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.     

Mean–variance hedging of contingent claims with random maturity

We study the mean–variance hedging of an American-type contingent claim that is exercised at a random time in a Markovian setting. This problem is motivated by applications in the areas of employee stock option valuation, credit risk, or equity-linked life insurance policies with an underlying risky asset value guarantee. Our analysis is based on dynamic programming and uses PDE techniques. In particular, we prove that the complete solution to the problem can be expressed in terms of the solution to a system of one quasi-linear parabolic PDE and two linear parabolic PDEs. Using a suitable iterative scheme involving linear parabolic PDEs and Schauder's interior estimates for parabolic PDEs, we show that each of these PDEs has a classical C^{1, 2} solution. Using these results, we express the claim's mean–variance hedging value that we derive as its expected discounted payoff with respect to an equivalent martingale measure that does not coincide with the minimal martingale measure, which, in the context that we consider, identifies with the minimum entropy martingale measure as well as the variance-optimal martingale measure. Furthermore, we present a numerical study that illustrates aspects of our theoretical results.     

Mean Reversion and the Comovement of Equilibrium Spot and Futures Prices: Implications from Alternative Data‐Generating Processes

The comovements of spot and futures prices are characterized by six binary variables, including the term structure curvature of futures prices. These variables are used to uniquely identify 48 possible comovement patterns. Among them, 24 cases are associated with mean reversion, which is defined as a state when spreads between futures and spot prices are shrinking. These pattern frequencies are then calculated on a daily basis with the futures prices of 10 commodities, including precious metal, agricultural, and financial commodities. The results are further compared to simulation output from three data‐generating processes: a bivariate pure random walk, a mixed random walk with first‐order autoregression (AR(1)), and an error‐correction representation. The mean‐reverting frequencies for all 10 commodities are about 50%. Around half of the time, spot and futures prices are moving toward each other, and the rest of the time they move in the same direction. The symmetry of these results implies that the existence of substantial shocks originated from futures markets; thus, this is consistent with the risk premium view of futures trading. Also, although all simulation models produce similar mean‐reversion frequencies, the patterns of comovements of spot and futures prices are different, and the price dynamics depend heavily on whether the market is dominant contango or backwardation. Furthermore, the error‐correction model outperforms the random‐walk model for agricultural commodities, and the mixed random walk with AR(1) is hardly distinguishable from the pure random walk. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:769–796, 2001     

Convergence of optimal expected utility for a sequence of discrete‐time markets

We examine Kreps' conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete‐time economies that “approach” the BSM economy in a natural sense: The nth discrete‐time economy is generated by a scaled n‐step random walk, based on an unscaled random variable ζ with mean 0, variance 1, and bounded support. We confirm Kreps' conjecture if the consumer's utility function U has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function U with asymptotic elasticity equal to 1, for ζ such that .     

Do S&P 500 index options violate the martingale restriction?

The study tests Longstaff's martingale restriction on S&P 500 index options over the period 1990–1994. Assuming the S&P index follows a lognormal distribution results in systematic violations of the martingale restriction, the implied index value from options consistently overestimating the market value. Adopting a generalized distribution, allowing for nonnormal third and fourth moments, produces economically insignificant rejections of the martingale restriction. A simulation analysis supports the empirical results from the lognormal model in the presence of nonnormal skewness and kurtosis. Overall, the results support the conclusion that the no-arbitrage assumption coupled with the generalized distribution offers a good working model for S&P index options over the period studied. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 499–521, 1999     

EXACT SOLUTION OF A MARTINGALE STOCHASTIC VOLATILITY OPTION PROBLEM AND ITS EMPIRICAL EVALUATION

Exact explicit solution of the log-normal stochastic volatility (SV) option model has remained an open problem for two decades. In this paper, I consider the case where the risk-neutral measure induces a martingale volatility process, and derive an exact explicit solution to this unsolved problem which is also free from any inverse transforms. A representation of the asset price shows that its distribution depends on that of two random variables, the terminal SV as well as the time average of future stochastic variances. Probabilistic methods, using the author's previous results on stochastic time changes, and a Laplace–Girsanov Transform technique are applied to produce exact explicit probability distributions and option price formula. The formulae reveal interesting interplay of forces between the two random variables through the correlation coefficient. When the correlation is set to zero, the first random variable is eliminated and the option formula gives the exact formula for the limit of the Taylor series in Hull and White's (1987) approximation. The SV futures option model, comparative statics, price comparisons, the Greeks and practical and empirical implementation and evaluation results are also presented. A PC application was developed to fit the SV models to current market prices, and calculate other option prices, and their Greeks and implied volatilities (IVs) based on the results of this paper. This paper also provides a solution to the option implied volatility problem, as the empirical studies show that, the SV model can reproduce market prices, better than Black–Scholes and Black-76 by up to 2918%, and its IV curve can reproduce that of market prices very closely, by up to within its 0.37%.     

BETTER THAN DYNAMIC MEAN‐VARIANCE: TIME INCONSISTENCY AND FREE CASH FLOW STREAM

As the dynamic mean‐variance portfolio selection formulation does not satisfy the principle of optimality of dynamic programming, phenomena of time inconsistency occur, i.e., investors may have incentives to deviate from the precommitted optimal mean‐variance portfolio policy during the investment process under certain circumstances. By introducing the concept of time inconsistency in efficiency and defining the induced trade‐off, we further demonstrate in this paper that investors behave irrationally under the precommitted optimal mean‐variance portfolio policy when their wealth is above certain threshold during the investment process. By relaxing the self‐financing restriction to allow withdrawal of money out of the market, we develop a revised mean‐variance policy which dominates the precommitted optimal mean‐variance portfolio policy in the sense that, while the two achieve the same mean‐variance pair of the terminal wealth, the revised policy enables the investor to receive a free cash flow stream (FCFS) during the investment process. The analytical expressions of the probability of receiving FCFS and the expected value of FCFS are derived.     

Market‐specific Sunk Export Costs: The Impact of Learning and Spillovers

Firms may face sunk costs when entering an export market. Previous studies have focused on global or country‐specific sunk export costs. This study analyses the importance of market‐specific sunk export costs (defining ‘market’ as a product–country combination). We also study how market‐specific export costs can be affected by various kinds of learning and spillover effects. We use firm‐level panel data for Norwegian seafood exports distributed on products and countries. The results lend support to the hypothesis of market‐specific sunk costs. We also find evidence of learning and spillover effects, particularly within the same product group.     

The CBOE S&P 500 three‐month variance futures

In this article, we study the market of the Chicago Board Options Exchange S&P 500 three‐month variance futures that were listed on May 18, 2004. By using a simple mean‐reverting stochastic volatility model for the S&P 500 index, we present a linear relation between the price of fixed time‐to‐maturity variance futures and the VIX². The model prediction is supported by empirical tests. We find that a model with a fixed mean‐reverting speed of 1.2929 and a daily‐calibrated floating long‐term mean level has a good fit to the market data between May 18, 2004, and August 17, 2007. The market price of volatility risk estimated from the 30‐day realized variance and VIX² has a mean value of −19.1184. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:48–70, 2010     

A MODEL‐FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER‐REPLICATION THEOREM

We propose a Fundamental Theorem of Asset Pricing and a Super‐Replication Theorem in a model‐independent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as options written on this risky asset. As a technical condition, we assume the existence of a traded option with a superlinearly growing payoff‐function, e.g., a power option. This condition is not needed when sufficiently many vanilla options maturing at the horizon T are traded in the market.     

On the Existence of Minimax Martingale Measures

Embedding asset pricing in a utility maximization framework leads naturally to the concept of minimax martingale measures. We consider a market model where the price process is assumed to be an ^d‐semimartingale X and the set of trading strategies consists of all predictable, X‐integrable, ^d‐valued processes H for which the stochastic integral (H.X) is uniformly bounded from below. When the market is free of arbitrage, we show that a sufficient condition for the existence of the minimax measure is that the utility function u : → is concave and nondecreasing. We also show the equivalence between the no free lunch with vanishing risk condition, the existence of a separating measure, and a properly defined notion of viability.     

Examining the Return–Volatility Relation for Foreign Exchange: Evidence from the Euro VIX

We compare the return–volatility relation for the euro currency to the equivalent relation for the equity market, examining the sign, symmetry, and strength of the relation. We employ the euro‐currency exchange‐traded fund (FXE) and its associated option implied volatility index (the EVZ), whereas previous studies only employ equities and/or realized volatility. The equity studies find a negative asymmetric return–volatility relation for implied volatility, with a strong relation when large market movements occur. We find that the euro return–volatility relation can possess either a positive or negative sign, is asymmetric, and has a weaker relation. Thus, the sign and strength of the euro relation differs from the equivalent equity relation. Our quantile regressions show that both the positive and negative contemporaneous returns of the euro result in increased volatility in the extreme quantiles of the conditional distribution, with the contemporaneous effect showing a stronger relation when the euro depreciates. We also find that the volume of the euro‐currency ETF options affects the return–volatility relation for the euro ETF. Overall, the results here expand the concept originally restricted to equities, with the surprising results that the return‐implied volatility relation is weaker and the asymmetric return sometimes is positive for the euro currency. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:74–92, 2014     

The index futures markets: Is screen trading more efficient?

This article uses a nonparametric test based on the arc‐sine law (see, e.g., Feller, 1965 ), which involves comparing the theoretical distribution implied by an intraday random walk with the empirical frequency distribution of the daily high/low times, in order to address the question of whether the abandonment of pit trading has been associated with greater market efficiency. If market inefficiencies result from flaws in the market microstructure of pit trading, they ought to have been eliminated by the introduction of screen trading. If, on the other hand, the inefficiencies are a reflection of investor psychology, they are likely to have survived, unaffected by the changeover. We focus here on four cases. Both the FTSE‐100 and CAC‐40 index futures contracts were originally traded by open outcry and have moved over to electronic trading in recent years, so that we are able to compare pricing behavior before and after the changeover. The equivalent contracts in Germany and Korea, on the other hand, have been traded electronically ever since their inception. Our results overwhelmingly reject the random‐walk hypothesis both for open‐outcry and electronic‐trading data sets, suggesting there has been no increase in efficiency as a result of the introduction of screen trading. One possible explanation consistent with our results would be that the index futures market is characterized by intraday overreaction. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:337–357, 2004     

Mean‐variance efficiency of the market portfolio and futures trading

We derived an intertemporal capital asset pricing model in which the mean‐variance efficiency of the market portfolio is neither a necessary nor a sufficient condition. We obtained this result by modeling a frictionless, continuously open financial market in which nonredundant futures contracts are available for trade, in addition to cash assets. Introducing such contracts modifies the way investors optimally allocate their wealth. Their portfolios then comprise the riskless asset, a perturbed mean‐variance‐efficient portfolio of cash assets, and a perturbed mean‐variance‐efficient portfolio of futures contracts. Furthermore, a (3 + K) mutual fund separation is obtained, with K being the number of economic state variables, in lieu of the usual (2 + K) fund separation. Mean‐variance efficiency of the market portfolio is a necessary condition only when cash assets are the sole traded assets. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:329–346, 2001     

How sukuk shapes firm performance

With the large expansion of Islamic finance in the recent years, sukuk , which are the Sharia‐compliant substitute to conventional bonds, are now becoming more prominent. The aim of this study was to examine the impact of sukuk issuance on firm performance. To do so, we analyse how stock market performance and operating performance (OP) are influenced by issuance of sukuk and bonds on a sample of Malaysian listed companies. We consider the short‐term and medium‐term stock market reaction through the computation of cumulative abnormal returns and buy‐and‐hold abnormal returns. We investigate the impact on OP by performing regressions and by calculating abnormal operating performance (AOP) so that we can compare how issuance affects similar firms. We find that sukuk issuance generates a negative stock market reaction both in the short term and in the medium term. We also find evidence that issuing sukuk hampers OP. The analysis of AOP shows that sukuk issuers have better performance than their matched bond issuers, but that sukuk contributes to reduce the gap in performance over time. Overall, our results support the view that sukuk issuance hampers stock market performance, but that it is not attributable to a signalling effect on the bad financial situation of the issuer. We interpret our findings as evidence of adverse selection taking place on the financed projects and agency problems stemming from the specific sukuk structuring with stock market investors more reluctant to invest in sukuk issuers.     

Gifts as conduits in choice overload environments

This study investigates competing for theoretical stances (i.e., choice overload vs. choice cornucopia) and explores how increases in spending occur in high and low choice conditions following receiving promotional gift offers in a service consumption setting. This study includes a nonobtrusive field experiment (n = 200) that includes measured and manipulated variables: purchase versus nonpurchase conditions and size of expenditures. The study's context tests the use of two versus five promotional gift options and two levels of gift value (6 vs. €20). Findings using symmetrical (analysis of variance [ANOVA]) and asymmetrical (fuzzy set qualitative comparative analysis [fsQCA]) methods of analysis support the choice overload hypothesis in this unobtrusive field experiment. Also, spending in the high versus low choice condition increased when hotel guests were offered a high‐value gift for using room service. Given the nature of the nonobtrusive field experiment, this study provides valuable information for marketers and consumers regarding the moderating effects of promotional gifts in many option environments. While prior studies explore the conditions of choice cornucopia versus choice overload, to date few or possibly no attempts to identify practical ways of reducing the negative effects of choice overload.     

MARKOWITZ'S PORTFOLIO OPTIMIZATION IN AN INCOMPLETE MARKET

In this paper, for a process S , we establish a duality relation between K_p , the     - closure of the space of claims in     , which are attainable by "simple" strategies, and     , all signed martingale measures     with     , where   p ≥ 1, q ≥ 1  and     . If there exists a     with     a.s., then K_p consists precisely of the random variables     such that ϑ is predictable S -integrable and     for all     . The duality relation corresponding to the case   p = q = 2  is used to investigate the Markowitz's problem of mean–variance portfolio optimization in an incomplete market of semimartingale model via martingale/convex duality method. The duality relationship between the mean–variance efficient portfolios and the variance-optimal signed martingale measure (VSMM) is established. It turns out that the so-called market price of risk is just the standard deviation of the VSMM. An illustrative example of application to a geometric Lévy processes model is also given.     

The hidden martingale restriction in Gram‐Charlier option prices

A hidden martingale restriction is developed for option pricing models based on Gram–Charlier expansions of the normal density function. The restriction is hidden behind a reduction in parameter space for the Gram–Charlier expansion coefficients. The resulting restriction is invisible in the option price. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27: 517–534, 2007     

LIQUIDITY IN A BINOMIAL MARKET

We study the binomial version of the illiquid market model introduced by Çetin, Jarrow, and Protter for continuous time and develop efficient numerical methods for its analysis. In particular, we characterize the liquidity premium that results from the model. In Çetin, Jarrow, and Protter, the arbitrage free price of a European option traded in this illiquid market is equal to the classical value. However, the corresponding hedge does not exist and the price is obtained only in L² ‐approximating sense. Çetin, Soner, and Touzi investigated the super‐replication problem using the same supply curve model but under some restrictions on the trading strategies. They showed that the super‐replicating cost differs from the Black–Scholes value of the claim, thus proving the existence of liquidity premium. In this paper, we study the super‐replication problem in discrete time but with no assumptions on the portfolio process. We recover the same liquidity premium as in the continuous‐time limit. This is an independent justification of the restrictions introduced in Çetin, Soner, and Touzi. Moreover, we also propose an algorithm to calculate the option’s price for a binomial market.     

FORECASTING VOLATILITY WITH THE MULTIFRACTAL RANDOM WALK MODEL

We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill‐posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space; formally, this object is an infinite range log volatility. For this object and the nonlimiting object, we obtain precise prediction formulas and we apply them to the problem of forecasting volatility and pricing options with the MRW model in the absence of a reliable estimate of σ and T.