Out-of-the-money Research Articles

Which trader's order-splitting strategy is effective? The case of an index options market

This study extends the recent study by Chae and Lee (2011) who empirically examine order-splitting and stealth-trading behaviours in the Korea Stock Price Index 200 (KOSPI200) options market, which is the single most liquid derivative market in the world. By analysing the high-quality data set, which identifies and describes all investors in the options market, we find that split orders submitted by institutional investors are substantially informative, whereas those of domestic individuals negatively contribute to the price discovery process. The inferiority of the order-splitting strategies of these individuals is more prominent when they trade deep Out-of-The-Money (OTM) options.

Limits to Market Making and the Skewness Risk Premium in Options Markets

The finance literature has found it challenging to explain empirically observed option returns, most notably in the case of out-of-the-money (OTM) equity index puts. I propose liquidation risk in options markets, defined as the possibility of forced selling of speculative positions following a liquidity shock, as a major driver of the relative pricing of OTM put vs. call options (option-implied skewness) as well as their relative returns (skewness risk premium). Employing size and sign of speculative net long positions (OSP) in a panel of commodity futures options markets as a key proxy for liquidation risk, I find that both implied skewness as well as the skewness risk premium are positively correlated with OSP and that these effects are stronger when funding conditions deteriorate. I also provide direct evidence of the price effects during such liquidation events. Trading strategies designed to theoretically exploit the skewness premium yield up to 2.5 percent per month and load significantly on risk factors related to the ease of funding for financial intermediaries.

Technical trading with open interest: evidence from the German market

This article investigates whether options' open interest can be incorporated successfully into technical trading strategies. A set of 2040 trading rules is applied to the German index DAX 30 and to the 10 German stocks with the highest market capitalization. The results show that open interest rules, when combined with information from the spot market, can improve the predictive power of technical trading rules. Both put and call open interest appear to contain information regarding future equity prices while the open interest differential performs very poorly. Best results are achieved for the DAX index, showing economically significant profits even when transaction costs are taken into account whereas the results are more mixed for individual options. Across all assets, out-of-the-money (OTM) calls and in-the-money (ITM) puts exhibit the strongest forecasting power for the utilized rules.

The Impact of Option Strategies in Financial Portfolios Performance: Mean-Variance and Stochastic Dominance Approaches

This study employs the mean-variance (MV) criterion, Capital Asset Pricing Model (CAPM) statistics and stochastic dominance (SD) analysis to investigate the performance of option strategies, including writing out-of-the-money (OTM) covered call and buying in-the-money (ITM) protective put, with that of the pure-stock investment by analysing the French data in the entire 1999 year. Our results from MV criterion show that none of these three strategies dominate one another but our CAPM statistics show that in general buying ITM protective-put strategy obtains the highest performance, followed by the writing OTM covered-call strategy while the naked stock obtains the smallest values. This confirms the superiority of ITM protective-put strategy, followed by OTM covered-call strategy by using the Beta coefficient, Sharpe ratio, Treynor and Jensen indices. As the return distributions of these strategies are non-normal, the MV criterion and the CAPM statistics may not be appropriate to assess the relative performance measurement of the portfolios. We further investigate the performance by employing SD approach. Our SD findings reveal that most of the buying covered-call and writing protective - put strategies are superior to their corresponding pure-stock strategy, as in general the former stochastically dominates the latter in the sense of first order SD. This infers that there may exist an anomaly of the existence of an arbitrage opportunity in option trading that all types of non-satiated investors will increase their wealth and utility by switching from the pure unhedged stock strategy to their corresponding buying protective - put or writing covered-call strategies. In addition, we find the dominance relationship between the two hedged positions is not as clear as the comparison with their unhedged positions, but on average more buying ITM protective put outperforms writing OTM covered call in the sense of the first-order SD. In short, our results confirm that option introduction improve significantly the performance of unhedged portfolios, especially buying ITM protective put.

The lead‐lag relationship between stock index options and the stock index market

PurposeThe purpose of this paper is to examine the price discovery role of the Korea Composite Stock Price Index 200 (KOSPI 200) stock index options market in contrast to other developed options markets.Design/methodology/approachThe price discovery roles of the stock and options markets using the error‐correction model derived from the co‐integration relationship are examined. Various analyses are conducted. First, Heston's stochastic volatility option pricing model is employed to confirm its usefulness, and compare the results with the Black and Scholes (BS) model. Second, whether the out of the money (OTM) options purchased by individual investors have a stronger price discovery role than options with other moneyness is examined. Finally, whether options have a stronger price discovery role in bullish or bearish markets than in normal markets is tested.FindingsIt is found that stock index prices lead implied index prices estimated from option prices using both BS and Heston models. In regards to the OTM options, the lead‐effect of real stock index to implied index prices holds. Also it is shown that there is a weak rise in the lead effect of the options to the stock index, but the lead effect of stock index market rules over that of the options market.Originality/valueThe paper examines the price discovery role of the KOSPI 200 stock index options market in contrast to other developed options markets and the results indicate that the consensus on the Korean financial markets may be incorrect.

Predicting nominal exchange rate movements using skewness information from options prices

AbstractThis paper uses a measure of the relative price of out‐of‐the‐money (OTM) European put and call currency options to forecast daily movements in the dollar/euro exchange rate over the period of January 2002–June 2004. As these OTM options are pure bets on future movements of the exchange rate, their relative price contains information about the market's estimate of the relative probabilities of appreciation or depreciation of the euro over the life of the options. Forecasts that include the relative price of the OTM options offer significantly better out‐of‐sample predictions of tomorrow's exchange rate than either the simple random walk or an interest rate parity model. These results offer new insight into the puzzle of the day‐to‐day volatility of currency prices that should be driven by slow‐moving macro fundamentals. Copyright © 2009 John Wiley & Sons, Ltd.

Modeling the Dynamics of Implied Volatility Surfaces

The objective of this study is to model implied volatility surfaces and identify risk factors that account for most of the randomness in the volatility surface. The approach is similar to the Dumas, Fleming and Whaley (DFW) (1998) study; we use moneyness (e.g., in forward price) and out-of-the-money (OTM) put-call options on FTSE100 index. After these adjustments, the nonlinear parametric optimization technique is employed to estimate different models of DFW in order to characterize the implied volatility surfaces and produce smooth implied volatility surfaces. Next, principal component analysis (PCA) is applied to the implied volatility surfaces to extract principal components that account for most of the dynamics in the shape of the surface. Hence, we estimate and obtain smooth implied volatility surfaces with the parametric models that account for both smile and time to maturity, and, therefore, the constant volatility model fails to explain the variations in the surfaces. Finally, we find that the first three principal components can explain about 69-82% of the variances in the implied volatility surfaces. The applications of our study are hedging of derivatives positions, trading, risk management, and policy making.

Variance swap volatility dispersion

Several trading institutions are actively engaged in ‘volatility dispersion’ strategies. These involve selling volatility on the index and buying volatility on the components. This trade was traditionally done using at the money (ATM) straddles. An important practical problem with this approach is that market prices move and cause the original ATM options to become out of the money (OTM) and lose their vega exposure. Even if volatility moved as expected by the trader, the profit potential of the trade would be greatly diminished as the options lost their vega. To correct this problem, a new style of trading has emerged in which some practitioners are trading this strategy using a ‘variance swap’ approach. This has the advantage that both legs of the trade have relatively constant vega exposure, regardless of stock market movements.

The Unexpected Value of Litigation

In this article suggest that litigation can be analyzed as though it is a competitive research and development project. Developing this analogy, we present a two stage real option model of the litigation process that involves sequential information revelation and bargaining over the surplus generated by early settlement. Litigants are risk neutral and have no private information. The model generates results that, we believe, have analytic and normative significance for the economic analysis of litigation. From an analytic perspective, we demonstrate that negative expected value (NEV) lawsuits are analogous to out of the money call options held by plaintiffs and that every NEV lawsuit is credible if the variance of the information revealed during the course of the litigation is sufficiently large. This finding helps explain the prevalence of a class of lawsuits that has proved puzzling to traditional, expected value-based modes of litigation analysis. The model also suggests that risk neutral defendants can act as though they are risk averse and that risk neutral plaintiffs can act as though they are risk seeking because increases in variance can increase a lawsuit's settlement option value just as it increases a call option's value without regard to the holder's degree of risk aversion. Models that presume defendants' relative risk aversion may therefore rely on an unnecessary assumption. Our model also suggests that a lawsuit's option settlement value is not a monotonically increasing function of the variance of the information revealed during the litigation. In particular, at low levels of variance a lawsuit's option settlement value may equal its traditional expected value, but as variance increases its option settlement value can display a discontinuity after which its option settlement value becomes a monotonically increasing function of variance. NEV lawsuits can also display dead zones - regions of variance over which the claim is not credible even though it is credible over higher or lower levels of variance. Comparative statics analysis also quantifies the extent to which a lawsuit's settlement value increases as plaintiff's litigation expenses occur later in the litigation process, as the ratio of defendant to plaintiff litigation expense increases, and as plaintiff bargaining power increases. From a normative perspective, we offer an impossibility conjecture suggesting that the mere presence of an irreducible degree of uncertainty endemic to the litigation process can be sufficient to prevent private litigation incentives from equating to socially optimal incentives, even if one adopts all other assumptions necessary to equate private and social incentives. It follows that it may be impossible to articulate normative principles of law through substantive standards that ignore the uncertainty inherent in the litigation process and the procedural environment in which the litigation occurs.

Information flow between the stock and option markets: Where do informed traders trade?

This paper investigates the flow of information between the equity and options markets. We argue that informed traders, in deciding where to place their trades, are not entirely indifferent to option moneyness, degree of information asymmetry, and option liquidity. Unlike some previous studies that find information to flow unilaterally from equity to options markets, we control for the above factors and discover feedback relations between trades in out-of-the-money (OTM) options and the underlying equities. The finding is consistent with the pooling equilibrium hypothesis, which asserts that informed traders trade in both the equity and options markets. Some informed traders are probably attracted to the out-of-the money options because of their higher liquidity, lower premiums, and higher delta-to-premium ratios, hence, lending support to the liquidity and leverage hypothesis.

Some evidence in the trading and pricing of equity LEAPS

This paper documents some evidence in the trading and pricing of equity Long-term Equity Antici Pation Securities (LEAPS). The main findings on trading are that LEAPS open interest, trading volume, and put/call ratio are seasonal on a yearly basis possibly due to the impact of the “melding” process that is unique to equity LEAPS. This paper also finds that the Black–Scholes Option Pricing Model, in general, overprices or underprices out-of-the-money (OTM) or in-the-money (ITM) equity LEAPS calls, respectively, and the model tends to overprice when the options are very deep in-the-money (VDITM). Furthermore, the evidence indicates that the deviations of the Black–Scholes prices from the observed option market prices are more pronounced in equity LEAPS than in standard options, suggesting that the Black–Scholes Option Pricing Model is less well suited to the pricing of equity LEAPS than to the pricing of standard options.

On the Pricing of Credit Spread Options: A Two Factor HW–BK Algorithm

In this article we describe what a credit spread option (CSO) is and show a tree algorithm to price it. The tree algorithm we have opted for is a two factor model composed by a Hull and White (HW) one factor for the interest rate process and a Black-Karazinsky (BK) one factor for the default intensity. As opposed to the tree model of Schonbucher 1999 the intensity process cannot become negative. Having as input the risk free yield curve and market implied default probability curve the model by construction will price correctly the associated defaultable bond. We then use Market data to calibrate the model to price an at the money (ATM) CSO call and then test it to price an out of the money (OTM) Bermudan CSO call on a CDS. Furthermore the discussions in this paper show in practice the difficulties and challenges faced by financial institutions in marking to market those instruments.

The Price of the Smirk: Returns to Delta and Vega Neutral Portfolios of S&P 500 Futures Options

We construct portfolios of S&P500 futures and their associated options, which are long out of (in) the money puts and short out of (in) the money calls, and which are delta (price) and vega (volatility) neutral, with respect to a GARCH type model for the underlying price. These systematically earn less (more) than the riskless return. We give evidence that this loss is not a payment for insurance against a market crash, by separately including a deep out of the money put in the portfolio, which makes it neutral to a market crash, but does not substantially alter the result. Our result is consistent with a market imperfection interpretation of the smirk: out of the money puts are too dear, relative to out of the money calls, perhaps because these puts are valuable in providing portfolio insurance. Our strategies do not earn excessive profits, and so we argue that the smirk will not disappear in an efficient market.

What could potentially aggravate implicit volatility 'smile' and 'asymmetry'? – a note

This research note shows that the implied Black-Scholes volatility calculated using the bisection algorithm can have significant biases, which are more severe for in-themoney (ITM) options than for out-of-the-money (OTM) options. The biases are shown to have important implications as they could potentially aggravate the well-documented smile or smirk and asymmetry of implied Black-Scholes volatility for equity options. The findings caution the use of bisection algorithm for the calculation of Black-Scholes implied volatility. This research note also shows that the biases can be eliminated using the optimization algorithm which uses at least the first derivative of the objective function.

Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?

We show in any economy trading options, with investors having mean-variance preferences, that there are arbitrage opportunities resulting from negative prices for out of the money call options. The theoretical implication of this inconsistency is that mean-variance analysis is vacuous. The practical implications of this inconsistency are investigated by developing an option pricing model for a CAPM type economy. It is observed that negative call prices begin to appear at strikes that are two standard deviations out of the money. Such out-of-the money options often trade. For near money options, the CAPM option pricing model is shown to permit estimation of the mean return on the underlying asset, its volatility and the length of the planning horizon. The model is estimated on S&P 500 futures options data covering the period January 1992- September 1994. It is found that the mean rate of return though positive, is poorly identified. The estimates for the volatility are stable and average 11%, while those for the planning horizon average 0.95. The hypothesis that the planning horizon is a year can not be rejected. The one parameter Black-Scholes model also marginally outperforms the three parameter CAPM model with average percentage errors being respectively, 3.74% and 4.5%. This out performance of the Black-Scholes model is taken as evidence consistent with the mean-variance analysis being vacuous in a practical sense as well. The capital asset pricing model (CAPM) of Sharpe (1964), Lintner (1965) and Mossin (1966) was derived as a general equilibrium consequence of the portfolio decisions made by investors, with mean variance preferences, investing in a single risk free asset and a finite number of risky assets whose joint probability distribution is known to all investors. The CAPM model has had a long history of use and statistical evaluation in the finance literature, with the notable recent contributions of Fama and French (1992, 1995), Jaganathan and Wang (1995), Kothari, Shanken and Sloan (1995) and Roll and Ross (1994). In particular, the recent paper by Fama and French (1995) argues that 'Beta is dead' as it has no explanatory value in explaining stock price returns. This paper argues that the CAPM is vacuous as it implies the existence of arbitrage opportunities for deep out-of-the money options. Hence the title 'was beta still born?'. The existence of a CAPM equilibrium was first established in the finite asset context by Hart (1974), Nielsen (1990) and for an infinite asset economy by Dana