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This paper aims to enhance a co-skew-based risk measurement methodology initially introduced in Polimenis, by extending it for the joint estimation of the jump betas for two stocks.

The authors introduce the possibility of idiosyncratic jumps and analyze the robustness of the estimated sensitivities when two stocks are jointly fit to the same set of latent jump factors. When individual stock skews substantially differ from those of the market, the requirement that the individual skew is exactly matched is placing a strain on the single stock estimation system.

The authors argue that, once the authors relax this restrictive requirement in an enhanced joint framework, the system calibrates to a more robust solution in terms of uncovering the true magnitude of the latent parameters of the model, at the same time revealing information about the level of idiosyncratic skews in individual stock return distributions.

Allowing for idiosyncratic skews relaxes the demands placed on the estimation system and hence improves its explanatory power by focusing on matching systematic skew that is more informational. Furthermore, allowing for stock-specific jumps that are not related to the market is a realistic assumption. There is now evidence that idiosyncratic risks are priced as well, and this has been a major drawback and criticism in using CAPM to assess risk premia.

Since jumps in stock prices incorporate the most valuable information, then quantifying a stock's exposure to jump events can have important practical implications for financial risk management, portfolio construction and option pricing.

This approach boosts the “signal-to-noise” ratio by utilizing co-skew moments, so that the diffusive component is filtered out through higher-order cumulants. Without making any distributional assumptions, the authors are able not only to capture the asymmetric sensitivity of a stock to latent upward and downward systematic jump risks, but also to uncover the magnitude of idiosyncratic stock skewness. Since cumulants in a Levy process evolve linearly in time, this approach is horizon independent and hence can be deployed at all frequencies.

The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of volatility, both discrete and continuous, and then we summarize some selected empirical findings from the literature. In particular, in the first sections of this chapter, we discuss important developments in volatility models, with focus on time-varying and stochastic volatility as well as nonparametric volatility estimation. The models discussed share the common feature that volatilities are unobserved and belong to the class of missing variables. We then provide empirical evidence on “small” and “large” jumps from the perspective of their contribution to overall realized variation, using high-frequency price return data on 25 stocks in the DOW 30. Our “small” and “large” jump variations are constructed at three truncation levels, using extant methodology of Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev, and Diebold (2007), and Aït-Sahalia and Jacod (2009a, 2009b, 2009c). Evidence of jumps is found in around 22.8% of the days during the 1993–2000 period, much higher than the corresponding figure of 9.4% during the 2001–2008 period. Although the overall role of jumps is lessening, the role of large jumps has not decreased, and indeed, the relative role of large jumps, as a proportion of overall jumps, has actually increased in the 2000s.

Due to disequilibrium between supply and demand in the option market, the option market‐maker is under exposure to certain risks because of their net option positions. This paper aims to pay attention to whether the risk award affects the option price and the shape of implied volatility in the market‐maker system.

The paper first eliminates the part of implied volatility explained by underlying asset's stochastic volatility‐jump price process, and second sorts out market investors' net demand data from TAIEX Options tick by tick deal data and then finally considers three market maker's risks – unhedgeable risk, capital constrain risk and asymmetric information risk, and how they affect implied volatility's level and slope.

Through the research in the TAIEX Option market, the paper finds that, under unhedgeable risk, net demand pressure has a significant impact on implied volatility. Especially, unhedgeable risk due to underlying asset's stochastic volatility has the best explanation for implied volatility level, and unhedgeable risk due to underlying asset's jump can explain implied volatility slope to some extent. Capital constrain risk and asymmetric information risk have an insignificant impact on implied volatility.

The findings in this study suggest that the risk award affects the option price and the shape of implied volatility in the market‐maker system and different risks have different effects on the level and slope of option implied volatility.

This paper finds the influence factors of the option price in the market‐maker system. It's useful for China's financial government and investors to learn the price tendency and regular pattern in the future China option market.

This is the first time that a net demand pressure based option pricing model is used, which is derived by Garleanu, Pedersen and Poteshman, to study the TAIEX Options' implied volatility. And the paper improves the methods eliminating the part of implied volatility explained by underlying asset's stochastic volatility‐jump price process.

This paper tries to empirically investigate whether the jump risk of Korean stock market may be statistically useful in explaining the Korean CDS (5Y) premium rate. This paper uses the jump-diffusion model with heteroscedasticity to estimate the conditional volatility of KOSPI from 7/2/2007 to 7/30/2010.

The total volatility of Korean stock market is decomposed into a heteroscedasticity and a jump risk by using the jump-diffusion model. The finding is that the jump risk in stead of heteroscedasticity in Korean stock market can explain the Korean CDS premium rate.

The previous theoretical studies on default correlations analyze them only when the firm value moves continuously. Unlike these researches, this paper examines them when the firm value is exposed to jump risks and these jump risks between firms are correlated. Under these conditions, the effects of the correlated jump risks on default correlations are the followings. First, as stated in the previous study, this paper also states that the default correlations increase and then decrease with time. Second, there is a big difference between the existing study and this paper in the aspect of the firms' credit qualities. In the previous study, over a long horizon, default correlations of lower credit qualities of firms are lower than those of higher credit qualities of firms. However, under the jump-diffusion model we are able to obtain the opposite result to the previous study, which is that the jump-diffusion model is consistent with the empirical study in the case of lower credit qualities of firms. Third, on default correlations between the speculative graded firms over a long horizon, this paper is more consistent with the empirical results rather than the previous theoretical study. On contrary, on default correlations between the investment graded firms over a short horizon, the result is completely the opposite. Finally, in contrast to the diffusion model of Merton (1974) where default correlations over a short period are insignificant, default correlations under the jump-diffusion model may be consistent with the empirical results due to correlated jump risks.

This study examines whether KOSPI200 intra-day return has jump risk and heteroscedasticity and we compare the estimation result of intra-day return and that of daily return. The sample covers from January 2, 2004 to July 31, 2014. We use 30-minute intervals for measuring KOSPI200 intra-day return. It seems this study finds the importance of the consideration of the intra-day data in Korean Stock Market. While some of the parameters of the daily returns for the jump are not significant, but those of intra-day returns are significant over the sample period. Also, the intra-day volatility has shown U-shaped or reverse J-shaped curve. In particular the pattern of intra-day volatility seems to come from the jump risk, which is interpreted as the information inflow in the market.

The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which can meet the requirements of option traders and practitioners during tumultuous periods in the future.

Envisioning the fact, the all option-pricing models normally does wrong valuation relative to market. For estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset return data, we have used the nonlinear least-square method. As an approach, we analyzed model prices by dividing the option data into 15 moneyness-maturity groups – depending on the time to maturity and strike price. The prices are compared analytically by continuously updating the parameters of two models using cross-sectional option data on daily basis. Estimated parameters then used to figure out the forecasting performance of models with corresponding BS and market – for pricing day-ahead option prices and implied volatility.

The outcomes of the paper reveal that the jump-diffusion models are a better substitute of classical BS, thus improving the pricing bias significantly. But compared to jump-diffusion model of Merton’s, the model of Bates’ can be applied more uniquely to find out the pricing of three popularly traded categories: deep-out-of-the-money, out-of-the-money and at-the-money of Nifty index options.

The outcome of this research work reveals that the jumps are important components of pricing dynamics of Nifty index options. Incorporation of jump-diffusion process into option pricing of Nifty index options leads to a higher pricing effectiveness, reduces the pricing bias and gives values closer to the market. As the models have been tested in extreme conditions to determine the dominant effectuality, the outcome of this paper helps traders in keeping the investment protected under normal conditions.

The specific period chosen for this study is very unique; it canvasses the extreme up and down limits (jumps) of the Indian capital market and provides the most apt situation for testifying the pricing competitiveness of the models in question. To testify the robustness of models, they have been put into a practical implication of complete cycle of financial frame.

This paper gives a selective review on some recent developments of nonparametric methods in both continuous and discrete time finance, particularly in the areas of nonparametric estimation and testing of diffusion processes, nonparametric testing of parametric diffusion models, nonparametric pricing of derivatives, nonparametric estimation and hypothesis testing for nonlinear pricing kernel, and nonparametric predictability of asset returns. For each financial context, the paper discusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to financial data. Their relative strengths and weaknesses are discussed. Much theoretical and empirical research is needed in this area, and more importantly, the paper points to several aspects that deserve further investigation.

This paper aims to examine the nexus between the pricing of market-wide volatility risk and distress risk in the cross-section of portfolio returns for the 1990-2011 time period. The author expands upon prior research by constructing an ex post factor that mimics aggregate volatility risk based on the new VIX index of the Chicago Board Options Exchange, termed FVIX, as well as focuses on volatility risk in crisis versus non-crisis time periods.

The author investigates the relationship between volatility and distress risk using several techniques in the empirical finance literature. Specifically, the author investigates the behavior of correlations between risk factors as well as the correlations between factor loadings when using the Fama and French research portfolios as our test assets for different time periods. Additionally, the author examines the variation in the volatility factor loadings across the size- and value-sorted portfolios and assesses whether augmenting conventional pricing models with a volatility factor leads to a higher goodness-of-fit in pricing the 25 size- and value-sorted portfolios.

The author’s results suggest that factor volatilities are high during periods of market turmoil. In addition, the author presents evidence indicating that a factor mimicking innovation in volatility (based on the new VIX) is correlated with the market and momentum factors, while exhibiting the uncorrelated behavior with respect to the size, value and liquidity factors when using data from 1990 through 2011. In this paper, the author finds that the aggregate volatility factor’s correlation with the market and momentum factors increases during crisis periods. In periods of relative market tranquility, correlations decrease significantly. In examining multivariate factor loadings for the test assets, the results provide no clear pattern with regard to the variation of the volatility loadings across the book-to-market and size dimensions. Furthermore, the author finds that conventional pricing models are comparable to FVIX-augmented pricing models, in terms of goodness-of-fit, when pricing the 25 Fama-French size- and value-sorted portfolios. Additionally, when using the FVIX volatility factor to proxy for aggregate volatility risk, the coefficients are never significant statistically, thus revealing that innovations in aggregate volatility based on the new VIX index do not constitute a priced risk factor in the cross-section of returns.

The author’ finding indicates an absence of strong variation of the volatility factor loadings across the Fama-French research portfolios. In particular, the asset pricing results cast doubt on whether a factor mimicking innovations in aggregate volatility based on the new VIX index is priced. In agreement with prior research, the author believes that the inseparability of volatility and jump risk in the VIX can be a possible explanation of the current findings in this paper.

This paper aims to present the results of further investigating the Polimenis (2012) stochastic model, which aims to decompose the stock return evolution into positive and negative jumps, and a Brownian noise (white noise), by taking into account different noise levels. This paper provides a sensitivity analysis of the model (through the analysis of its parameters) and applies this analysis to Google and Yahoo returns during the periods 2006-2008 and 2008-2010, by means of the third central moment of Nasdaq index. Moreover, the paper studies the behavior of the calibrated jump sensitivities of a single stock as market skew changes. Finally, simulations are provided for the estimation of the jump betas coefficients, assuming that the jumps follow Gamma distributions.

In the present paper, the model proposed in Polimenis (2012) is considered and further investigated. The sensitivity of the parameters for the Google and Yahoo stock during 2006-2008 estimated by means of the third (central) moment of Nasdaq index is examined, and consequently, the calibration of the model to the returns is studied. The associated robustness is examined also for the period 2008-2010. A similar sensitivity analysis has been studied in Polimenis and Papantonis (2014), but unlike the latter reference, where the analysis is done while market skew is kept constant with an emphasis in jointly estimating jump sensitivities for many stocks, here, the authors study the behavior of the calibrated jump sensitivities of a single stock as market skew changes. Finally, simulations are taken place for the estimation of the jump betas coefficients, assuming that the jumps follow Gamma distributions.

A sensitivity analysis of the model proposed in Polimenis (2012) is illustrated above. In Section 2, the paper ascertains the sensitivity of the calibrated parameters related to Google and Yahoo returns, as it varies the third (central) market moment. The authors demonstrate the limits of the third moment of the stock and its mixed third moment with the market so as to get real solutions from (S1). In addition, the authors conclude that (S1) cannot have real solutions in the case where the stock return time series appears to have highly positive third moment, while the third moment of the market is significantly negative. Generally, the positive value of the third moment of the stock combined with the negative value of the third moment of the market can only be explained by assuming an adequate degree of asymmetry of the values of the beta coefficients. In such situations, the model may be expanded to include a correction for idiosyncratic third moment in the fourth equation of (S1). Finally, in Section 4, it is noticed that the distribution of the error estimation of the coefficients cannot be considered to be normal, and the variance of these errors increases as the variance of the noise increases.

As mentioned in the Findings, the paper demonstrates the limits of the third moment of the stock and its mixed third moment with the market so as to get real solutions from the main system of equations (S1). It is concluded that (S1) cannot have real solutions when the stock return time series appears to have highly positive third moment, while the third moment of the market is significantly negative. Generally, the positive value of the third moment of the stock combined with the negative value of the third moment of the market can only be explained by assuming an adequate degree of asymmetry of the values of the beta coefficients. In such situations, the model proposed should be expanded to include a correction for idiosyncratic third moment in the fourth equation of (S1). Finally, it is noticed that the distribution of the error estimation of the coefficients cannot be considered to be normal, and the variance of these errors increases as the variance of the noise increases.