Search results

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.

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.