Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Merton jump-diffusion”
This research improves option pricing models using Heston, GARCH, and jump diffusion models.
problem Inaccurate option pricing due to Black-Scholes assumptions.
method Monte Carlo simulation, GARCH model, Heston model, Merton jump-diffusion model.
result Heston model produces estimates closer to market prices, Merton model performs well for volatile assets, GARCH model improves volatility forecasts.
The paper extends Merton's model to include log-Heston and affine jump processes for option pricing.
problem Developing a pricing model for options in affine generalized Merton models.
method Generalizing Merton's model to include log-Heston and affine jump processes, proposing an approximation method for the latter.
result An approximation method for affine jump processes allows for the pricing of European options.
Compact scheme solves option pricing for jump-diffusion models.
problem Solving option pricing equations under jump-diffusion models.
method Fourth-order compact scheme for PIDEs, employing smoothing operator.
result Fourth-order convergence rate achieved for option pricing.
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…
New method for calculating forex options using LRM for Lévy models.
problem Calculating local risk minimization for forex options in Lévy models.
method Transformed representation of LRM into fast Fourier transform form.
result Validated the method on Merton jump-diffusion and variance gamma models.
Operator splitting schemes for American options under the two-asset Merton jump-diffusion modelmath.NA
The paper develops and tests operator splitting schemes for American options in a complex model.
problem Efficient numerical solution of American options under a two-asset Merton jump-diffusion model.
method Adaptation of IMEX and ADI operator splitting schemes to solve the two-dimensional PIDCP.
result Investigates and compares the convergence and performance of eight operator splitting methods.
Improved option pricing for assets with jumps and spikes.
problem Inaccurate pricing of European and American options using lognormal diffusion.
method Developed a jump-diffusion model and reduced complexity of pricing algorithms.
result Reduced complexity of European option pricing from O(n^3) to O(n ln n).
Deep learning improves option pricing in incomplete markets.
problem Optimal pricing and hedging in incomplete jump diffusion markets.
method Stackelberg game approach, deep learning (feedforward and LSTM networks).
result Deep learning algorithm outperforms traditional methods in incomplete markets.
Study on hedging CVA in jump-diffusion setting using Monte Carlo simulations.
problem Hedging Credit Valuation Adjustment (CVA) in financial portfolios.
method Monte Carlo simulation in Black-Scholes and Merton jump-diffusion settings.
result Hedging CVA is crucial for stable trading strategies, especially in jump-diffusion settings.
Hybrid model outperforms benchmarks in financial forecasting.
problem Robust asset price forecasting in finance.
method Combining LSTM with Neural Levy Processes using Grey Wolf Optimizer and ANN calibration.
result Hybrid model outperforms base LSTM and other models.
This paper extends static hedging for European options over multiple maturities.
problem Hedging European options over multiple time periods.
method Developed a spanning relation for multiple shorter-term options using a Markovian framework.
result Demonstrated a practical implementation using Gaussian Quadrature for finite sets of shorter-term options.
Compact method for option pricing under jump-diffusion models.
problem Pricing European and American options with jumps.
method Compact finite difference method using Crank-Nicolson Leap-Frog scheme.
result Fourth-order convergence rate achieved with smoothing operators.
Study markets without safe assets, deriving option pricing equations.
problem No riskless asset in financial markets.
method Derive Black-Scholes-Merton equations for various risky asset dynamics.
result Option pricing equations for different risky asset dynamics.
ROMs speed up option pricing under stochastic volatility and jump-diffusion models.
problem Efficiently pricing European and American options under complex stochastic models.
method Reduced order modeling using POD and penalty method for early exercise constraints.
result Pricing with ROMs is orders of magnitude faster than full order models.
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.
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strik…
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.
The paper predicts cryptocurrency prices using a path-dependent Monte Carlo simulation.
problem Forecasting cryptocurrency prices with volatility and jumps.
method Merton's jump diffusion model with machine learning, traditional, and statistical methods.
result Introduced a path-dependent Monte Carlo simulation for cryptocurrency price prediction.
A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion modelsq-fin.CP
New deep learning method for option pricing in jump-diffusion models.
problem Option pricing in jump-diffusion models with high-dimensional assets.
method Implicit-explicit minimizing movement time-stepping approach using deep ANNs.
result Consistent and asymptotically correct solutions for large underlyings.
We derive error estimates for multinomial approximations of American options in a multidimensional jump--diffusion Merton's model. We assume that the payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates for such type of approximations were not obtained before. Our main tool is the strong approxi…
Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamicsq-fin.MF
The article provides representations of exchange option prices under SVJD dynamics.
problem Modeling and pricing exchange options under stochastic volatility and jumps.
method Develops representations for European and American exchange options using SVJD dynamics and equivalent martingale measures.
result Derives integro-partial differential equations and representations for exchange option prices.
Proposes MLEs for MMJDM with EM-algorithm.
problem Estimating stock prices with varying drift and volatility.
method EM-algorithm for MLEs of MMJDM.
result Validated with simulated data and fitted to Amazon and Netflix stock prices.
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…
Hermite Polynomial-based Valuation of American Options with General Jump-Diffusion Processesq-fin.CP
New method uses Hermite polynomials for American option valuation.
problem Valuation of American options with complex jump-diffusion dynamics.
method Hermite polynomial expansions of transition density and early exercise premium.
result Converging approximations to true option prices and exercise boundaries.
The aim of this chapter is to show how option prices in jump-diffusion models can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial integro-differential equation (PIDE) in one-dimension for the American put and the European va…
A new method for pricing exchange options under stochastic volatility and jumps.
problem Pricing European and American exchange options with stochastic volatility and jumps.
method Equivalent martingale measure, numeraire choice, integral transforms, Kolmogorov backward equation, integral equations.
result Reduced exchange option pricing to a one-dimensional problem of a call option.
New methods estimate Asian option prices more efficiently.
problem Estimating the price of discretely monitored Asian options.
method General multilevel Monte Carlo methods.
result Estimates with standard deviation in expected time.
The paper values and hedges EPS products with jumps and default risks.
problem Valuation and risk management of EPS products under financial crises and default risks.
method Developed pricing frameworks using jump-diffusion and default models, derived closed-form formulas, and analysed hedging strategies.
result Quantified residual losses from counterparty default risk and defined default-adjusted premiums.
This paper develops a novel numerical method for pricing American options in a two-asset jump-diffusion model.
problem Pricing American options under correlated two-asset jump-diffusion models using finite difference methods often fails to preserve monotonicity and accurately discretize jump integrals.
method Introduces a novel monotone integration scheme to solve 2-D Partial Integro-Differential Equations (PIDEs) efficiently and accurately.
result The proposed method ensures convergence to the viscosity solution of the variational inequality and is both -stable and consistent.
Combines option pricing and portfolio theory for optimal hedging.
problem Optimal hedging of European options in various price dynamics.
method Derives optimal holdings and unhedged risk for different price dynamics.
result Derives solutions for various price dynamics including binomial, diffusion, volatility, volatility-of-volatility, and jump diffusion.
Modeling financial information flows using random switches.
problem Understanding how new information sources affect financial markets.
method Modeling continuous-time information flows with random switches and Lévy bridges.
result The model captures complex information dynamics and can price financial options.
The current research on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite of their pronounced effect on the tail of the loss distribution. Here, we take a …
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generaliz…
A new method uses Gaussian processes and deep kernel learning to price high-dimensional American options efficiently.
problem Challenges in pricing high-dimensional American options, especially with excessive computational costs.
method Modified Gaussian process regression with deep kernel learning and sparse variational Gaussian processes.
result The method outperforms least squares Monte Carlo in high-dimensional scenarios, especially with Merton's jump diffusion model.
Efficiently simulates jump diffusion bridge paths without discretization error.
problem Efficient simulation of jump diffusion bridge sample paths.
method Develops a mathematical framework to simulate finite-dimensional sample path skeletons.
result Simulates (jump) diffusion bridge sample paths without discretization error.
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 challenges the notion that asset return doesn't affect Black-Scholes-Merton model.
problem The role of asset return in the Black-Scholes-Merton model.
method Refutation of the claim through simplified stochastic calculus approach.
result The expected rate of return of the underlying asset does affect the Black-Scholes-Merton model.
Study evaluates cryptocurrency option pricing models, finds Kou and Bates models perform best.
problem High volatility and low liquidity in cryptocurrency futures contracts make traditional option pricing models unreliable.
method Calibrated and evaluated the performance of six option pricing models (Black-Scholes, Merton Jump Diffusion, Variance Gamma, Kou, Heston, and Bates) on BTC and ETH futures options.
result Kou and Bates models achieve the lowest pricing errors, with Kou outperforming Bates for BTC and ETH options respectively.
Polynomial Jump-Diffusion Modelsq-fin.MF
Develops a new mathematical framework for financial asset pricing.
problem Financial asset pricing models with excess log returns.
method Polynomial jump-diffusions in a semimartingale context, moment expansions.
result Shows preservation of polynomial property under transformations and Lévy time change.
The study compares Fourier-based pricing methods, identifying the most efficient and accurate.
problem Comparing CPU effort and pricing biases of Fourier-based implementations.
method Numerical analysis of seven Fourier-based implementations, focusing on truncation and discretization errors.
result The multi-strike version of the COS method is notably faster, and the strike-optimized Carr Madan's formula is both faster and more accurate.
Researchers find a timing error in Black-Scholes-Merton option pricing model.
problem Timing error in Black-Scholes-Merton option pricing model.
method Discovered a timing mistake in Merton's 1971 model and showed misspecification in continuous and discrete time.
result Invalidates seminal contributions to the literature including Black-Scholes (1973) and Merton (1971).
Solves the Merton investment-consumption problem using a new approach.
problem Infinite-horizon Merton investment-consumption problem in a constant-parameter Black-Scholes-Merton market.
method Simple and elegant argument involving a stochastic perturbation of the utility function.
result Overcomes complications in existing primal verification proofs.
Paper presents an analytical solution to Merton Garman model using symmetries.
problem Developing an analytical solution to the Merton Garman model.
method Perturbation theory around an exact solution with Galilean symmetry.
result Perturbative solution performs well compared to Monte Carlo simulations.
Paper uses Gibbs sampler with jump diffusion for European option pricing.
problem Estimating market parameters for jump diffusion models in option pricing.
method Gibbs sampler applied to jump diffusion model for estimating drift, volatility, jump intensity, and occurrence.
result Demonstrates impact of jump effects on European call option and annuity pricing.
Quantum Encoding and Analysis on Continuous Time Stochastic Process with Financial Applicationsquant-ph
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.
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
problem Improving prediction of default portfolios using complex models.
method Applying Merton model with log-normal intensity function to Poisson process, discussing temporal correlation effects.
result Power decay model provides better generalization for long-term default portfolio data.
Developed Merton's model for public companies using observed liabilities.
problem Estimating default risk for public companies.
method Campbell and Shiller's approximation method for risk-neutral values and default probabilities.
result Formulas and ML estimators for public companies' default probabilities.