Develops a semi-analytic method for auto-callable accrual notes valuation.
problem Valuation of auto-callable structures with accrual features subject to barrier conditions.
method Extends recent studies of multi-assessed binaries to time-dependent parameters, using a semi-analytic approach.
result The semi-analytic approach is more advantageous for high precision valuation compared to Monte Carlo methods.
Efficient semi-analytic methods for pricing double barrier options with time-dependent parameters.
problem Pricing and calibration of double barrier options with time-dependent parameters.
method Two approaches: General Integral transform method and Heat Potential method.
result Semi-analytic techniques are more efficient for pricing double barrier options than traditional numerical methods.
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.
Semi-analytical approach for optimal wealth management contributions.
problem Optimizing contributions to achieve a financial goal with uncertain returns.
method Controlled backward Kolmogorov equation and Schrodinger equation solution.
result Semi-analytical solutions for efficient frontiers in control space.
New method for pricing barrier options in time-dependent λ-SABR model.
problem Pricing barrier options in the time-dependent λ-SABR model.
method Modified integral transform method and Fourier-Bessel series solution.
result Semi-analytical solution for barrier options in λ-SABR model.
A new model prices Bermudan swaptions without calibration.
problem Calibration of Bermudan swaptions models.
method Semi-analytical pricing model using swap rates and correlations.
result No product-specific calibration required.
New method for pricing SOFR futures options, solving both American and Asian exercise styles.
problem Lack of pricing models for SOFR futures options post-LIBOR transition.
method Developed a new version of the GIT method to solve semi-analytically.
result Obtained option prices, exercise boundaries, and Greeks for American and Asian options.
A new method solves SABR and Heston equations for option pricing.
problem Solving SABR and Heston equations for option pricing.
method Semi-analytical method based on path integrals, integrating analytically one set and numerically the other using Monte-Carlo.
result Compact expressions for correlated stochastic variables, efficient for Vanilla and Asian options.
Accurate approximations for Gaussian moments through sigmoid/softmax mappings.
problem Accurate computation of moments of Gaussian variables through sigmoid/softmax functions.
method Semi-analytical approximations involving numerical adjustments of parametric forms.
result Highly accurate approximations (5% error at most).
Developing a semi-analytical approximation for general default intensity models
problem Accurate and efficient pricing of default intensity models
method Path-integral formalism
result Accurate results for the Black-Karasinski model
It is shown that, in dimensions <8, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
This work provides a semi-analytic approximation method for decoupled forwardbackward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around the small-variance limit …
Develops a semi-analytic resampling method for Lasso regression.
problem Statistical fluctuations and high computational cost in Lasso resampling.
method Semi-analytic message passing algorithm based on state evolution analysis.
result Significant reduction in computational time and improved inference accuracy.
A multi-dimensional extension of the structural default model with firms' values driven by diffusion processes with Marshall-Olkin-inspired correlation structure is presented. Semi-analytical methods for solving the forward calibration problem and backward pricing problem in three dimensions are developed. The model is…
The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is non-negative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical solution for European options.…
Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, thou…
Develops a new method for pricing barrier options in time-dependent Heston model.
problem Pricing barrier options in a time-dependent Heston model with stochastic volatility.
method General Integral Transforms (GIT) method for a two-dimensional integral representation.
result Shows that the GIT method can be extended to two drivers with inhomogeneous correlation.
Efficient hybrid method for pricing barrier options with stochastic volatility.
problem Valuation of barrier options on assets with stochastic volatility.
method Combining Monte Carlo simulation and semi-analytical heat potential method.
result Our method provides better accuracy and is orders of magnitude faster than existing methods.
Study efficient pricing for barrier options in stochastic-volatility models with leverage correction.
problem Barrier options are sensitive to volatility dynamics, especially leverage, making accurate pricing difficult.
method Developed a class of continuous-path stochastic-clock volatility models and a systematic small-ρ expansion to incorporate leverage.
result Transform-only pricing formulas for barrier derivatives are fast and numerically stable, even for negative leverage.
New method for pricing American options in time-dependent models, improving accuracy and efficiency.
problem Pricing American options in time-dependent models with improved accuracy and efficiency.
method Semi-analytical pricing using a nonlinear Volterra integral equation and numerical methods.
result Improved accuracy and efficiency in pricing American options compared to forward finite difference solvers.
Paper presents a new method for pricing American options with hybrid dividends.
problem Complex pricing of American options with discrete and continuous dividends.
method Uses the GIT method to transform pricing problem into an integral equation.
result The GIT method provides a powerful alternative to traditional numerical techniques.
Efficiently calibrates Heston model with time-varying parameters for financial derivatives.
problem Calibrating Heston model with time-dependent parameters.
method Simple and numerically efficient approach using semi-analytical formulas and Gauss-Kronrod quadrature.
result Improves Heston model's performance in selected cases.
Study the hitting density of Ornstein-Uhlenbeck process, providing semi-analytical solutions.
problem First passage hitting density of Ornstein-Uhlenbeck process.
method Two complementary formulations, heat potentials, linear Volterra integral equations, Abel equation approximation, numerical solutions.
result Semi-analytical solutions for hitting density of Ornstein-Uhlenbeck process.
Paper examines floating exercise boundaries for American options in time-inhomogeneous models.
problem Floating exercise boundaries in time-inhomogeneous models with negative interest rates or yields.
method Semi-analytical approach for pricing American options.
result Specialized pricing methodologies are required for models with floating exercise boundaries.
New method for superhedging without assuming continuous claims.
problem Superhedging without assuming upper semicontinuous contingent claims.
method Established a generalized duality for model-free superhedging using Choquet's capacitability theorem.
result Generalized duality for superhedging given marginal distributions without continuity assumptions.
Study on stock loans with forced liquidation.
problem Sensitivity of stock loan contracts to model parameters.
method Derive semi-analytic solution for stock loan with forced liquidation.
result Sensitivity of stock loan contracts to model parameters.
Analyzes multifractality caused by fat-tailed distributions in time series.
problem Quantifying multifractality induced by fat-tailed distributions in time series data.
method Examines different types of fat-tailed distributions using Tsallis statistics and nonextensive analysis.
result Developed semi-analytical formulas to distinguish true multifractality from spurious multifractality.
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on dividend-paying-stocks. Moreover, the barriers may be monitored either continuously or disc…
We simplify no-arbitrage bounds calculation for financial derivatives.
problem Calculating robust replication of forward-start straddles from market data.
method Proposed a discretisation scheme and a new linear programming approach to the dual problem.
result Reconciled two approaches: semi-infinite linear programming and optimal martingale measures.
We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasiński interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Loève expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for nu…
We examine the dynamics of the bid and ask queues of a limit order book and their relationship with the intensity of trade arrivals. In particular, we study the probability of price movements and trade arrivals as a function of the quote imbalance at the top of the limit order book. We propose a stochastic model in an …
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and accurate predictions for the value of a large class of options, including those wi…
We develop a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework. Utilizing the class of affine processes, this model produces positive LIBOR rates and spreads, while the dynamics are analytically tractable under defaultable forward measures. This leads to explicit formul…
Review of Gerber-Shiu function for practical actuarial science.
problem Difficulty in numerical approximation and statistical inference of Gerber-Shiu function.
method Comprehensive review of formulations, surplus processes, numerical methods, and statistical inference.
result Enhanced understanding and practical guide for Gerber-Shiu function.
We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consist…
Developed a method to estimate PLRNNs from neural data, revealing dynamics of working memory.
problem Reconstructing neural dynamics from experimental data for computational analysis.
method Semi-analytical maximum-likelihood estimation using state space models.
result 5-state PLRNN model captures essential working memory dynamics.
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.
A three-dimensional extension of the structural default model with firms' values driven by correlated diffusion processes is presented. Green's function based semi-analytical methods for solving the forward calibration problem and backward pricing problem are developed. These methods are used to analyze bilateral count…
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
Study cliquet options in a jump-diffusion model with Lévy processes.
problem Pricing cliquet options in a complex financial model with jumps.
method Developed semi-analytic expressions using Lévy process distribution and Fourier transform.
result Inferred semi-analytic expressions for cliquet option prices and derived Greeks.
Paper calibrates GARCH diffusion model for option pricing using PDE methods.
problem Lack of fast, semi-analytic solution for GARCH diffusion model option pricing.
method PDE-based finite difference solver for accurate calibrations.
result PDE calibration of GARCH diffusion model to SPX options.
Develops asset pricing models with mean field game theory for heterogeneous agents.
problem Tackles equilibrium asset pricing in incomplete markets with heterogeneous agents.
method Uses mean field game theory and mean field backward stochastic differential equations (BSDEs).
result Derives equilibrium risk premium and shows market clearing in the large population limit.
Develops ML method for solving financial equations.
problem Solving financial equations efficiently and accurately.
method Combines semi-analytical and numerical techniques.
result Significantly faster and more accurate solutions.
Improved neural network surrogates for ICF using manifold and cycle consistency.
problem Modeling and predicting complex physical processes in inertial confinement fusion.
method Training neural network surrogates that are consistent with the physical manifold and cyclically consistent.
result Surrogates are superior in predictive performance, more resilient to sampling artifacts, and more data efficient.
New method for pricing discrete Asian and Lookback options under Heston model.
problem Efficient pricing of discrete Asian and Lookback options under Heston model.
method Data-driven approach using artificial neural networks and stochastic collocation points.
result High accuracy and significant computational time reduction compared to classical methods.
We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters. A successful joint calibration t…
The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.
problem Asset pricing in a market with partial observation and heterogeneous agents.
method Mean field game theory, exponential quadratic Gaussian framework, Kalman-Bucy filtering theory.
result Characterization of equilibrium risk premium through mean field BSDE and construction of unobservable risk premium process.
Robust index tracking strategy improves performance during market downturns.
problem Optimizing asset management with uncertainty in asset distributions.
method Forward-looking approach using Bregman divergence for robust optimization.
result The robust index tracking strategy outperforms the non-robust strategy during market downturns.