Pricing efficiency of the S&P 500 index market: Evidence from the Standard & Poor's Depositary Receipts

Standard & Poor's Depositary Receipts (SPDRs) are exchange traded securities representing a portfolio of S&P 500 stocks. They allow investors to track the spot portfolio and better engage in index arbitrage. We tested the impact of the introduction of SPDRs on the efficiency of the S&P 500 index market. Ex‐post pricing efficiency and ex‐ante arbitrage profit between SPDRs and futures were also examined. We found an improved efficiency in the S&P 500 index market after the start of SPDRs trading. Specifically, the frequency and length of lower boundary violations have declined since SPDRs began trading. This result is consistent with the hypothesis that SPDRs facilitate short arbitrage by simplifying the process of shorting the cash index against futures. Tests of pricing efficiency comparing SPDRs and futures suggested that index arbitrage using SPDRs as a substitute for program trading in general results in losses. Although short arbitrages earn a small profit on average, gains are statistically insignificant. A trade‐by‐trade investigation showed that prices are instantaneously corrected after the presence of mispricing signals, introducing substantial risk in arbitraging. Evidence in general supported pricing efficiency between SPDRs and the S&P 500 index futures—both ex‐post and ex‐ante. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:877–900, 2002     

An intraday test of pricing and arbitrage opportunities in the New Zealand bank bill futures market

This paper examines pricing and arbitrage opportunities in the New Zealand bank bill futures market using an intraday data set. The key findings are: (a) the implied forward rate model yields biased estimates of the bill futures yield but the bias is small and not economically significant; (b) ex post synthetic bill opportunities are more numerous than ex post quasi‐arbitrage opportunities but the yield enhancements are minor; (c) ex post quasi‐arbitrage opportunities are substantially less frequent and less profitable than reported by prior studies using closing data; and (d) arbitrage opportunities decline when execution delays are introduced but the declines are not statistically significant. In broad terms, the bill futures market is efficient with respect to quasi‐arbitrage but less so with respect to synthetic bill opportunities. The results also suggest that arbitrage opportunities are not generally available to arbitrageurs without access to the interbank bill market. The incidence of arbitrage opportunities is on a par with levels reported in intraday studies of stock index and foreign exchange markets. This illustrates the importance of using high frequency data to assess transactional efficiency in financial markets. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:519–555, 2002     

A Study of Arbitrage Efficiency Between the FTSE‐100 Index Futures and Options Contracts

Despite the importance of the London markets and the significance of the relationship for market makers, little published research is available on arbitrage between the FTSE‐100 Index futures and the FTSE‐100 European index options contracts. This study uses the put–call–futures parity condition to throw light on the relationship between options and futures written against the FTSE Index. The arbitrage methodology adopted in this study avoids many of the problems that have affected prior research on the relationship between options or futures prices and the underlying index. The problems that arise from nonsynchroneity between options and futures prices are reduced by the matching of options and futures prices within narrow time intervals with time‐stamped transaction data. This study allows for realistic trading and market‐impact costs. The feasibility of strategies such as execute‐and‐hold and early unwinding is examined with both ex‐post and ex‐ante simulation tests that take into consideration possible execution time lags for the arbitrage trade. This study reveals that the occurrence of matched put–call–futures trios exhibits a U‐shaped intraday pattern with a concentration at both open and close, although the magnitude of observed mispricings has no discernible intraday pattern. Ex‐post arbitrage profits for traders facing transaction costs are concentrated in at‐the‐money options. As in other major markets, despite important microstructure differences, opportunities are generally rapidly extinguished in less than 3 min. The results suggest that arbitrage opportunities for traders facing transaction costs are small in number and confirm the efficiency of trading on the London International Financial Futures and Options Exchange. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:31–58, 2002     

Pricing dynamics of index options and index futures in Hong Kong before and during the Asian financial crisis

This article studies the impact of the Asian financial crisis on index options and index futures markets in Hong Kong. We employed a time‐stamped transaction data set of the Hang Seng Index options and futures contracts that were traded on the Hong Kong Futures Exchange. The results show that during the crisis period, the arbitrage profits, and the standard deviations of these profits increased in both ex‐post and ex‐ante analyses. In a market turbulent time, market volatility brings a higher arbitrage profit level. However, despite the increased market volatility, the profitability of the arbitrage trades declined substantially with longer execution time lags in the ex‐ante analysis. This suggests that the HSI futures and options markets are mature and resilient. A multiple regression analysis on the ex‐post arbitrage profit also suggests that there were structural changes during the Asian financial crisis and the Hong Kong government intervention periods. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 145–166, 2000     

Decimalization,ETFs and futures pricing efficiency

This study investigates the impact of decimalization (penny pricing) on the arbitrage relationship between index exchange‐traded funds and E‐mini index futures. The empirical results reveal that subsequent to penny pricing, there is a significant fall in the mean ex ante arbitrage profit, especially in the cases with higher transaction costs. Using the ordinary least squares and quantile regressions to control for the influences of changes in other market characteristics, it is found that the overall pricing efficiency has deteriorated in the post‐decimalization period. These results are consistent with the hypothesis that, due to the lowered market depth and increased execution risks, the introduction of decimalization has in general resulted in weakening the ability and the willingness of arbitrageurs to initiate arbitrage trades, which subsequently leads to a reduction in the general efficiency of the cash/futures pricing system. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 29:157–178, 2009     

Optimal No‐Arbitrage Bounds on S&P 500 Index Options and the Volatility Smile

This article shows that the volatility smile is not necessarily inconsistent with the Black–Scholes analysis. Specifically, when transaction costs are present, the absence of arbitrage opportunities does not dictate that there exists a unique price for an option. Rather, there exists a range of prices within which the option's price may fall and still be consistent with the Black–Scholes arbitrage pricing argument. This article uses a linear program (LP) cast in a binomial framework to determine the smallest possible range of prices for Standard & Poor's 500 Index options that are consistent with no arbitrage in the presence of transaction costs. The LP method employs dynamic trading in the underlying and risk‐free assets as well as fixed positions in other options that trade on the same underlying security. One‐way transaction‐cost levels on the index, inclusive of the bid–ask spread, would have to be below six basis points for deviations from Black–Scholes pricing to present an arbitrage opportunity. Monte Carlo simulations are employed to assess the hedging error induced with a 12‐period binomial model to approximate a continuous‐time geometric Brownian motion. Once the risk caused by the hedging error is accounted for, transaction costs have to be well below three basis points for the arbitrage opportunity to be profitable two times out of five. This analysis indicates that market prices that deviate from those given by a constant‐volatility option model, such as the Black–Scholes model, can be consistent with the absence of arbitrage in the presence of transaction costs. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1151–1179, 2001     

How electronic trading affects bid‐ask spreads and arbitrage efficiency between index futures and options

This paper examines the impact of switching to electronic trading on the relative pricing efficiency of Hang Sang Index futures and options contracts traded on the Hong Kong exchange. The study is motivated by the recent shift in 2000 from the pit to an electronic trading platform. Electronic trading leads to lower bid‐ask spreads and less price clustering than floor trading in both the options and futures markets. Mispricing between futures and options drops significantly after the change. Quicker correction of mispricing indicates a significant improvement in dynamic inter‐market arbitrage efficiency with electronic trading. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:375–398, 2005     

Effects of reduced government deficiency payments on post‐harvest wheat marketing strategies

Effects of reducing government deficiency payments on a wheat producer's post‐harvest marketing strategies are evaluated. The deficiency payment is predicted using an average option pricing model to properly value both intrinsic and time values of the deficiency payment. The biggest loss to producers from reducing deficiency payments is reduced revenue. The deficiency payment program was no better than hedging strategies in reducing post‐harvest risk, and when grain was sold at harvest, it even increased post‐harvest risk. Many producers will compensate for reduced deficiency payments by increasing use of futures or options contracts. For some producers, however, the optimal strategy is to sell wheat at harvest, because of high opportunity cost, storage cost, or risk aversion. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:243–263, 2000     

ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS

We develop a theory of robust pricing and hedging of a weighted variance swap given market prices for a finite number of co‐maturing put options. We assume the put option prices do not admit arbitrage and deduce no‐arbitrage bounds on the weighted variance swap along with super‐ and sub‐replicating strategies that enforce them. We find that market quotes for variance swaps are surprisingly close to the model‐free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi‐infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model‐independent and probability‐free setup. In particular, we use and extend Föllmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the “log contract” and similar connections for weighted variance swaps. Our results take the form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk‐neutral expectations of discounted payoffs.     

Is the KOSPI 200 Options Market Efficient? Parametric and 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 KOSPI 200 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 that 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 KOSPI 200 options market.     

What moves the tail? The determinants of the option‐implied probability density function of the DAX index

In this article a study of the option‐implied probability density function (PDF) of German stock returns is presented. The use of option prices allows for the quantification of the risk‐neutral probability of large movements in the DAX index. Using daily data for the period from December 1995 to May 2002, the mixture of log‐normals specification with a constant maturity of 49 days is estimated. The time series behavior of the option‐implied PDF during episodes of market turbulence is discussed at the outset. The main purpose of the study is to consider the relationship of summary measures of the option‐implied PDF to macroeconomic news, information from the U.S. stock market, and risk premia. The results suggest the existence of a significant spillover from the U.S. stock market. Returns and the volatility of U.S. stock prices have a strong effect on changes in the lower DAX tail probability, but also on the higher moments of the option‐implied PDF. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:515–536, 2005     

The economic significance of conditional skewness in index option markets

This study examines whether conditional skewness forecasts of the underlying asset returns can be used to trade profitably in the index options market. The results indicate that a more general skewness‐based option‐pricing model can generate better trading performance for strip and strap trades. The results show that conditional skewness model forecasts, when combined with forward‐looking option implied volatilities, can significantly improve the performance of skewness‐based trades but trading costs considerably weaken the profitability of index option strategies. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:378–406, 2010     

Option pricing under extended normal distribution

This article proposes a closed pricing formula for European options when the return of the underlying asset follows extended normal distribution, that is, any different degrees of skewness and kurtosis relative to the normal distribution induced by the Black‐Scholes model. The moment restriction is suggested, so that the pricing model under any arbitrary distribution for an underlying asset must satisfy the arbitrage‐free condition. Numerical experiments and comparison of empirical performance of the proposed model with the Black‐Scholes, ad hoc Black‐Scholes, and Gram‐Charlier distribution models are carried out. In particular, an estimation of implied parameters such as standard deviation, skewness, and kurtosis of the return on the underlying asset from the market prices of the KOSPI 200 index options is made, and in‐sample and out‐of‐sample tests are performed. These results not only support the previous finding that the actual density of the underlying asset shows skewness to the left and high peaks, but also demonstrate that the present model has good explanatory power for option prices. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:845–871, 2005     

MODEL‐INDEPENDENT NO‐ARBITRAGE CONDITIONS ON AMERICAN PUT OPTIONS

We consider the pricing of American put options in a model‐independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting, we are able to provide conditions on the American put prices which are necessary for the absence of arbitrage. Moreover, if we further assume that there are finitely many European and American options traded, then we are able to show that these conditions are also sufficient. To show sufficiency, we construct a model under which both American and European options are correctly priced at all strikes simultaneously. In particular, we need to carefully consider the optimal stopping strategy in the construction of our process.     

Step‐reset options: Design and valuation

This study proposes a new design of reset options in which the option's exercise price adjusts gradually, based on the amount of time the underlying spent beyond prespecified reset levels. Relative to standard reset options, a step‐reset design offers several desirable properties. First of all, it demands a lower option premium but preserves the same desirable reset attribute that appeals to market investors. Second, it overcomes the disturbing problem of delta jump as exhibited in standard reset option, and thus greatly reduces the difficulties in risk management for reset option sellers who hedge dynamically. Moreover, the step‐reset feature makes the option more robust against short‐term price movements of the underlying and removes the pressure of price manipulation often associated with standard reset options. To value this innovative option product, we develop a tree‐based valuation algorithm in this study. Specifically, we parameterize the trinomial tree model to correctly account for the discrete nature of reset monitoring. The use of lattice model gives us the flexibility to price step‐reset options with American exercise right. Finally, to accommodate the path‐dependent exercise price, we introduce a state‐to‐state recursive pricing procedure to properly capture the path‐dependent step‐reset effect and enhance computational efficiency. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:155–171, 2002     

Pricing American exchange options in a jump‐diffusion model

A way to estimate the value of an American exchange option when the underlying assets follow jump‐diffusion processes is presented. The estimate is based on combining a European exchange option and a Bermudan exchange option with two exercise dates by using Richardson extrapolation as proposed by R. Geske and H. Johnson (1984). Closed‐form solutions for the values of European and Bermudan exchange options are derived. Several numerical examples are presented, illustrating that the early exercise feature may have a significant economic value. The results presented should have potential for pricing over‐the‐counter options and in particular for pricing real options. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:257–273, 2007     

The Chinese equity index options market

Using Bakshi et al. (2000), and Bakshi and Kapadia's (2003) methodology, this paper studies the Chinese equity index options market that has been developing since 2015. Empirical evidence shows that the market price of call (put) option is generally lower (higher) than their Black-Scholes prices with historical volatility. The prices of the options do not support the one-dimensional diffusion model properties. We find 61.79% (63.25%) of delta-hedged gains in call (put) options to be negative. The analysis of the non-zero delta-hedged gain suggests that the investors are mainly trading on additional volatility risk in the options market in China.     

Valuing stock options when prices are subject to a lower boundary

This study examines the implications for stock option pricing when the domain of the stock price is constrained by a lower boundary. The valuation strategy starts from the familiar geometric Brownian motion framework of Black & Scholes (1973). However, an instantaneously reflecting lower boundary will be superimposed such that a reflected geometric Brownian motion arises. The particular nature of reflection in this approach precludes arbitrage opportunities such that risk‐neutral option valuation techniques can straightforwardly be applied. It will be shown that ignoring lower boundaries can lead to a substantial undervaluation of option prices. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:231–247, 2008     

Empirical performance of alternative pricing models of currency options

This article examines the out‐of‐sample pricing performance and biases of the Heston’s stochastic volatility and modified Black‐Scholes option pricing models in valuing European currency call options written on British pound. The modified Black‐Scholes model with daily‐revised implied volatilities performs as well as the stochastic volatility model in the aggregate sample. Both models provide close and similar correspondence to actual prices for options trading near‐ or at‐the‐money. The prices generated from the stochastic volatility model are subject to fewer and weaker aggregate pricing biases than are the prices from the modified Black‐Scholes model. Thus, the stochastic volatility model may provide improved estimates of the measures of option price sensitivities to key option parameters that may lead to more effective hedging and speculative strategies using currency options. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:265–291, 2000     

Empirical tests of canonical nonparametric American option‐pricing methods

Alcock and Carmichael (2008, The Journal of Futures Markets, 28, 717–748) introduce a nonparametric method for pricing American‐style options, that is derived from the canonical valuation developed by Stutzer (1996, The Journal of Finance, 51, 1633–1652). Although the statistical properties of this nonparametric pricing methodology have been studied in a controlled simulation environment, no study has yet examined the empirical validity of this method. We introduce an extension to this method that incorporates information contained in a small number of observed option prices. We explore the applicability of both the original method and our extension using a large sample of OEX American index options traded on the S&P100 index. Although the Alcock and Carmichael method fails to outperform a traditional implied‐volatility‐based Black–Scholes valuation or a binomial tree approach, our extension generates significantly lower pricing errors and performs comparably well to the implied‐volatility Black–Scholes pricing, in particular for out‐of‐the‐money American put options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:509–532, 2010