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…
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48 results for “Jump rates”
A new model for short rates using pure-jump processes.
problem Modeling short rates with bounded behavior and affine bond prices.
method Sum of pure-jump Ornstein-Uhlenbeck processes for mean-reversion, with affine bond price representations.
result The model can be market-consistently calibrated and has an explicit option pricing formula.
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…
Jump-telegraph models for the short rate: pricing and convexity adjustments of zero coupon bondsq-fin.MF
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…
Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulationsq-fin.RM
Study on interest rate model with jumps, proving strong convergence in simulations.
problem Analytical solutions for complex interest rate models with jumps are difficult.
method Employed truncated Euler-Maruyama techniques to prove strong convergence.
result Justified strong convergence for Monte Carlo calibration and valuation.
Extended CIR process with jumps at fixed dates for modeling overnight rates.
problem Modeling overnight rates with jumps at predetermined dates.
method Formal definition and existence proof of a CIR process with stochastic discontinuities.
result Extended CIR process inherits affine property and non-negativity.
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…
New neural method for inferring Markov jump processes.
problem Inference in Markov jump processes is challenging.
method Variational inference using neural ODEs and backpropagation.
result Trains neural representations of data to approximate process rates.
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…
Develops a new method for pricing GMWBs with jumps and stochastic interest rates.
problem Pricing guaranteed minimum withdrawal benefits (GMWBs) with jumps and stochastic interest rates.
method Combines semi-Lagrangian method with Fourier pricing and Green's function.
result Mathematically demonstrates convergence to the viscosity solution of the HJB-QVI.
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…
Near-Maturity Asymptotics of Critical Prices of American Put Options under Exponential Lévy Modelsq-fin.MF
Study near-maturity convergence rates of American put prices in Lévy models.
problem Analyzing convergence rates of optimal exercise prices in Lévy models.
method Examined two settings: jumps of unbounded and bounded variation, deriving near-maturity expansions.
result Near-maturity convergence rate of optimal exercise price is of order √(T-t).
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.
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.
problem System identification for autonomous Markov jump linear systems with complete state observations.
method Proposes switched least squares method for identification and derives rates of convergence.
result Data-independent rate of convergence is , showing strong consistency.
This work models overnight rates with jumps and discontinuities, extending classical short-rate models.
problem Capturing the jump behavior and discontinuities in overnight rates for accurate modeling.
method Developed a term structure modeling framework based on overnight rates, accommodating stochastic discontinuities.
result Simple specifications can capture the jump behavior of overnight rates, and explicit valuation formulas are provided.
Formula for European option pricing under jump diffusion model.
problem Option pricing under complex stochastic processes.
method Infinite series of Black-Scholes terms for Levy-driven processes.
result Series solution converges with a radius of convergence.
Numerical approximation of hybrid Poisson-jump Ait-Sahalia-type interest rate model with delayq-fin.RM
This paper modifies the Ait-Sahalia model to better describe interest rate behaviors.
problem Inadequate specifications of the original Ait-Sahalia model to explain various interest rate phenomena.
method Proposes a modified hybrid Poisson-jump Ait-Sahalia model and uses truncated EM techniques for numerical approximation.
result Validates the modified model using Monte Carlo simulations for bond and barrier option payoffs.
We introduce a class of interest rate models, called the -CIR model, which gives a natural extension of the standard CIR model by adopting the -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.
problem Creating efficient generative models for complex data distributions.
method Piecewise deterministic Markov processes (PDMPs) with explicit expressions for jump rates and kernels.
result Efficient training and simulation methods for PDMP-based generative models.
New method estimates volatility for Lévy processes with unbounded jumps efficiently.
problem Efficient estimation of volatility for Lévy processes with unbounded jumps.
method Developed a new estimator based on high-order expansions of truncated moments.
result Method outperforms existing alternatives in estimating volatility.
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…
Dirac Processes and Default Riskq-fin.PR
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.
problem Financial pricing under multiple interest rates and collateralization.
method Derives a change of measure formula for recursive conditional expectations in a jump-diffusion setting.
result Generalizes the change of numéraire technique for 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.
problem Estimating volatility of processes with jumps of unbounded variation.
method Developed a new volatility estimator using debiasing of truncated realized quadratic variation.
result Method outperforms existing alternatives in simulations.
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…
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.
problem Valuing derivatives in markets without a traded risk-free bond.
method Introduces common Levy jump dynamics, uses Ito-Levy calculus, FFT, and COS algorithms.
result Calibrations show jump models reduce pricing errors and fit volatility smiles better than Black-Scholes.
Modelling the term structure of interest rates á la Heath-Jarrow-Morton but with non Gaussian fluctuationscond-mat.other
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…
The Fourier estimator of spot volatility: Unbounded coefficients and jumps in the price processq-fin.CP
Study Fourier estimator for spot volatility with unbounded coefficients and jumps.
problem Estimating spot volatility with unbounded coefficients and jumps in price process.
method Fourier estimator for spot volatility, convergence analysis for unbounded coefficients and jumps.
result Convergence of trigonometric polynomial to volatility's path, almost sure convergence of reconstructed volatility.
This paper models short rates with jumps using PDEs.
problem Capturing jumps and spikes in interest rates.
method PDE approach for pricing interest rate derivatives.
result Established Feynman-Kač representation and derived solutions.
Unified model for equity option pricing and interest-rate risk assessment.
problem Pricing short and medium-term equity options and interest-rate risk.
method Developed a stochastic modeling framework using Heston, Bates, and CIR models, calibrated using Fourier inversion and FFT.
result Calibration stability and convergence of parameter sets across models.
Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Spaceq-fin.RM
New model for insurance states using Markov jump processes with non-countable state space.
problem Modeling insurance states with non-countable state spaces.
method Developed a new Thiele's differential equation for continuous time rehabilitation rates.
result Allows for consistent calculation of reserves in disability insurance.
Bayesian inference for Levy density with Gibbs posterior in discrete sampling.
problem Inference on Levy density for financial models with jumps.
method Gibbs posterior framework using a loss function for intractable likelihood.
result Gibbs posterior achieves nearly optimal rate of convergence under certain conditions.
Hybrid model improves synthetic equity data generation.
problem Generating realistic synthetic financial time series.
method Discretized excess growth rates into states with Poisson jumps, estimating parameters directly.
result Framework achieved high pass rates for distributional and volatility clustering tests.
Approximate hedging with proportional transaction costs in stochastic volatility models with jumpsq-fin.MF
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 …
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 …
Optimal investment with insurable background risk and nonlinear portfolio allocation frictionsq-fin.MF
Investment and insurance decisions are studied in a model with nonlinear portfolio frictions and background risk.
problem Investment and insurance decisions under a model with nonlinear portfolio frictions and background risk.
method Dynamic programming approach to find optimality conditions.
result Agent can choose to assume, partially assume, or purchase total insurance against adverse jumps in wealth.
Study on implied volatility of an affine jump-diffusion model.
problem Characterize implied volatility of an affine jump-diffusion model.
method Explicit moment generating function derived from solving ODEs; large deviation principle applied.
result Asymptotic behaviors of implied volatility in large-maturity and large-strike regimes characterized.
Study optimal investment-reinsurance strategy for insurers under random coefficients and jumps.
problem Optimal investment-reinsurance strategy for insurers with random coefficients and jumps.
method Solves backward stochastic differential equations with jumps under a convex cone constraint.
result Optimal strategy and value remain the same even with random coefficients and jumps.
SJDs unify masked, continuous, and hybrid diffusion models.
problem Unified modeling of diffusion processes.
method Continuous-time Markov processes with token embeddings and hazard rates.
result Unified model recovers masked, continuous, and hybrid diffusion as limits.
A primer on perpetualsq-fin.MF
The paper explores perpetual contracts in a financial market without arbitrage.
problem Modeling perpetual contracts in a continuous-time financial market.
method Derive model-free and semi-robust expressions for perpetual contracts' funding and discount rates.
result Explicit replication strategies for perpetual contracts are derived, relating them to traditional financial instruments.
In this paper we study perpetual American call and put options in an exponential Lévy model. We consider a negative effective discount rate which arises in a number of financial applications including stock loans and real options, where the strike price can potentially grow at a higher rate than the original discount f…
We develop a simple routine unifying the analysis of several important recently-developed stochastic optimization methods including SAGA, Finito, and stochastic dual coordinate ascent (SDCA). First, we show an intrinsic connection between stochastic optimization methods and dynamic jump systems, and propose a general j…
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization p…
This paper uses entropy to derive stock price dynamics and option valuation.
problem Deriving stock price dynamics and option valuation from information constraints.
method Develops an entropic inference framework to derive stochastic processes from information constraints, representing price changes through two channels: continuous and jump.
result The derived dynamics is the Merton jump diffusion, with Geometric Brownian Motion as the no jump limit.
We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral appro…