yield risk. Initial illustrations show that the implied convenience yield risk is not necessarily consistent between stockmarket and derivative market participants. Finally, we calculate the sensitivities of petroleum firm values to changes in oil prices, the convenience yield observable on NYMEX, and oil price volatilities. These partial derivatives show some of the complexities in the dynamic hedging process of using the contingent claims approach to valuing (and hedging) real assets.     

EMPIRICAL TESTS OF THE EFFICIENCY OF THE CURRENCY OPTION MARKET

Tests of a hedge and a rational boundary of the efficiency of the currency option market are conducted in this study. These tests use transactions data and account for the effects of currency and option bid/ask spreads, synchronization of option prices and underlying exchange rates, market depth, execution lags, and transaction costs. Currency options, unlike domestic stock options, exhibit continuous dividends. The nature of the option and of the data set employed makes the immediate exercise lower bound test one of the purest tests of market efficiency to date. Results reported here indicate no ability to earn abnormal economic or riskless arbitrage profit for the period when these tests are conducted.     

S&P 100 Index Option Volatility

Using transaction data on the S&P 100 index options, we study the effect of valuation simplifications that are commonplace in previous research on the timeseries properties of implied market volatility. Using an American-style algorithm that accounts for the discrete nature of the dividends on the S&P 100 index, we find that spurious negative serial correlation in implied volatility changes is induced by nonsimultaneously observing the option price and the index level. Negative serial correlation is also induced by a bid/ask price effect if a single option is used to estimate implied volatility. In addition, we find that these same effects induce spurious (and unreasonable) negative cross-correlations between the changes in call and put implied volatility.     

No-arbitrage conditions for storable commodities and the modeling of futures term structures

One distinguishable feature of storable commodities is that they relate to two markets: cash market and storage market. This paper proves that, if no arbitrage exists in the storage-cash dual markets, the commodity convenience yield has to be non-negative. However, classical reduced-form models for futures term structures could allow serious arbitrages due to the high volatility of the convenience yield. To avoid negative convenience yield, this paper proposes a semi-affine arbitrage-free model, which prices futures analytically and fits futures term structures reasonably well. Importantly, our model prices commodity-related contingent claims (such as calendar spread options) quite differently with classical models.     

Relative performance of bid–ask spread estimators: Futures market evidence

The issue of transaction costs is the mainstay of the equity market microstructure. Research in the microstructure of futures markets has lagged behind. A primary reason is that futures exchanges in the U.S. do not record bid–ask quotes, requiring these costs to be imputed from transaction price data. A reliable estimator of bid–ask spreads would significantly enhance microstructure research in futures markets. Unique intraday data from the Sydney Futures Exchange (SFE) that include both transaction prices and bid–ask spreads allow us to compare bid–ask spread estimation techniques proposed in the literature against the benchmark of actual spreads in a futures market, and thus identify the best-performing estimator. To maximize relevance, we impose all the constraints that apply in U.S. futures data to perform our estimations. We find that the four bid–ask spread estimators considered significantly underestimate the actual spreads. However, simple moments-based estimators perform better in predicting spreads.