The study extends asset pricing models to include time-dependent volatility and age-dependent regime switching.
problem Asset pricing in a market with time-varying interest rates and volatilities.
method Extension of Markov-modulated models to semi-Markov processes with age-dependent and time-dependent volatility.
result Option pricing in the extended model is equivalent to solving an integral equation.
This paper presents a methodology to introduce time-dependent parameters for a wide family of models preserving their analytic tractability. This family includes hybrid models with stochastic volatility, stochastic interest-rates, jumps and their non-hybrid counterparts. The methodology is applied to Heston's model. A …
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on how to further improve the calibration procedure.
A new model adapts Hurst parameter in real-time for volatility forecasting.
problem Capturing volatility dynamics and clustering in financial markets.
method Rough Bergomi model with EWMA-driven time-dependent Hurst parameter.
result Empirical validation shows superior performance in diverse asset classes.
Path integral method calculates PDBS option prices with time-dependent parameters.
problem Pricing proportional double-barrier step options with time-dependent interest rates and volatilities.
method Path integral method applied to a quantum mechanical analogy of barrier options.
result Derivation of pricing kernel for PDBS options with time-dependent parameters.
This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics dVt=κt(θt−Vt)dt+λtVtdBt. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, e…
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.
The paper approximates rough lognormal model using Markovian processes.
problem Modeling rough lognormal volatility in financial markets.
method Applying Markovian approximation to fractional Brownian motion (DO process) to lognormal volatility model.
result Uniformly good approximation of fractional BM for all Hurst exponents H ∈ [0,1].
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relati…
Closed-form solution found for American put option boundary.
problem Finding the optimal exercise boundary for American put options.
method Three models of stock price dynamics with time-dependent parameters, leading to a closed-form solution for the exercise boundary.
result Explicit closed-form solution for the optimal exercise boundary of American put options.
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and…
Solves utility maximization with uncertainty in drift and volatility.
problem Maximizing terminal wealth with uncertainty in stock drift and volatility.
method Explicit solutions for utility maximization under Knightian uncertainty.
result Solves robust optimization problems with various utility functions.
Develops semi-closed form solutions for barrier and American options on time-dependent OU process.
problem Valuation of barrier and American options on a time-dependent Ornstein-Uhlenbeck process.
method Semi-closed form solutions involving numerical solution of Fredholm equations and integration of Jacobi theta functions.
result Method is more efficient than backward finite difference method and can be as efficient as forward finite difference solver with better accuracy and stability.
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.
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major financial indices. We find in all these data sets a very similar behavior that …
We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the sho…
Study finds time-varying volatility and multifractality in Bitcoin, with asymmetry weakening as market efficiency increases.
problem Investigating time-varying properties of Bitcoin's volatility and multifractality.
method Rolling window method to examine daily Bitcoin returns and multifractal properties over time.
result Volatility asymmetry in Bitcoin changes over time, becoming less pronounced as market efficiency increases.
The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.
problem Large deviation principles for stochastic volatility models with reflection.
method Sample path and small-noise large deviation principles for the log-price process.
result Asymptotic behavior of binary barrier options and call prices in the small-noise regime.
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.
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.
New method solves SLV models faster using Lie algebra.
problem Local stochastic volatility models.
method Wei-Norman factorization method and Lie algebraic techniques.
result Reduces time-dependent SLV models to autonomous PDEs.
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partitio…
This work extends variance reduction for path-dependent derivatives to affine stochastic volatility models.
problem Pricing path-dependent derivatives in affine stochastic volatility models.
method Prove large deviations principle, apply Esscher transform, use Varadhan's lemma.
result Numerical efficiency demonstrated on Heston model with and without jumps.
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable and only the price is known. Diffusion theory has many common points with the res…
A new volatility model calibrates SPX & VIX smiles with 6 parameters.
problem Joint calibration of SPX and VIX smiles with a simple model.
method Quintic Ornstein-Uhlenbeck volatility model with polynomial volatility process.
result Remarkable joint fits of SPX-VIX smiles with only 6 parameters.
In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated, which is unrealistic. It turns out that if a non-zero correlation is included in …
We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small…
Researchers develop explicit approximations for European put options in stochastic volatility models.
problem Developing accurate approximations for European put option prices in stochastic volatility models.
method Exploits expansions of the mixing representation of the put option price using Malliavin calculus.
result Explicit formulas for option prices and error bounds are derived, with closed-form solutions under piecewise-constant parameters.
New stock market index captures market chaos and volatility.
problem Capturing the chaotic nature of stock market volatility.
method Tensor-based embedding of stock market information, time-dependent dynamical system model.
result Bidirectional causal relation between realized and implied volatility.
We develop closed-form approximations for European put options under stochastic volatility models.
problem Tackling the pricing of European put options under stochastic volatility models with time-dependent parameters.
method Using a second-order Taylor expansion around the mean of the argument, we write the option price as an expectation of a Black-Scholes formula. We then simplify the resulting expectations and derive closed-form pricing formulas under the assumption of piecewise-constant parameters.
result We derive closed-form pricing formulas and bounds on the remainder term generated by the Taylor expansion, showing that the errors are well within acceptable ranges for practical applications.
Entropy measure quantifies volatility correlation and risk diversity in asset portfolios.
problem Quantifying volatility correlation and risk diversity in asset portfolios.
method Kullback-Leibler cluster entropy DC[P∥Q] for empirical and model probability distributions of realized volatility. result Portfolio built on diversity indexes derived from Kullback-Leibler entropy measure of realized volatility exhibits better performance.
We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the variance, find an analytic formula for the time-dependent probability distribution of…
The study finds solutions to a financial equation related to volatility.
problem Finding solutions to a financial equation related to volatility.
method Using a zero-curvature condition and soliton theory, the study derives a variant of the Harry Dym equation and finds its travelling wave solutions.
result A family of travelling wave solutions to a variant of the Harry Dym equation is found.
This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and st…
The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the use of the numerical scheme for Heston or SABR type stochastic volatility model…
The purpose of this paper is to construct the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility depending on the option price. We review a method how to transform the problem into a solution of a time depending nonlinear parabolic equation defined on a fixed domain. R…
New SVM models correct mean of volatility processes to satisfy efficient market hypothesis.
problem Capturing complex market behavior while maintaining efficient market hypothesis.
method Propose mean-corrections for generalized Taylor SVM models.
result Models satisfy efficient market hypothesis and capture complex market behavior.
The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A motivation for studying the nonlinear Black--Scholes equation with a nonlinear vola…
This paper improves SABR/LMM for better practical use in global banks.
problem Inflexibility of existing SABR/LMM models.
method Develops a comprehensive SABR/LMM model with time-dependent skew and smile.
result Provides a flexible and practical SABR/LMM model for global banks.
Researchers find the optimal exercise time for American options using a specific type of diffusion process.
problem Finding the optimal time to exercise American options with a time-dependent Ornstein-Uhlenbeck process.
method Optimal stopping problem, probabilistic arguments, non-linear Volterra-type integral equation, Picard iteration algorithm.
result They derive a non-linear Volterra-type integral equation and prove the exercise boundary's Lipschitz continuity and differentiability almost everywhere.
Paper proposes an efficient method for pricing FX options with stochastic volatility and interest rates.
problem Pricing foreign exchange options in a model with stochastic interest rates and volatility.
method Developed a RBF--FD method to solve the associated PDE numerically.
result Demonstrates efficiency in terms of accuracy and computational cost for pricing FX options.
The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law prob…
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.
WamOL uses PINNs to efficiently calibrate IVS from sparse data.
problem Calibrating time-dependent IVS from sparse market data.
method Physics-Informed Neural Networks (PINNs) with adaptive reweighting.
result WamOL outperforms in calibrating intraday IVS from uneven data.
A new method estimates time-varying parameters without Kalman filtering.
problem Estimating time-varying parameters in models with abrupt changes or structural breaks.
method Regression-based or GLS-based approach that avoids Kalman filtering.
result Smoothed estimates identical to Kalman-smoothed estimates, with negligible pile-up problem.
Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract underlying asset follows a geometric Brownia…
Study of coupled Hawkes processes with rough-volatility limits.
problem Understanding coupled Hawkes processes with rough-volatility limits.
method Proving weak convergence of rescaled intensity vector to stochastic Volterra equations.
result Limiting components exhibit different degrees of roughness and cross-decorrelation law.
The paper uses deep learning to detect asset price bubbles in tech stocks.
problem Detecting financial asset price bubbles using deep learning.
method Deep learning techniques applied to call option prices for financial asset bubbles detection.
result The proposed deep learning algorithm provides a theoretical foundation for positive and continuous stochastic asset price processes.