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Index Option Returns from an Anchoring Perspective

Index Option Returns from an Anchoring Perspective

Statistical inference with index option returns is difficult due to the highly volatile, non-linear and skewed nature of such returns. Constantinides, Jackwerth, and Savov (2013) construct a panel of leverage adjusted returns (with targeted market beta of one) from S&P 500 index options. Portfolios are constructed separately for call and put options. An option portfolio is constructed by combining an index option (either call or put) with a risk-free asset in such a manner that the weight on the option is equal to its inverse price elasticity with respect to the underlying index value. Such leverage adjustment, aimed at achieving a market beta of one, reduces the variance and skewness and renders the returns close to normal.
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Effects of market sentiment in index option pricing: a study of CNX NIFTY index option

Effects of market sentiment in index option pricing: a study of CNX NIFTY index option

The entire research has been divided into two parts. In the first part Black-Scholes option price (using previous day implied volatility) and CS option price (using previous day implied volatility, skewness and kurtosis) is compared to find out which is pricing the option closer to the actual market price. In the next part the percentage excess price (as described in section 1) during Bullish and Bearish period is compared to find out whether there is any significant difference between them. If there is any significant difference then a series of t test (assuming samples with unequal variances) for various hypothesised mean difference between percentage excess price during Bearish and Bullish period is carried out till the null hypothesis is accepted. This is to find the average percentage excess price paid for sentiments in Indian Index option market.
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Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

. Due to analytically intractable likelihood functions and hence the lack of available efficient estimation procedures, SV models were until re- cently viewed as an unattractive class of stochastic processes compared to other time-varying volatility processes, such as ARCH/GARCH models. Moreover, to calculate option prices based on SV models we need, besides parameter estimates, a representation of the unobserved historical volatility, which is again far from being straightforward to obtain. Therefore, while the SV generalization of option pric- ing has, thanks to advances in econometric estimation techniques, recently been shown to improve over the Black-Scholes model in terms of the explanatory power for asset-return dynamics, its empiri- cal implications on option pricing itself have not yet been adequately tested due to the aforementioned lack of a representation of the unobserved volatility. Can the SV generalization of the option pric- ing model help resolve the well-known systematic empirical biases associated with the Black-Scholes model, such as the volatility “smile” (e.g. Rubinstein (1985)), asymmetry of such “smile” or “smirk” (e.g. Stein (1989))? How substantial is the gain, if any, from such generalization compared to rel- atively simpler models? The purpose of this paper is to answer the above questions by studying the empirical performance of SV models in pricing options on the S&P500 index, and investigating the re- spective effect of stochastic interest rates, stochastic volatility, and asymmetric asset returns on option prices in a multivariate SV model framework.
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The relationship between implied and realised volatility: Evidence from the Australian stock index option market

The relationship between implied and realised volatility: Evidence from the Australian stock index option market

good news enters into the market between the trade of option and the time when closing index level and futures price are recorded, then the recorded index level or futures price will be higher than the index level or futures price simultaneously corresponding to the option price, indicating that implied call (put) volatility underestimates (overestimates) the true implied volatility. A similar situation can happen with bad news which may lead to deviations in the opposite direction. In reality, good news and bad news come randomly, and hence the two effects can offset each other and the computed implied volatility will not deviate consistently from the true volatility. However, this non-synchronous measurement does cause an errors-in- variables problem (EIV), which leads to the correlation between the explanatory variable and the error term in our subsequent regressions.
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IMPLIED VOLATILITY SKEWS AND STOCK INDEX SKEWNESS AND KURTOSIS IMPLIED BY S&P 500 INDEX OPTION PRICES

IMPLIED VOLATILITY SKEWS AND STOCK INDEX SKEWNESS AND KURTOSIS IMPLIED BY S&P 500 INDEX OPTION PRICES

to calculate theoretical prices on each date are reported in columns 3-5. To assess the out-of- sample forecasting power of skewness- and kurtosis- adjustments, the implied standard deviation (ISD), implied skewness coefficient (ISK), and implied kurtosis coefficient (IKT) for each date are estimated from prices observed on the trading day immediately prior to each date listed in column 1. For example, the first row of Exhibit 5 lists the date 2 December 1993, but columns 3-5 report that day’s standard deviation, skewness and kurtosis estimates obtained from 1 December prices. Thus, out-of-sample parameters ISD, ISK and IKT reported in columns 3-5, respectively, correspond to one-day lagged estimates. We use these one-day lagged values of ISD, ISK and IKT to calculate theoretical skewness- and kurtosis-adjusted Black-Scholes option
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Optimal Option Portfolio Strategies: Deepening the Puzzle of Index Option Mispricing

Optimal Option Portfolio Strategies: Deepening the Puzzle of Index Option Mispricing

relative risk aversion investors always find it optimal to short OTM puts, and only with distorted probability assessments using cumulative prospect theory and anticipated utility are they able to obtain positive weights for puts. In contrast, we find that there are many periods when this does not apply. For example, in July 1997, the OOPS takes a long position of 0.7% in OTM put options. In their setting, they have a static setting - constant weights in each option over time – and a smaller opportunity set – only one option strategy at a time. It is clearly not the case that the OOPS methodology simply sells volatility at all times. There is a strong correlation, 0.94, between the sum of call weights and the sum of put weights. Figure 6 shows that the optimal portfolio is short OTM puts most of the time (85% of the months), but partially hedges this position with other options.
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On the demand pressure hypothesis in option markets: the case of a redundant option

On the demand pressure hypothesis in option markets: the case of a redundant option

A large amount of literature has documented a price change for stocks added to various indexes (Shleifer (1986), Harris and Gurel (1986), and Biktimirov et al. (2004)). To explain stock price behavior around index changes, several hypotheses have been offered (Biktimirov et al. (2004)). According to the price pressure hypothesis, buying pressure causes a temporary increase in the stock price to induce investors to sell their shares. Harris and Gurel (1986) observe event-day stock price changes reversing twenty days later and interpret these findings as evidence of price pressure. Recently, Gârleanu et al. (2009), and Bollen and Whaley (2004) investigate the relation between the demand for options and the price of options. Gârleanu et al. develop a model where option market makers cannot hedge their inventories perfectly. They show that a demand pressure phenomenon exists in the derivative markets since a demand pressure in an option raises its price. The expensiveness of an option is then positively related to the option demand of non-market makers. Bollen and Whaley (2004) examine two alternative hypotheses for the relation between demand for options and implied volatilities; the limits to arbitrage hypothesis and the volatility information hypothesis. Investors with information about future volatility use options. Since their trade contains information, option prices are then affected. Bollen and Whaley report evidence that changes in implied volatility are related to net buying pressure and show that their results are consistent with the limits to the arbitrage hypothesis. Kang and Park (2008) investigate the Korean index option market to examine how the net buying pressure impacts the implied volatility of options. They argue that their results are not consistent either with the limit to arbitrage hypothesis or with the volatility information hypothesis but are best explained by the directional information hypothesis. If prices are expected to rise, informed traders buy call options and sell put options. Since these positions contain information, an increase in option price and a decrease in put price will result.
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Anchoring Heuristic in Option Prices

Anchoring Heuristic in Option Prices

Constantinides, Jackwerth and Savov (2013) uncover a number of interesting empirical facts regarding leverage adjusted index option returns. They find that over a period ranging from April 1986 to January 2012, the average percentage monthly returns of leverage-adjusted index call and put options are decreasing in the ratio of strike to spot. They also find that leverage adjusted put returns are larger than the corresponding leverage adjusted call returns. The empirical findings in Contantinides et al (2013) are inconsistent with the Black-Scholes/CAPM framework, which predicts that the leverage adjusted returns should be equal to the return from the underlying index. That is, they should not fall with strike, and the leverage adjusted put option returns should not be any different than the leverage adjusted call returns.
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Expected Option Returns

Expected Option Returns

Because we use zero-beta straddles to establish that index option returns appear to be too low for existing models, a natural interpretation of our results is that stochastic volatility is priced in the returns of index options. In a related paper, Buraschi and Jackwerth ~ 1999 ! find evidence that vola- tility risk is priced in options markets. Our final tests examine some evi- dence that stochastic volatility is priced in markets quite different from the index option market. We look at the average returns of zero-beta straddles formed with futures options on four other assets and find that straddles on assets with volatilities that are positively correlated with market volatility tend to earn negative returns. We estimate time-series regressions of CRSP’s size-decile portfolio returns on the market return and a straddle return fac- tor and find a distinct pattern in the sensitivities of the size portfolios to the straddle factor. These results offer some preliminary confirmation that vol- atility risk is priced in more than just options markets.
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Binary Option Signals

Binary Option Signals

Customers accepting these Terms and Conditions explicitly acknowledge that the Binary Option Signals does provide a service and not a product. Dissatisfaction with the provided services is not a reason for validly obtain a reimbursement of the paid fees before Binary Option Signals and/or the selected payment method. Other unaccepted reasons include but are not limited to: (i) unwise risk management leading to unsuccessful trading; (ii) undiligent follow-up of the written signals and/or of the price levels provided live by BINARY OPTION SIGNALS; (iii) dissatisfaction with regard to the amount of and/or the success rate reached by the written signal provided live on the Table; (iv) dissatisfaction with the selected broker even if this broker is included in the “recommended list” displayed on the Site, included but not limited to the poor performance of the trading platform and/or the refusal of withdrawal requests by the customer; (v) failure to cancel the subscription prior to the next billing cycle. It is the responsibility of buyer of service to notify of cancellation to Binary Option Signals or take the appropriate steps to cancel subscription prior to the day of the next billing cycle. Failure to do so will results in a continuous billing cycle
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Strategic option pricing

Strategic option pricing

In this study a one period option pricing game is developed and presented. If the buyer of a call option bets on what will happen and the seller of a call op- tion decides what happens, then, without a doubt, insight into the true nature of openness (risk) is required. Given the strategic behaviour of both the sell- er and the buyer of a call option two results are presented. Firstly it has been shown how the seller’s maximum premium is calculated. Secondly it is we dem- onstrated that in a specific strategic setting and in the non-strategic Cox and others (1979) setting, the results are the same, if the objective probabilities for the states of the world and the so-called CRR risk neutral probabilities for the states of the world are the same.
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SURVIVAL IS THE ONLY OPTION!

SURVIVAL IS THE ONLY OPTION!

The firm offers a broad range of services specific to financial institutions including regulatory compliance audits (consumer compliance and BSA/AML), IT audit, internal [r]

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Heterogeneity and option pricing

Heterogeneity and option pricing

The formal analysis of the equilibrium underpinnings of the Black-Scholes option pricing formula (for example Bick (1987, 1990) and He and Leland (1993)) retains the presumption of a representative agent. Yet heterogeneity among investors is embedded in most informal discussions of options markets. For example, Cox and Rubinstein (1985, p. 54) give the “use of certain kinds of special knowledge” as one reason for the existence of trade in options. According to such popular views, agents with bullish expectations (perhaps based on “special knowledge”) will be attracted to out-of-the-money calls (written, presumably, by others with more bearish
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The British Call Option

The British Call Option

The paper is organised as follows. In Section 2 we present a basic motivation for the British call option. It should be emphasised that the full financial scope of the option goes beyond these initial considerations (especially regarding the provision of high returns that appears as an additional benefit). In Section 3 we formally define the British call option and present some of its basic properties. This is continued in Section 4 where we derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary (the early- exercise premium representation) and show that the rational exercise boundary itself can be characterised as the unique solution to a nonlinear integral equation (Theorem 1). Many of these arguments and results stand in parallel to those of the British put option [11] and we follow these leads closely in order to make the present exposition more transparent and self- contained (indicating the parallels explicitly where it is insightful). In Section 5 we derive the ‘British put-call symmetry’ relations which express the arbitrage-free price and the rational exercise boundary of the British call option in terms of the arbitrage-free price and the rational exercise boundary of the British put option where the roles of the contract drift and the interest rate have been swapped (Theorem 2). These relations provide a useful insight into the British payoff mechanism (at the level of put and call options) that is of both theoretical and practical interest. We note that similar symmetry relations are known to be valid for the American put and call options written on stocks paying dividends (see [2]) where the roles of the dividend yield and the interest rate have been swapped instead. Using these results in Section 6 we present a financial analysis of the British call option (making comparisons with the European/American call option). This analysis provides more detail/insight into the full scope of the conclusions briefly outlined above.
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PFNA. With Augmentation Option.

PFNA. With Augmentation Option.

Insert the extraction screw over the guide wire and through the sleeve assembly using gentle counterclockwise pressure to attach the extrac- tion screw to the PFNA blade (note “attach”[r]

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NS Option Instruction

NS Option Instruction

When multiple NS Appliances are defined in the network configuration information file (XML definition) specified using the -file option, the gateway for all NS Appliances to be created w[r]

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Oklahoma and Its Option

Oklahoma and Its Option

Conditions for Receiving Benefits: While the benefits are subject to minimum requirements, the employer may set out the conditions for receiving those benefits. For example, continued medical benefits could be conditioned on using the employer’s selected provider and on following the recommended treatment. Enhanced Claims Management: The employer may set out conditions for separating occupational and non-occupational conditions, determine what conditions are compensable, direct the choice of medical provider and treatment option, control the types of drugs used, determine when the employee must return to work, etc. The benefit plan may also provide for lump sum settlements.
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A note on the alpha-quantile option

A note on the alpha-quantile option

In this note we have presented properties and features of a new financial instrument, the α-quantile option, introduced first by Miura (1992), which is at the moment only a “theoretical” object since it is not yet traded in the market. The Dassios-Port-Wendel identity has been employed to simulate initial prices and Greeks of the α-quantile. In view of the analytical structure of this option the simulations not surprisingly show consistent characteristics to other Euro-type option contracts. The problem of obtaining numerically the mid-contract value of the option remains unsolved. In fact, for this case pricing formulas and numerical approximations cannot avoid the set of occupation times needed to define the α-quantile itself and which makes this process not Markovian.
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Family medicine as a career option

Family medicine as a career option

For the 2003 and 2004 cohorts, we have adequate data at  all DCPs from entry to exit. For the class of 2005 at DCP  4 and the class of 2006 at DCP 3, however, the response  rate  was  15%  or  lower  due  to  turnover  in  our  research  staff,  and  responses  should  be  interpreted  with  caution.  These  4  cohorts  were  used  to  assess  trends  in  medi- cal  students’  thinking  about  career  choices  during  their  time  in  medical  school.  The  number  and  proportion  of  students in these 4 classes who considered family medi- cine as a career option at the 5 different DCPs are shown  in Table 2.  The  drop  in  the  number  considering  family  medicine as a career option between DCP 2 and DCP 3 is  obvious  (nearly  20  percentage  points)  for  years  2003  to  2005 and is statistically significant (P < .001). For the class  of 2006, the drop was not significant (P = .08) (Table 3).
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Option Pricing in an Oligopolistic Setting

Option Pricing in an Oligopolistic Setting

[4] and [14] in their seminal works showed that the construction of a risk-less hedge between the option and its underlying asset, allows the derivation of an option pricing formula regardless of investors risk preferences. In these derivations, it is assumed that taxes and transaction costs are zero, and that the market works perfectly, or in other words, that the capital asset pricing applies at each instant of time. The main advantages of the Black–Scholes model are that their formula is a function of “observable” variables and that the model can be extended to the pricing of any type of option. Thus, the Black and Scholes model has been extended since the seventies by several authors to account for other observable variables and to tackle several financial issues 1 .
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