Simplifies pricing options in jump-diffusion models using gauge transformations.
problem Pricing European options in affine jump-diffusion models.
method Gauge transformation in the dual space to reduce to diffusion model pricing.
result A general procedure for calculating Φ and applications in pricing and estimation. New model estimates corporate defaults using pure jump processes, capturing extreme events.
problem Estimating corporate defaults using standard diffusion models that underestimate short-term probabilities.
method Introduced pure jump processes with negative jumps only, derived formulas, calibrated parameters, and implemented practical tools.
result Models redistribute credit risk towards shorter maturities, improving short-term default probability estimates.
New extremal metrics found on Kähler manifolds.
problem Constructing extremal metrics on Kähler manifolds.
method Test configurations for strictly semistable Kähler manifolds.
result Infinitely many new examples of manifolds with extremal Kähler metrics.
Robustly detects jumps in high-frequency CIR and CKLS models.
problem Jump detection in high-frequency jump-diffusion processes.
method MDPDE-based robust estimators for drift and diffusion coefficients.
result Maximum of normalized residuals converges to Gumbel distribution.
Study proposes pricing mechanism for cryptocurrency options.
problem High speculation, volatility, and discontinuity in cryptocurrency markets.
method Proposes a pricing mechanism based on SVCJ model with co-jumps.
result Shows significant contemporaneous anti-correlation between jumps in price and volatility.
A method to identify new classes of price jumps in financial markets.
problem Separating endogenous and exogenous causes of price jumps.
method Wavelet-based representation of jump time-series.
result Identification of new classes of jumps and investigation of co-jumps.
The standard intensity-based approach for modeling defaults is generalized by making the deterministic term structure of the survival probability stochastic via a common jump process. The survival copula of the vector of default times is derived and it is shown to be explicit and of the functional form as dealt with in…
Cryptocurrency, the most controversial and simultaneously the most interesting asset, has attracted many investors and speculators in recent years. The visibly significant market capitalization of cryptos also motivates modern financial instruments such as futures and options. Those will depend on the dynamics, volatil…
The paper models stock returns using q-Gaussians and negative binomials.
problem Modeling stock return distributions and pricing options.
method Proposes a generalized jump-diffusion model and uses q-Gaussians and negative binomial distributions. result An explicit option pricing formula is derived.
Method detects jumps in high-frequency order prices using local minima.
problem Detecting jumps in high-frequency order prices with noisy data.
method Developed methods to estimate, locate and test for jumps using local minima of best ask quotes.
result Consistently estimated jump sizes and times, established asymptotic properties of tests, and demonstrated faster convergence rates.
New framework analyzes pre-stock jump trading behaviors using multivariate time series analysis.
problem Understanding micro-trading behaviors before stock price jumps.
method Multivariate time series analysis considering temporal information.
result Identifies highly informative attributes for predicting price jumps.
Quantum theory reinterprets financial pricing by focusing on observable price transitions.
problem Traditional financial models rely on latent variables; this paper proposes a new observable approach.
method Shift operators, spectral calculus, and Lindblad semigroups are used to define observable frequency operators and convolution generators.
result The framework leads to a nonlocal pricing equation that converges to classical Black-Scholes-Merton under small mesh limits.
Develops a climate risk model for asset managers.
problem Climate-related risks affecting asset performance and productivity.
method Uses the Vasicek model with downward jumps to represent climate impacts on asset dynamics.
result Expected losses increase over time due to climate-related extreme events.
Extremal length is a conformal invariant that transfers naturally to the discrete setting, giving square tilings as a natural combinatorial analog of conformal mappings. Recent work by S. Hersonsky has explored generalizing these ideas to three-dimensional cube tilings. The connections between discrete extremal length …
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…
The paper reviews recent statistical methods for financial markets, focusing on jumps, volatility, and microstructure noise.
problem Analyzing financial market data with statistical models.
method Review and development of statistical methods for financial markets, including jump tests, rough volatility, and microstructure noise.
result Established a minimax lower bound for volatility recovery and proposed new statistical methods for financial market analysis.
New method for Bayesian inference of Lévy-driven SDEs with jumps.
problem Bayesian inference for Lévy-driven SDEs is challenging due to discontinuities and heavy tails.
method Neural exponential tilting framework for variational inference.
result Accurately captures jump dynamics and reliable posterior inference in heavy-tailed regimes.
New method for efficient pricing of double barrier options in Lévy models.
problem Difficulties in accurately and quickly calculating prices of double barrier options in jump models.
method GWR-SINH method based on Gaver-Wynn-Rho acceleration applied to Bromwich integral.
result Accurate and fast calculations of prices of double barrier options in jump models achieved.
We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previ…
Prices in financial markets exhibit extreme jumps far more often than can be accounted for by external news. Further, magnitudes of price changes are correlated over long times. These so called stylized facts are quantified by scaling laws similar to, for example, turbulent fluids. They are believed to reflect the comp…
News might trigger jump arrivals in financial time series. The "bad" and "good" news seems to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable est…
We quantify how co-jumps impact correlations in currency markets. To disentangle the continuous part of quadratic covariation from co-jumps, and study the influence of co-jumps on correlations, we propose a new wavelet-based estimator. The proposed estimation framework is able to localize the co-jumps very precisely th…
Quantum computing speeds up analysis of financial stochastic processes.
problem Challenging simulation and analysis of continuous time stochastic processes.
method Established a quantum framework for efficient state preparation and information extraction.
result Extraction of path-dependent and history-sensitive information from stochastic processes efficiently.
Neural jump model improves option pricing accuracy.
problem Jump risk in option pricing.
method Neural jump stochastic differential equation model with Gumbel-Softmax gradient learning.
result Neural jump components significantly improve option pricing accuracy.
We study the role of co-jumps in the interest rate futures markets. To disentangle continuous part of quadratic covariation from co-jumps, we localize the co-jumps precisely through wavelet coefficients and identify statistically significant ones. Using high frequency data about U.S. and European yield curves we quanti…
We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity, using a jump-adapted discretisation in which the jump times are computed and added to the standard uniform dis- cretisation times. The key component in multilevel analy…
Develops a new model for pricing without arbitrage opportunities.
problem Arbitrage opportunities in standard jump-diffusion models.
method Introduces a multi-type jump-diffusion model with diffusion-dependent jumps.
result Derives no-arbitrage condition linking drift to model parameters.
Empirical study finds variance swap rate is affine in spot variance for S&P500 data.
problem Investigating the relationship between variance swap rate and spot variance.
method Empirical analysis using S&P500 data from 2006-2018, testing different models.
result Affine relationship between variance swap rate and spot variance is supported.
Extends nonlinear filtering to predictable jump times.
problem Filtering with jumps in both signal and observation, especially when jump times are known.
method Derive Kushner-Stratonovich and Zakai equations for predictable discontinuities.
result Extends classical nonlinear filtering results to a setting with predictable discontinuities.
The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the exist…
Efficiently reconstructs jump-diffusion processes from data using neural networks.
problem Reconstructing jump-diffusion processes from data.
method Temporally decoupled squared Wasserstein distance method using parameterized neural networks.
result Enhanced reconstruction of jump-diffusion processes from data.
The paper models financial data with multivariate jump processes.
problem Capturing the dynamics of financial data with jumps.
method Defined multivariate point processes driven by stochastic jumps, providing stability conditions.
result Nonlinear models fit financial data best, showing jumps cluster during crises.
Model predicts jump risk premia influencing cryptocurrency futures and option performance.
problem Capturing asymmetric and time-varying skewness in cryptocurrency returns.
method Bivariate Hawkes process with positive and negative jump premia.
result Inferred jump risk premia predict futures cost of carry and option performance.
A machine learning method for short-maturity options with jumps and stochastic volatility.
problem Short-maturity options with jumps and stochastic volatility.
method Differential machine learning method combining supervision and PIDE-residual penalty.
result Improves jump-term approximation and reduces Greeks errors compared to baselines.
RL for jump-diffusions applies to financial portfolio selection and option hedging.
problem Optimizing control in systems with jump-diffusion dynamics.
method Entropy-regularized exploratory control with stochastic policies, using existing diffusion algorithms with modifications.
result RL algorithms and parameterizations are invariant to jumps in jump-diffusion systems.
In order to understand the origin of stock price jumps, we cross-correlate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and aro…
In this note we investigate the consistency under inversion of jump diffusion processes in the Foreign Exchange (FX) market. In other terms, if the EUR/USD FX rate follows a given type of dynamics, under which conditions will USD/EUR follow the same type of dynamics? In order to give a numerical description of this pro…
The paper introduces walks with jumps for modeling neuron activity in hyperbolic space.
problem Encoding neuron activity sequences in hyperbolic space.
method Introducing walks with jumps in hyperbolic geometry to model neuron activity.
result Endpoints of walks with jumps do not fully encode the sequence of jump times.
In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection and fitting, and in volatility estimation. In this paper, we give a novel estimat…
Develops efficient methods for approximating densities of financial models with jumps.
problem Approximating densities of affine jump diffusions with state-independent jump intensities.
method Recursive approach for deriving closed-form solutions to moments, constructing density approximations via moment matching.
result Superior computational efficiency and precision in option pricing and simulation compared to existing techniques.
Study on short-term behavior of ATM-IV for jump-diffusion model.
problem Analyzing the short-time behavior of ATM-IV for a specific stochastic volatility model.
method Used Malliavin Calculus techniques to derive expressions for ATM-IV level and skew.
result Short-time behavior of ATM-IV level is consistent for all pure-jump Lévy processes.
Study short maturity Asian options in jump-diffusion models with local volatility.
problem Analyzing Asian options pricing in models with jumps and local volatility.
method Asymptotic analysis for short maturity, considering fixed and floating strike options.
result Explicit results for Asian option prices in several models, including Merton, double-exponential, and Variance Gamma models.
The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options, mesh-based methods are applied in a number of papers but it is well-known that the…
Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure is the Kalman-EM (KEM) algorithm. However the KEM approach assumes log-normal pr…
Predicting stock jumps using liquidity and technical indicators.
problem Predicting intraday stock jumps in finance.
method Divide trading day into 5-minute intervals, use liquidity measures and technical indicators, apply machine learning algorithms.
result Initial evidence of predictability of jump arrivals and directions using level-2 stock data.
New insights into Khovanov polynomials using tangle calculus.
problem Understanding the structure and evolution of Khovanov polynomials for long braids.
method Application of tangle calculus and evolution theory to Khovanov polynomials, focusing on jumps and thickness.
result Jumps in evolution are less frequent than expected, with most contributions being non-jumping.
In this article, we consider a Markov process X, starting from x and solving a stochastic differential equation, which is driven by a Brownian motion and an independent pure jump component exhibiting state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability …
Enhances RL for jump processes using MSBVE algorithm.
problem Challenges in continuous-time RL with jumps and noise.
method Introduces MSBVE algorithm to minimize quadratic variation error.
result MSBVE algorithm outperforms MSTDE in jump processes.