Asymmetric Jumps Research Articles

Pricing VIX options based on mean-reverting models driven by information

Financial time series are dynamic and influenced by different types of information from the market. In this study, we propose new models for SPX and VIX options using the Hawkes process, jump process with stochastic intensity, and tempered stable process to capture these changes in financial time series based on three distinct characteristics of market information. We calculate the VIX option pricing formula using these models and find that the simplified VIX model based on VIX characteristics has significantly less pricing error than the consistent VIX model derived from the SPX model. Additionally, our findings suggest that the tempered stable process effectively models the volatility of VIX, sparse large jumps, and infinitesimal jumps. It also shows potential as an alternative to Brownian motion for representing volatility. Conversely, jump processes with stochastic jump intensities adeptly describe asymmetric jumps, and their integration with Brownian motion provides a more accurate depiction of the VIX’s volatility and jump dynamics. Finally, the introduction of jump processes into mean-reverting models for the VIX indicates a relatively low correlation between volatility magnitudes and the current VIX levels. This research contributes to the theory of SPX and VIX options and offers guidance for the development of other information-driven economic models.

Crude oil volatility index forecasting: New evidence based on positive and negative jumps from Chinese stock market

This article investigates the crude oil volatility index (OVX) forecasting from the perspective of cross-market asymmetric effects of Chinese stock market jumps. We calculate six kinds of positive and negative jumps based on the high-frequency data of stock returns which are used to represent the asymmetric shocks of stock markets. Principal component analysis (PCA) and momentum of predictability (MoP) strategy are employed separately to synthesize the information of asymmetric jumps. Our empirical results find that considering the positive and negative jumps in Chinese stock market helps to improve the forecasting ability of OVX, especially under the MoP strategy. The out-of-sample model confidence set (MCS) tests and Diebold-Mariano (DM) tests, the evaluation of economic significance and the robustness tests further verify our results.

An Energy Transfer-Based Bifurcation Detection Method for Nonlinear Rotating Systems: Enables Accurate Capture of Period-Doubling Bifurcation and Instability

Rotor systems are widely used in industrial power generation and propulsion. Once the nonlinear contact stiffness and oil film force are taken into account, the dynamics and stability of rotor systems become quite complex, often accompanied by super-harmonic and chaotic motions. Furthermore, conventional methods face limitations in real-time detection of the bifurcations and complex nonlinear motions. This research investigates the bifurcations and stability induced by nonlinear factors in a rotor-bearing system from an energy perspective. Dynamic equations of a rotor-bearing system considering cubic term stiffness are established, the steady responses are obtained by the fourth-order Runge–Kutta method. The relationship between the bifurcations and energy transfers is analyzed numerically, the proposed stability criterion is validated by comparing the Lyapunov exponents. The bistable phenomenon of period-3[Formula: see text] ([Formula: see text]) motion is discussed in terms of numerical results and experiments which corresponds to the asymmetric jumps of the generalized energy. It is found that bifurcations and unstable motions of the nonlinear system can be captured accurately by detecting the energy transfers, the proposed generalized energy curve exhibits more detailed information than the conventional speed-up curve. These findings provide a new perspective on studying bifurcations and stability of rotating systems, which can be further applied in the condition monitoring, stability prediction as well as the design of nonlinear energy sink, representing significant progress in converting theory into engineering applications for rotor systems.

Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene

Among the variety of correlated states exhibited by twisted bilayer graphene, cascades in the spectroscopic properties and in the electronic compressibility occur over larger ranges of energy, twist angle and temperature compared to other effects. This suggests a hierarchy of phenomena. Using a combined dynamical mean-field theory and Hartree calculation, we show that the spectral weight reorganisation associated with the formation of local moments and heavy quasiparticles can explain the cascade of electronic resets without invoking symmetry breaking orders. The phenomena reproduced here include the cascade flow of spectral weight, the oscillations of remote band energies, and the asymmetric jumps of the inverse compressibility. We also predict a strong momentum differentiation in the incoherent spectral weight associated with the fragile topology of twisted bilayer graphene.

Do VIX futures contribute to the valuation of VIX options?

AbstractAs the volatility index (VIX) is nontradable, most investors use the exchange‐traded VIX futures to hedge their exposures in VIX options. However, the information role of VIX futures in pricing VIX options is not fully explored empirically. This paper derives two types of VIX option pricing formula using VIX index and VIX futures as state variables accordingly based on a simple discrete‐time VIX dynamics with long memory and asymmetric jumps. Empirical results show that models utilizing VIX futures significantly outperform competing models based on S&P 500 index (SPX) returns, realized volatility, or the VIX index itself. Our findings are robust in out‐of‐sample.

Impacts of asymmetry on forecasting realized volatility in Japanese stock markets

This study investigates the most important asymmetric property for forecasting realized volatility in the Japanese futures and spot stock markets. We employ heterogeneous autoregressive (HAR) models allowing for three types of asymmetry: positive and negative realized semivariance (RSV), asymmetric jumps, and leverage effect. We find a clear difference among HAR models allowing for asymmetry. The HAR model with leverage effect performs best among asymmetric models. Additionally, the forecast performance of the HAR model with RSV is superior to that with asymmetric jumps. The asymmetric jump components do not produce better forecast performance compared with the standard HAR models. The empirical results indicate that asymmetric information, particularly leverage effect and RSV, yields better modeling and more accurate forecast performance for the realized volatility of Japanese stock markets.

Pricing Bitcoin under Double Exponential Jump-Diffusion Model with Asymmetric Jumps Stochastic Volatility

The objective of this study is, to show the importance of incorporating jumps in both returns and volatility dynamics for Bitcoin. For that purpose, we introduce the Double Exponential Jump-Diffusion model with Stochastic Volatility (DEJDSVJ) that contains asymmetric jumps. The use of the Markov Chain Monte Carlo methods for estimation has proved the meaningful presence of jumps in Bitcoin price and volatility. Moreover, based on the Bitcoin options market, a comparison between the underlying model, the Double Exponential Jump Diffusion model (DEJD) with Stochastic Volatility (no Jumps) and the Stochastic Volatility (SV) shows the goodness of the DEJDSVJ model’s calibration over others for pricing Bitcoin options.

A short cut: Directly pricing VIX futures with discrete‐time long memory model and asymmetric jumps

AbstractThis paper proposes a simple but rich framework to directly price volatility index (VIX) futures by applying the heterogeneous autoregressive structure and asymmetric jumps to the logarithm of the VIX. Compared with other discrete‐time models, our model imposes fewer parameter constraints. The analytical solution is also free from time‐consuming and sometimes unstable numerical integration. Empirical results suggest that our model can significantly reduce pricing errors compared with existing models using realized variance, both in‐ and out‐of‐sample. The improvement indicates that besides looking for a better measure of current volatility, it is also important to utilize information embedded in the VIX itself.

Cascade of phase transitions and Dirac revivals in magic-angle graphene.

Twisted bilayer graphene near the magic angle1-4 exhibits rich electron-correlation physics, displaying insulating3-6, magnetic7,8 and superconducting phases4-6. The electronic bands of this system were predicted1,2 to narrow markedly9,10 near the magic angle, leading to a variety of possible symmetry-breaking ground states11-17. Here, using measurements of the local electronic compressibility, we show that these correlated phases originate from a high-energy state with an unusual sequence of band population. As carriers are added to the system, the four electronic 'flavours', which correspond to the spin and valley degrees of freedom, are not filled equally. Rather, they are populated through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moiré lattice. At each transition, a single spin/valley flavour takes all the carriers from its partially filled peers, 'resetting' them to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near charge neutrality reappears after each integer filling. Measurement of the in-plane magnetic field dependence of the chemical potential near filling factor one reveals a large spontaneous magnetization, further substantiating this picture of a cascade of symmetry breaking. The sequence of phase transitions and Dirac revivals is observed at temperatures well above the onset of the superconducting and correlated insulating states. This indicates that the state thatwe report here, with its strongly broken electronic flavour symmetry and revived Dirac-like electronic character, is important in the physics of magic-angle graphene, forming the parent state out of which the more fragile superconducting and correlated insulating ground states emerge.

Pricing VIX options with stochastic skew and asymmetric jumps

Pricing VIX options with stochastic skew and asymmetric jumps

Pricing VIX derivatives with free stochastic volatility model

This paper aims to develop a new free stochastic volatility model, joint with jumps. By freeing the power parameter of instantaneous variance, this paper takes Heston model and 3/2 model for special examples, and extends the generalizability. This model is named after free stochastic volatility model, and it owns two distinctive features. First of all, the power parameter is not constrained, so as to enable the data to voice its authentic direction. The Generalized Methods of Moments suggest that the purpose of this newly-added parameter is to create various volatility fluctuations observed in financial market. Secondly, even upward and downward jumps are separately modeled to accommodate the market data, this paper still provides the quasi-closed-form solutions for futures and option prices. Consequently, the model is novel and highly tractable. Here, it should be noted that the data on VIX futures and corresponding option contracts is employed to evaluate the model, in terms of its pricing and implied volatility features capturing performance. To sum up, the free stochastic volatility model with asymmetric jumps is capable of adequately capturing the implied volatility dynamics. Thus, it can be regarded as a model advantageous in pricing VIX derivatives with fixed power volatility models.

Measuring contagion risk in high volatility state among Taiwanese major banks

This paper studies the structural tail dependence and contagion risk especially in high volatility state between domestic (Taiwanese) and foreign banks. Aptly the two-state threshold copula GARCH provides the threshold regression and copulas to classify the actual volatility index into a high or in a low state and estimate the structural tail dependences using Kendall taus to probe the co-movement among banks. In high volatility state, the average Kendall taus and value at risk as well as expected shortfall are about two times larger than in low volatility state. The asymmetric jumps of Kendall taus appear more frequent in the subprime crisis whereas the symmetric trends of Kendall taus appear higher in Greek debt crisis. Among three copula models in low volatility state, Gaussian and Student-t copula models have established a more significant estimate than the Clayton copula model. However, in high volatility state, Clayton copula model could still produce an acceptable estimate. Empirically, using Clayton copula in high volatility state has demonstrated clearly intensive tail jumps capable to distinguish the contagion risk.

Dynamic asset allocation with asymmetric jump distribution

PurposeThe purpose of this paper is to solve the optimal dynamic portfolio problem under the double-exponential jump diffusion (DEJD) distribution, which can allow the asset returns to jump asymmetrically.Design/methodology/approachThe authors solve the problem by solving the HJB equation. Meanwhile, in the presence of jump component in the asset returns, the investor may suffer a large loss due to high leveraged position, so the authors impose the short-sale and borrowing constraints when solving the optimization problem.FindingsThe authors provide sufficient conditions such that the optimal solution exists and show theoretically that the optimal risky asset weight is an increasing function of jump-up probability and average jump-up size and a decreasing function of average jump-down size.Research limitations/implicationsIn this study, the authors assume that the jump-up and jump-down intensities are constant. In the future, the authors will relax the assumption and allows the jump intensities to be time varying.Practical implicationsEmpirical studies based on Chinese Shanghai stock index data show that the jump distribution of Shanghai index returns is asymmetric, and the DEJD model can fit the data better than the log-normal jump-diffusion model. The numerical results are consistent with the theoretical prediction, and the authors find that the less risk-averse investor will suffer more economic cost if ignoring asymmetric jump distribution.Originality/valueThis study first examines how asymmetric jumps affect the investor’s portfolio allocation.

Pricing currency options under double exponential jump diffusion in a Markov-modulated HJM economy

Extending the framework of Amin and Jarrow (J Int Money Financ 10:310–329, 1991) and Bo et al. (Insur Math Econ 46:461–469, 2010), this study provides a theoretical exploration of currency options pricing under the presence of interest-rate regime shifts and exchange-rate asymmetric jumps. Evidence of interest-rate regime shifts inferred from UK and US zero coupon bond yields provides support for the regime-switching specifications which we reflect upon the domestic and foreign forward rates. Results of statistical tests conducted on JPY/USD and EUR/USD FX rates provide further support the rationale behind using a double exponential jump diffusion process within a Markov modulated Heath–Jarrow–Morton economy. Our numerical results suggest that, the pricing performance of our model is closely comparable to the Bo-Wang-Yang model for at-the-money options, yet yields improvements in percentage root mean errors for in-the-money options.

Analogy Making and the Structure of Implied Volatility Skew

An analogy based call option pricing model is put forward. The model provides a new explanation for the implied volatility skew puzzle. The analogy model is consistent with empirical findings about returns from well studied option strategies such as covered call writing and zero-beta straddles. The analogy based stochastic volatility and the analogy based jump diffusion models are also put forward. The analogy based stochastic volatility model generates the skew even when there is no correlation between the stock price and volatility processes, whereas, the analogy based jump diffusion model does not require asymmetric jumps for generating the skew.

Open-End Knock-Outs on Bond Futures: Valuation, Properties and Estimation of Hidden Profit Drivers

This paper is the first on retail Structured Financial Products (SFPs) from the fixed-income area, namely open-end knock-outs (OEKOs) on government bond futures. We develop and apply a valuation algorithm for OEKOs to analyze the issuers' profit. On the basis of a simple superhedging strategy we disclose the profit drivers for the issuers. The crucial profit drivers, the 'margin factor' and the 'rollover fee', are set by the issuers and can be regarded directly as costs to the investors. But even disregarding these drivers there exists a 'hidden' interest gain. However, asymmetric jumps in the interest rate dynamics may lead to significant gap risks which can considerably lower the issuers' benefit, even below zero. Since the crucial profit drivers of OEKOs are not directly observable, we estimate them by analyzing an extensive data set of OEKO prices. Inter alia, depending on the issuer we find that the profit drivers can take values of up to 60% p.a. on average.

On the Asymmetric Zero-Range in the Rarefaction Fan

We consider one-dimensional asymmetric zero-range processes starting from a step decreasing profile leading, in the hydrodynamic limit, to the rarefaction fan of the associated hydrodynamic equation. Under that initial condition, and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps, we derive the Law of Large Numbers for a second class particle, under the initial configuration in which all positive sites are empty, all negative sites are occupied with infinitely many first class particles and there is a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle it picks randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation, through some sort of renormalization function. By coupling the constant-rate totally asymmetric zero-range with the totally asymmetric simple exclusion, we derive limiting laws for more general initial conditions.

Analogy Making and the Structure of Implied Volatility Skew

An analogy based option pricing model is put forward. If option prices are determined in accordance with the analogy model, and the Black Scholes model is used to back-out implied volatility, then the implied volatility skew arises, which flattens as time to expiry increases. The analogy based stochastic volatility and the analogy based jump diffusion models are also put forward. The analogy based stochastic volatility model generates the skew even when there is no correlation between the stock price and volatility processes, whereas, the analogy based jump diffusion model does not require asymmetric jumps for generating the skew.

An experimental investigation of the stability of the circular hydraulic jump

We present the results of an experimental investigation of the striking flow structures that may arise when a vertical jet of fluid impinges on a thin fluid layer overlying a horizontal boundary. Ellegaard et al. (Nature, vol. 392, 1998, p. 767; Nonlinearity, vol. 12, 1999, p. 1) demonstrated that the axial symmetry of the circular hydraulic jump may be broken, resulting in steady polygonal jumps. In addition to these polygonal forms, our experiments reveal a new class of steady asymmetric jump forms that include structures resembling cat's eyes, three- and four-leaf clovers, bowties and butterflies. An extensive parameter study reveals the dependence of the jump structure on the governing dimensionless groups. The symmetry-breaking responsible for the asymmetric jumps is interpreted as resulting from a capillary instability of the circular jump. For all steady non-axisymmetric forms observed, the wavelength of instability of the jump is related to the surface tension, σ, fluid density p and speed U v of the radial outflow at the jump through λ = (74 ± 7)σ/(ρU 2 ν ).

Non-linear response of a liquid bridge to a sinusoidal acceleration under microgravity

An experiment was performed aboard a sounding rocket on a long cylindrical liquid bridge, aiming at discerning the real transfer function of this liquid configuration to small acceleration loads, quantified by the liquid free-surface deformation divided by the axially imposed acceleration. The results were, however, in great discrepancy with theoretical predictions, showing asymmetric jumps of high amplitude in the evolution of the radial deformation of the liquid bridge, instead of a symmetric sinusoidal radial deformation (axisymmetry was preserved). It has been found now that a non-linear dynamic model perfectly explains this unexpected behaviour.