Efficiency Tests of the Foreign Currency Options Market

Based on a new options transactions data base from the Philadelphia Stock Exchange Foreign Currency Options Market, this paper examines the importance of the effect of nonsynchronous prices and transaction costs on the usual option market efficiency tests. The tests conducted are based on the transaction cost adjusted early exercise and put-call parity pricing boundaries applicable to the American foreign currency options market. The test results show that the put-call parity boundary tests are sensitive to both nonsynchronous prices and transaction costs. The early exercise boundary tests are sensitive to transaction costs but are not very sensitive to simultaneity of the option price and the underlying spot price. Under the no-transaction costs scenario, a large number of early exercise boundary violations is found even when simultaneous spot and option prices are used. These violations disappear when actual transaction costs are taken into account.     

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.     

Efficiency in index options markets and trading in stock baskets

Researchers have reported mispricing in index options markets. This study further examines the efficiency of the S&P 500 index options market by testing theoretical pricing relationships implied by no-arbitrage conditions. The effect of a traded stock basket, Standard and Poor’s Depository Receipts (SPDRs), on the link between index and options markets is also examined. We find that pricing efficiency within option markets improves but there is little evidence to support the hypothesis that a stock basket enhances arbitrage across markets. When transactions costs and short sales constraints are included, very few violations of inter-market pricing relationships such as put–call parity are reported. However, violations of within market pricing relationships such as the box spread remain frequent. Extensive analysis suggests that the results are robust.     

Evidence on the arbitrage efficiency of SPI index futures and options markets

This paper is concerned with arbitrage opportunities in the futures and futures option contracts traded on the Sydney Futures Exchange (SFE) within a put-call-futures-parity (PCFP) framework. Tick-by-tick transaction price data are employed so that the futures contracts, the call futures options and the put futures options can be matched within a one-minute interval. This paper also takes into account the realistic transaction costs that an arbitrager has to incur, including the implicit bid-ask spread. A thorough ex post analysis is first carried out. The results reveal a significant number of violations of the PCFP in the sample. Ex ante tests are then conducted whereby ex post profitable arbitrage strategies, signified by the matched trios of futures, put and call contracts, are executed with lags up to 3 min. The ex ante results are similar to the ex post results. However, further analysis reveals that the exploitability of the identified arbitrage opportunities is very limited due to the small trading volumes of the futures and options contracts. Thus, we conclude that there is no strong evidence against the arbitrage efficiency between the SPI index futures and options markets in Australia.      

Arbitrage tests of the efficiency of the foreign currency options market

In this paper the lower boundary, excercise price, and put-call parity conditions for foreign currency options are subjected to empirical testing. The tests are directed towards the examination of the hypothesis that the foreign currency option market is efficient. The evidence in the ex-post tests is inconsistent with this hypothesis since a large number of violations of theoretical conditions are found in the data.     

The volatility of temperature and pricing of weather derivatives

We propose an Ornstein–Uhlenbeck process with seasonal volatility to model the time dynamics of daily average temperatures. The model is fitted to approximately 45 years of daily observations recorded in Stockholm, one of the European cities for which there is a trade in weather futures and options on the Chicago Mercantile Exchange. Explicit pricing dynamics for futures contracts written on the number of heating/cooling degree-days (so-called HDD/CDD futures) and the cumulative average daily temperature (so-called CAT futures) are calculated, along with a discussion on how to evaluate call and put options with these futures as underlying.     

Put-call parity and the informational efficiency of the German DAX-index options market

Using transaction data for options on the German stock index (DAX), we examine the informational efficiency of this relatively new options market. Because DAX options are European style and the underlying index is a performance index, we avoid problems due to dividend estimation and the assessment of the early-exercise effect, which are encountered in existing studies. Ex-post and ex-ante tests are carried out to simulate trading strategies for exploiting put-call parity violations. We find that ex-post profits diminish dramatically when the implementation of the arbitrage strategies is delayed and/or after transaction costs are accounted for. In general, however, arbitrage restrictions, which rely on short selling of the component stocks of the index, tend to be violated more severely than those relying on long positions in these stocks. Given the short-selling restrictions in Germany, these apparent arbitrage opportunities cannot be easily exploited in practice. Furthermore, the results for different subsamples suggest that traders were subject to a learning process in pricing these relatively new instruments.     

Empirical Tests of the Pricing of Nikkei Put Warrants

The purpose of this study is to empirically examine the pricing of Nikkei put warrants, which are long-term put options written on the Nikkei 225 index. Using warrants traded on the Toronto Stock Exchange, this study performs various tests on the pricing models proposed by Dravid, Richardson, and Sun [11], Reiner [24], and Wei [31]. It is found that the models tend to overprice the warrants. The overpricing, possibly caused by the omission of the credit risk and the Extraordinary Event Clause, is found to be positively related to the degree to which the warrants are in the money, the volatility level, and the trading volume.     

Stochastic volatility options pricing with wavelets and artificial neural networks

Abstract

The paper describes an alternative options pricing method which uses a binomial tree linked to an innovative stochastic volatility model. The volatility model is based on wavelets and artificial neural networks. Wavelets provide a convenient signal/noise decomposition of the volatility in the nonlinear feature space. Neural networks are used to infer future volatility from the wavelets feature space in an iterative manner. The bootstrap method provides the 95% confidence intervals for the options prices. Market options prices as quoted on the Chicago Board Options Exchange are used for performance comparison between the Black‐Scholes model and a new options pricing scheme. The proposed dynamic volatility model produces as good as and often better options prices than the conventional Black‐Scholes formulae.     

Local risk factors in emerging markets: Are they separately priced?

We provide new evidence on the pricing of local risk factors in emerging stock markets. We investigate whether there is a significant local currency premium together with a domestic market risk premium in equity returns within a partial integration asset pricing model. Given previous evidence on currency risk, we conduct empirical tests in a conditional setting with time-varying prices of risk. Our main results support the hypothesis of a significant exchange risk premium related to the local currency risk. Exchange rate and domestic market risks are priced separately for our sample of seven emerging markets. The empirical evidence also suggests that although statistically significant, local currency risk is on average smaller than domestic market risk but it increases substantially during crises periods, when it can be almost as large as market risk. Disentangling these two factors is thus important in tests of international asset pricing for emerging markets.     

Pricing U.S. Dollar Index Futures Options: An Empirical Investigation

This paper develops a pricing model and empirically tests the pricing efficiency of options on the U.S. Dollar Index (USDX) futures contract. Empirical tests of the model indicate that the market consistently overprices these options relative to the derived model. This overpricing is more pronounced for out‐of‐the‐money options than for in‐the‐money options and more pronounced for put options than for call options. To validate the above results, delta neutral portfolios are created for one‐ and two‐day holding periods and consistently generate positive arbitrage profits, indicating that on average the market overprices the options on the USDX futures contracts.     

An empirical analysis of common stock call exercise: A note

This study tests the hypothesis that common stock call options are exercised rationally and in accordance with the commonly used frictionless markets boundary conditions. Using two years of historical early exercise data for common stock call options, the results show that contrary to the frictionless markets boundary conditions, approximately 20 percent of the early call exercise occurs at times other than ex-dividend dates. While most of the non-dividend related early exercise may be explained by transactions costs, a significant number of contracts appear to be exercised irrationally. These results suggest that failure to incorporate market frictions in option pricing models is likely to lead to specification error.     

Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme

This paper studies the three main markets for emission allowances within the European Union Emissions Trading Scheme (EU ETS): Powernext, Nord Pool and European Climate Exchange (ECX). The analysis suggests that the prohibition of banking of emission allowances between distinct phases of the EU ETS has significant implications in terms of futures pricing. Motivated by these findings, we develop an empirically and theoretically valid framework for the pricing and hedging of intra-phase and inter-phase futures and options on futures, respectively.     

Pricing volatility options under stochastic skew with application to the VIX index

In recent years, there has been a remarkable growth of volatility options. In particular, VIX options are among the most actively trading contracts at Chicago Board Options Exchange. These options exhibit upward sloping volatility skew and the shape of the skew is largely independent of the volatility level. To take into account these stylized facts, this article introduces a novel two-factor stochastic volatility model with mean reversion that accounts for stochastic skew consistent with empirical evidence. Importantly, the model is analytically tractable. In this sense, I solve the pricing problem corresponding to standard-start, as well as to forward-start European options through the Fast Fourier Transform. To illustrate the practical performance of the model, I calibrate the model parameters to the quoted prices of European options on the VIX index. The calibration results are fairly good indicating the ability of the model to capture the shape of the implied volatility skew associated with VIX options.     

A general closed-form spread option pricing formula

We propose a new accurate method for pricing European spread options by extending the lower bound approximation of Bjerksund and Stensland (2011) beyond the classical Black–Scholes framework. This is possible via a procedure requiring a univariate Fourier inversion. In addition, we are also able to obtain a new tight upper bound. Our method provides also an exact closed form solution via Fourier inversion of the exchange option price, generalizing the Margrabe (1978) formula. The method is applicable to models in which the joint characteristic function of the underlying assets forming the spread is known analytically. We test the performance of these new pricing algorithms performing numerical experiments on different stochastic dynamic models.     

Are structured products ‘fairly’ priced? An analysis of the German market for equity-linked instruments

Based on a unique data set, this paper examines the pricing of equity-linked structured products in the German market. The daily closing prices of a large variety of structured products are compared to theoretical values derived from the prices of options traded on the Eurex (European Exchange). For the majority of products, the study reveals large implicit premiums charged by the issuing banks in the primary market. A set of driving factors behind the issuers’ pricing policies is identified, for example, underlying and type of implicit derivative(s). For the secondary market, the product life cycle is found to be an important pricing parameter.     

Futures Options and the Volatility of Futures Prices

Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at-the-money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.     

TESTS OF THE BLACK-SCHOLES AND CONSTANT ELASTICITY OF VARIANCE CURRENCY CALL OPTION VALUATION MODELS

An adaptation of the Cox-Ross/Emanuel-MacBeth call option valuation model for constant elasticity of variance diffusion processes is tested here against an adaptation of the Black-Scholes call option valuation model for the pricing of call currency options. Synchronized transactions data supplied by the Philadelphia Exchange are used. A maximum likelihood estimation procedure indicates a significant association between currency return variances and exchange rate levels. The constant elasticity of variance model exhibits significantly superior pricing accuracy for predictive intervals of three or fewer trading days.     

Hedging efficiency in the Greek options market before and after the financial crisis of 2008

This study examines the hedging effectiveness of the emerging Greek options market before and after the financial crisis of 2008. We test the hypothesis of market efficiency by analyzing violations of FTSE/ASE-20 index option returns with respect to standard option theory, estimating option risk-premia, and testing the statistical significance of the returns to delta and delta–vega neutral straddles. Our empirical results suggest that, despite a certain level of mispricing, the Athens Derivatives Exchange maintained a relative level of efficiency before 2008. However, the economic crisis has had a significant impact on the Greek options market, as evidenced by more pronounced violations of theoretical predictions observed in option returns and risk-premia. These findings have direct implications for the risk management of international portfolios, since the feasibility and effectiveness of hedging exposure in Greek investments is found to have declined precisely when it is needed the most.     

EVIDENCE ON DELTA HEDGING AND IMPLIED VOLATILITIES FOR THE BLACK‐SCHOLES,GAMMA, AND WEIBULL OPTION PRICING MODELS

Modifying the distributional assumptions of the Black‐Scholes model is one way to accommodate the skewness of underlying asset returns. Simple models based on the compensated gamma and Weibull distributions of asset prices are shown to produce some improvements in option pricing. To evaluate these assertions, I construct and compare delta hedges of all S&P 500 options traded on the Chicago Board Options Exchange between September 2001 and October 2003 for the Weibull, Black‐Scholes, and gamma models. I also compare implied volatilities and their smiles (i.e., nonlinearities) among the three models. None of the three models improves over the others as far as delta hedging is concerned. Volatilities implied by all three models exhibit statistically significant smiles.