Empirical evidence suggests that fixed income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While [1] showed that no two-factor Cox-Ingersoll-Ross (CIR) model can exhibit USV, it has been unknown to date whether CIR models …
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48 results for “CIR++”
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.
ACI identifies cause-effect relationships and causal influence ranges in dynamical systems.
problem Detecting and quantifying causal influence ranges in complex systems.
method Bayesian data assimilation and assimilative causal inference (ACI) to trace causes back from observed effects.
result Mathematically rigorous formulations of forward and backward causal influence ranges (CIRs) for nonlinear dynamical systems.
We introduce MosAIc, an interactive web app that allows users to find pairs of semantically related artworks that span different cultures, media, and millennia. To create this application, we introduce Conditional Image Retrieval (CIR) which combines visual similarity search with user supplied filters or "conditions". …
CIR method constructs efficient prediction intervals with guaranteed coverage.
problem Efficiently constructing near-minimal prediction intervals with guaranteed coverage.
method Conditional Interquantile Regression (CIR) and CIR+ (enhanced version).
result Optimal balance between predictive accuracy and computational efficiency.
Proposes a new model to handle negative interest rates using CIR framework.
problem Negative interest rates and their impact on financial markets.
method Develops a new model based on Cox-Ingersoll-Ross (CIR) framework without shifting market rates.
result The model accurately reproduces market term structures and swaption prices.
It is well known that the Cox-Ingersoll-Ross (CIR) stochastic model to study the term structure of interest rates, as introduced in 1985, is inadequate for modelling the current market environment with negative short interest rates. Moreover, the diffusion term in the rate dynamics goes to zero when short rates are sma…
Stochastic delay differential equations (SDDE's) have been used for financial modeling. In this article, we study a SDDE obtained by the equation of a CIR process, with an additional fixed delay term in drift; in particular, we prove that there exists a unique strong solution (positive and integrable) which we call fix…
We propose a robust and stable lattice method which permits to obtain very accurate American option prices in presence of CIR stochastic interest rate without any numerical restriction on its parameters. Numerical results show the reliability and the accuracy of the proposed method.
Proposes a new model for negative interest rates that fits market data closely.
problem Negative interest rates and their impact on financial models.
method Uses a deterministic-shift extension of two independent CIR processes with Gram-Charlier expansion for swaption pricing.
result The model produces close swaption prices to market data.
New high-order approximations for CIR process using random grids.
problem Approximating the Cox-Ingersoll-Ross process with high order.
method Combining discretization schemes on different random grids.
result Weak approximations of order for all .
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 …
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 …
An Accurate Discretized Approach to Parameter Estimation in the CKLS Model via the CIR Frameworkstat.AP
The paper improves parameter estimation for interest rate models using the CIR and CKLS frameworks.
problem Improving parameter estimation for interest rate models.
method Employing Euler-Maruyama discretization to transform SDEs into linear regression problems.
result Established strong consistency and asymptotic normality of estimators for drift and volatility parameters.
I present the technique which can analyse some interest rate models: Constantinides-Ingersoll, CIR-model, geometric CIR and Geometric Brownian Motion. All these models have the unified structure of Whittaker function. The main focus of this text is closed-form solutions of the zero-coupon bond value in these models. In…
CIR method preserves relation for case-control studies.
problem Learning low-dimensional structure in case-control studies.
method Contrastive inverse regression (CIR) on Stiefel manifold.
result CIR outperforms other methods for high-dimensional data.
Corporate Bond Yield Curve Modeling: A Rating-Based Regime-Switching Generalized CIR Approachq-fin.PR
Develops a new model to better predict corporate bond yields.
problem Persistent shifts in interest rates undermine single-regime models.
method Regime-switching generalized CIR model with two-state short-rate process and credit factors.
result The model improves joint curve fit and delivers interpretable probabilities.
New model predicts credit spreads using stochastic CIR++ intensities.
problem Lack of continuous stochastic credit spread models and limited term structure models.
method Stochastic CIR++ model for default intensities in risk-neutral space.
result Model produces realistic credit spread term structure curves and consistent diffusion over time.
Study applies financial models to predict COVID-19 pandemic.
problem Predicting the spread of COVID-19 using financial market models.
method Implemented ARIMAX and Cox-Ingersoll-Ross (CIR) models, using Euler-Maruyama and Milstein methods for CIR*.
result CIR* framework provides accurate forecasts for pandemics.
Characterizes term structure models driven by Lévy processes.
problem Modeling non-negative short rates with Lévy processes.
method Analyzes affine term structure models driven by independent Lévy martingales.
result All possible solutions of the models can be obtained using stable processes.
We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of sto…
We investigate the joint description of the interest-rate term stuctures of Italy and an AAA-rated European country by mean of a --here proposed-- correlated CIR-like bivariate model where one of the state variables is interpreted as a benchmark risk-free rate and the other as a credit spread. The model is constructed …
This paper extends barrier option pricing to CIR and CEV models using semi-closed form solutions.
problem Pricing barrier options in time-dependent CEV and CIR models.
method Developed two new methods: Bessel potentials and generalized integral transform, both applied to Bessel processes.
result The methods provide more accurate and stable pricing compared to finite difference methods, especially for small and large maturities.
In this we paper we recast the Cox--Ingersoll--Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning with the ``squared Gaussian representation'' of the CIR model, we find a simple expression for the fundamental random variable X. By use of techniques fro…
The paper calibrates the G2++ model using deep learning for interest rates.
problem Calibrating interest rate models with deep learning.
method Calibrated G2++ model using Neural Networks trained on covariances and correlations of Zero-Coupon and Forward rates.
result Deep learning calibration outperforms classic methods.
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and switching problems admit …
Credit Valuation Adjustment (CVA) pricing models need to be both flexible and tractable. The survival probability has to be known in closed form (for calibration purposes), the model should be able to fit any valid Credit Default Swap (CDS) curve, should lead to large volatilities (in line with CDS options) and finally…
On the singular limit of solutions to the CIR interest rate model with stochastic volatilityq-fin.CP
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of …
Developed a simulation method for 3/2 stochastic volatility model.
problem Pricing options in the 3/2 stochastic volatility model.
method Explicit weak solution for the 3/2 model, using inverse CIR process property.
result Simulation algorithm performance comparable to other methods.
The paper derives closed-form approximations for mean-reverting SABR models and calibrates them to equity volatilities.
problem Calibration of mean-reverting SABR models to equity volatilities.
method Derive closed-form approximations using a CIR process for volatility, lognormal process for volatility, and CIR process for squared volatility. Calibrate to empirical volatilities using a computer algebra system.
result Calibrated mean-reverting SABR models provide excellent fits to equity volatilities with only five parameters per surface.
New financial price model using earning yield derived from CIR process.
problem Excess volatility and equity premium puzzles in financial markets.
method Proposes a new financial price process based on earning yield and Cox-Ingersoll-Ross (CIR) process.
result Derives analytically stylized facts of financial prices and returns, including power law distribution of returns and fat-tailed distribution of prices.
We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be cha…
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.
Asymptotic Separability of Diffusion and Jump Components in High-Frequency CIR and CKLS Modelsq-fin.ST
Robustly detects jumps in high-frequency CIR and CKLS models.
problem Jump detection in high-frequency jump-diffusion processes.
method MDPDE-based robust estimators for drift and diffusion coefficients.
result Maximum of normalized residuals converges to Gumbel distribution.
Improved MLMC method for barrier options with non-Lipschitz coefficients.
problem Efficiency improvement for barrier option pricing with non-Lipschitz diffusion.
method Interpolated Drift Implicit Euler MLMC method, Lamperti transformation, Brownian bridge technique.
result Improved efficiency of MLMC for barrier options with non-Lipschitz coefficients.
The paper studies affine models driven by independent Lévy processes and their calibration.
problem Characterizing and classifying affine models driven by Lévy processes.
method Analyzing the short rate equation with independent Lévy processes and characterizing the generator.
result A precise form of the generator and classification of affine models with canonical representations.
Pricing defaultable debt: some exact resultscond-mat.stat-mech
In this letter, I consider the issue of pricing risky debt by following Merton's approach. I generalize Merton's results to the case where the interest rate is modeled by the CIR term structure. Exact closed forms are provided for the risky debt's price.
The aim of this paper is to propose a new methodology that allows forecasting, through Vasicek and CIR models, of future expected interest rates (for each maturity) based on rolling windows from observed financial market data. The novelty, apart from the use of those models not for pricing but for forecasting the expec…
Develops high-order approximations for financial models, proving convergence and regularity.
problem Challenges in approximating and regularizing the Heston model due to its square root diffusion term.
method Random grid technique, Cox-Ingersoll-Ross (CIR) process, log-Heston process, PDE analysis.
result Achieves weak approximations of any order for smooth test functions in the Heston model, extending to log-Heston process.
The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process of a diffusion state variable driving default intensity and a default indicator process and time change it wi…
Two methods improve simulation of European call options under Heston model.
problem Efficient simulation of European call options under Heston model.
method Two strongly convergent and positivity-preserving methods for Cox-Ingersoll-Ross process under Lamperti transformation: truncated Euler and backward Euler methods.
result Explicit truncated Euler method is computationally effective and robust under high volatility, while implicit backward Euler method provides high accuracy and stability.
We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call non-linear affine processes. This is done as follows: given a set of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programm…
The study examines Hawkes processes and their long-term behavior.
problem Understanding the long-term behavior of Hawkes processes.
method Proving functional limit theorems under various conditions on the dispersion of child events.
result Functional limit theorems hold for Hawkes processes with different levels of child event dispersion.
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
problem Limited exploration of non-Gaussian diffusion models and corresponding Tweedie's formulae.
method Extended Tweedie's formulae to geometric Brownian motion, squared Bessel, and Cox-Ingersoll-Ross processes.
result Demonstrated potential of non-Gaussian models in image and financial time series generation.
In this paper, the valuation of European and path-dependent options in foreign exchange (FX) markets is considered when the currency exchange rate evolves according to the Heston model combined with the Cox-Ingersoll-Ross dynamics for the stochastic domestic and foreign short interest rates. The mixed Monte Carlo/PDE m…
This paper considers a mortgage contract where the borrower pays a fixed mortgage rate and has the choice of making prepayment. Assume the market interest follows the CIR model, a free boundary problem is formulated. Here we focus on the infinite horizon problem. Using variational method, we obtain an analytical soluti…
Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around . The Fourier transform techniques reduces calculation of probability distributions and option prices to evaluation of integrals whose i…
Paper approximates XVA for European contingent claims using BSDEs and polynomial expansions.
problem Computing Value Adjustment of European contingent claims with nonlinear features.
method Reduced-form approach, nonlinear Backward Stochastic Differential Equation (BSDE), change of numeraire, Taylor's polynomial expansion.
result Simple first-order approximation can be computationally efficient for CIR intensity model.