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.
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.
Defines a new integral for price paths with jumps.
problem Integrating with model-free price paths that include jumps.
method Defines integral G⋅S as a limit of simple integrals for adapted, càglàd processes and càdlàg price paths with jumps. result Defines a new integral for price paths with jumps.
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. 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.
The paper calculates prices for special options using mixed-exponential jumps.
problem Pricing special options in a mixed-exponential jump-diffusion model.
method Derive joint distributions of a mixed-exponential jump-diffusion process and its occupation times.
result Various joint distributions derived for pricing options.
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…
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.
Modified model predicts stock price jumps using Twitter sentiment.
problem Predicting stock price jumps based on market sentiment.
method Modified Levy jump-diffusion model with memory from Twitter sentiment, optimized with UKF.
result Algorithm provides good performance in identifying asset return trends.
Study pricing derivatives in markets with long-range dependence and jumps.
problem Deriving pricing formulas for derivatives in markets with long-range dependence and jumps.
method Developed a fractional integro-partial differential equation (PIDE) and used semigroup theory and finite-difference schemes for numerical solutions.
result Closed-form pricing formula for European options and numerical solution for general options.
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.
Study reveals jumps in crypto markets predict future prices.
problem Understanding jumps in high frequency digital asset markets.
method High frequency crypto data analysis, econometric modeling.
result Intra-day jumps significantly influence end of day returns.
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.
Paper presents fast methods for pricing energy derivatives using mean-reverting jump-diffusion models.
problem Pricing energy derivatives with mean-reverting and occasional spikes.
method Exact and fast simulation of spot price dynamics using Ornstein-Uhlenbeck and jump-diffusion processes.
result Apparent computational advantages of the proposed procedures for pricing Asian options, gas storages, and swings.
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.
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.
Paper develops semi-analytic method for American options in time-dependent jump-diffusion models.
problem Pricing American options in models with time-dependent and exponential jumps.
method Generalizes existing methods for barrier and American options to handle arbitrary time dependencies and solves the problem through algebraic and Fredholm-Volterra equations.
result Presents a semi-analytic solution for American options in time-dependent jump-diffusion models with exponential jumps.
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 prices and replicates various financial contracts on a risky asset with stochastic volatility and jumps.
problem Pricing and replicating financial contracts on assets with stochastic volatility and jumps.
method Develops pricing and hedging formulas for various financial contracts, independent of the volatility process dynamics.
result Pricing and hedging formulas for financial contracts are derived without dependence on the volatility process dynamics.
Study on pricing rules for income streams with partial insider information.
problem Determining the value of partial information in pricing rules for income streams.
method Analyzes three types of agents with varying levels of jump information and derives explicit state price densities.
result Explicit formulas for pricing rules with different levels of jump information are provided.
The article uses jump-telegraph models to price zero coupon bonds and adjust convexity.
problem Pricing zero coupon bonds and adjusting for convexity in a short rate model.
method Markov-modulated model with jumps, jump-telegraph process, expectation hypothesis.
result Closed formulas for term structure and forward rates are derived.
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.
This paper extends Black-Scholes model for illiquid markets with jumps.
problem Pricing derivative securities in markets with jumps and illiquidity.
method Generalizes Frey-Stremme model for Levy process with jumps, derives nonlinear PDE, proposes numerical scheme.
result Shows influence of large traders and jump intensity on option prices.
The paper prices European options in a model with changing regimes and jumps.
problem Pricing European options in a model with changing regimes and jumps.
method A regime-switching jump diffusion model with semi-Markov process.
result The locally risk minimizing price of European options is found.
We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential Lévy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the implied volatility converges to a non-constant limiting shape, which is a function of …
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).
The paper extends the market price of risk for electricity swap contracts, incorporating jump risk.
problem Pricing electricity swap contracts with consideration of jump risk.
method Introducing a Merton type model with jumps and transferring to the physical measure, comparing arithmetic and geometric averaging.
result A decomposition of swap's market price of risk into classical and market price of risk components.
Study geometric step options with jumps, deriving pricing equations and characterizations.
problem Pricing geometric step options in markets with jumps.
method Symmetry and parity relations, partial integro-differential equations, ordinary integro-differential equations.
result Derive semi-analytical pricing results for geometric step options.
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.
Improved scheme for option pricing in stochastic volatility models with jumps.
problem Efficiently pricing options in models with stochastic volatility and jumps.
method Developed a high-order compact finite difference scheme for SVCJ models.
result Achieves fourth order convergence compared to standard schemes.
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.
Non-spanning identification of scheduled event risk in option pricing.
problem Separating continuous surface from scheduled jump in option pricing.
method Modeling FOMC decisions, CPI releases, and NFP reports as deterministic-time jumps in risk-neutral option pricing.
result Improves held-out event-spanning pricing with Gaussian and two-component mixture jumps.
Detects jumps in financial asset prices with U-shape volatility.
problem Identifying jumps in financial asset prices with varying volatility.
method Threshold method applied to five-minute log-returns.
result Visualized jumps and volatility patterns for Apple Inc. (AAPL) stock.
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.
The model outperforms other models in option pricing, especially for short-term implied volatility.
problem Improper calibration and pricing of exotic options in financial models.
method Stochastic volatility model with double-exponential jumps, Fourier pricing techniques.
result The model outperforms other models in fitting the short-term implied volatility smile and pricing exotic options.
Develops a PIDE framework for option pricing with stochastic volatility and jumps.
problem Option pricing under stochastic volatility and jumps.
method PIDE framework derived from Lévy-type process, implemented via finite-difference discretization with FFT for nonlocal jump operator, calibrated using GMM.
result Stochastic volatility accounts for most pricing improvement, reducing implied-volatility RMSE by 39% compared to Black-Scholes.
We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro-differential equations. Conditions are provided under which preservation of convexity holds, i.e. under which the value, calculated under a chosen martingale measure, …
Study uses neural networks to value Bitcoin options considering price jumps and sentiment.
problem Valuing Bitcoin options under price jumps and market sentiment.
method Bivariate jump-diffusion model, incorporating Google search sentiment, and artificial neural networks.
result Derives a closed formula for Bitcoin option pricing and validates using high-volatile stocks.
The paper models financial asset prices with jumps and evaluates European option prices using numerical methods.
problem Modeling and pricing European options with jumps in delayed stochastic systems.
method Existence, uniqueness, and positivity of solutions to delayed stochastic differential equations with jumps. Application of Fourier transformation for analytical pricing and Monte-Carlo simulation with a logarithmic Euler-Maruyama scheme for numerical approximation.
result The logarithmic Euler-Maruyama scheme provides a positive and convergent method for approximating the solution to the delayed stochastic differential equations with jumps.
Study reveals frequent price jumps in Bitcoin market, influenced by trader behavior and market structure.
problem Understanding price dynamics and trader behavior in the Bitcoin market.
method Analysis of Mt. Gox exchange database to study Bitcoin price movements at tick level.
result Jumps in Bitcoin prices are frequent and predictable, influenced by order flow imbalance and trader aggressiveness.
New model for electricity pricing captures mean reversion and jumps.
problem Capturing mean reversion and jumps in electricity market prices.
method Exponential functional of a jump Lévy process, partial integro-differential equation (PIDE), finite differences method.
result European option value is the unique viscosity solution of a PIDE.
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.
Study prices compound and extendible options using mixed fractional Brownian motion with jumps.
problem Pricing compound and extendible options under mixed fractional Brownian motion with jumps.
method Analytic formula derived under risk-neutral measure, applied to extendible options, discussed special cases, provided numerical results.
result An analytic formula for pricing compound options derived.
This paper examines the problem of pricing spread options under some models with jumps driven by Compound Poisson Processes and stochastic volatilities in the form of Cox-Ingersoll-Ross(CIR) processes. We derive the characteristic function for two market models featuring joint normally distributed jumps, stochastic vol…
Study parameter sensitivities in bond pricing models with jumps.
problem Analyzing the impact of parameters on bond pricing models with jumps.
method Theoretical analysis and MATLAB simulations of a Brownian motion and compound Poisson process.
result Explicit call price formula and verification of sensitivities.
The paper provides approximations for pricing Asian options using a mixed fractional Brownian motion with jumps.
problem Pricing Asian options under a mixed fractional Brownian motion with jumps.
method Approximate closed-form solutions for arithmetic Asian options and power options.
result Analytical formulas for pricing arithmetic Asian options and power options are derived.
Paper derives option pricing formula for SVJ models with jumps.
problem Option pricing for models with finite activity jumps.
method Generic decomposition and explicit approximation formulas for SVJ models.
result Improved computation efficiency and insight into volatility smiles.
The paper proves that certain price paths with jumps have consistent quadratic variation.
problem Understanding the quadratic variation of price paths with jumps in financial models.
method Proving the quadratic variation is consistent across different partitions of time.
result The quadratic variation of model-free price paths with mild jumps is consistent and independent of partitions.