arXiv research

Study shows mean field games can have multiple solutions under certain conditions.

Develops a new method for pricing GMWBs with jumps and stochastic interest rates.

SGD can jump from high rank minima to low rank minima in DLNs, but not back.

Robustly detects jumps in high-frequency CIR and CKLS models.

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…

Study reveals strong co-jumping behavior in U.S. yield curves compared to Europe.

A new model for short rates using pure-jump processes.

Investigates consistency of FX rate dynamics under inversion.

In this article, we consider a Markov-modulated model with jumps for short rate dynamics. We obtain closed formulas for the term structure and forward rates using the properties of the jump-telegraph process and the expectation hypothesis. The results are compared with the numerical solution of the corresponding partia…

Study on interest rate model with jumps, proving strong convergence in simulations.

Extended CIR process with jumps at fixed dates for modeling overnight rates.

For node level graph encoding, a recent important state-of-art method is the graph convolutional networks (GCN), which nicely integrate local vertex features and graph topology in the spectral domain. However, current studies suffer from several drawbacks: (1) graph CNNs relies on Chebyshev polynomial approximation whi…

New neural method for inferring Markov jump processes.

We derived similar to Bo et al. (2010) results but in the case when the dynamics of the FX rate is driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform parameters which ensure that the martingale condition for the discounted foreign excha…

We compute and discuss the Esscher martingale transform for exponential processes, the Esscher martingale transform for linear processes, the minimal martingale measure, the class of structure preserving martingale measures, and the minimum entropy martingale measure for stochastic volatility models of Ornstein-Uhlenbe…

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…

Study near-maturity convergence rates of American put prices in Lévy models.

Method detects jumps in high-frequency order prices using local minima.

We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate) marked point processes and so-called non-linear wealth dynamics which allows to take …

Study identifies and validates a method for system identification of Markov jump linear systems.

This work models overnight rates with jumps and discontinuities, extending classical short-rate models.

Formula for European option pricing under jump diffusion model.

This paper modifies the Ait-Sahalia model to better describe interest rate behaviors.

We introduce a class of interest rate models, called the $α$-CIR model, which gives a natural extension of the standard CIR model by adopting the $α$-stable L{é}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign …

Generative models using PDMPs with explicit jump rates and kernels.

New method estimates volatility for Lévy processes with unbounded jumps efficiently.

Optimal insurance surplus management under stochastic interest rates and jumps.

In this paper, we are presenting a method for estimation of market parameters modeled by jump diffusion process. The method proposed is based on Gibbs sampler, while the market parameters are the drift, the volatility, the jump intensity and its rate of occurrence. Demonstration on how to use these parameters to estima…

We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes, which have not been used directly before because the dollar value of non-Real nu…

The paper develops a new formula for financial pricing under multiple interest rates and collateralization.

We propose a new model for pricing Quanto CDS and risky bonds. The model operates with four stochastic factors, namely: hazard rate, foreign exchange rate, domestic interest rate, and foreign interest rate, and also allows for jumps-at-default in the FX and foreign interest rates. Corresponding systems of PDEs are deri…

New method estimates volatility for processes with jumps of unbounded variation.

In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a Hamiltonian Monte Carlo algorithm using a continuous time Markov jump process, and ar…

Investigates optimal PPI strategies in jump-diffusion models to mitigate downside risk.

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and pu…

Extends option pricing framework without risk-free asset using Levy jumps.

We consider a generalization of the Heath Jarrow Morton model for the term structure of interest rates where the forward rate is driven by Paretian fluctuations. We derive a generalization of Itô's lemma for the calculation of a differential of a Paretian stochastic variable and use it to derive a Stochastic Differenti…

Study Fourier estimator for spot volatility with unbounded coefficients and jumps.

This paper models short rates with jumps using PDEs.

Unified model for equity option pricing and interest-rate risk assessment.

New model for insurance states using Markov jump processes with non-countable state space.

Bayesian inference for Levy density with Gibbs posterior in discrete sampling.

Hybrid model improves synthetic equity data generation.

We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size distribution we show that transaction costs can be approximately compensated by …

Investigates real-world interest rate dynamics using affine models.

Modified model for Quanto CDS pricing with stochastic recovery and reduced complexity.

Models for financial assets with jumps and Brownian motion.

We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak …