Study identifies current coupons for mortgage-backed securities.
problem Identifying current coupons for Agency backed TBA Mortgage Backed Securities.
method Doubly stochastic factor model with prepayment intensities dependent on current and origination mortgage rates. Solves a degenerate elliptic, non-linear fixed point problem using Schaefer's theorem.
result Existence and explicit approximation of current coupons provided, with numerical examples showing good performance.
In this paper, we establish a market model for the term structure of forward inflation rates based on the risk-neutral dynamics of nominal and real zero-coupon bonds. Under the market model, we can price inflation caplets as well as inflation swaptions with a formula similar to the Black's formula, thus justify the cur…
Study uses causal machine learning to assess coupon campaign impact on retailer sales.
problem Assessing the causal effect of a coupon campaign on retailer sales.
method Causal machine learning algorithms, subgroup analysis, optimal policy learning.
result Only two coupon categories (drugstore and other food) have a significant positive impact on sales.
Researchers analyze betting odds and free coupons to find exploitable gains.
problem Determining if customers can exploit free coupons for guaranteed gains.
method Using desirability theory and the Choquet integral, they evaluate odds and free coupons.
result Customers can exploit free coupons for guaranteed gains under certain conditions.
Gaussian Process Regression improves damage assessment in structural health monitoring.
problem Inaccurate damage quantification in varying conditions and environments.
method Gaussian Process Regression models with Damage Indices for probabilistic damage assessment.
result The method provides probability-based decision-making for structural health monitoring.
Pricing formulae for defaultable corporate bonds with discrete coupons under consideration of the government taxes in the united model of structural and reduced form models are provided. The aim of this paper is to generalize the comprehensive structural model for defaultable fixed income bonds (considered in [1]) into…
The paper analyzes the mathematics of the relationship between the default risk and yield-to-maturity of a coupon bond. It is shown that the yield-to-maturity is driven not only by the default probability and recovery rate of the bond but also by other contractual characteristics of the bond that are not commonly assoc…
Paper analyzes pricing model for bonds with early redemption.
problem Analyzing pricing of bonds with early redemption features.
method Structural approach for mathematical modeling of bond prices.
result Existence and uniqueness of default and early redemption boundaries proved.
Study uses VIX for zero-coupon Treasury rates, proving long-term stability and returns.
problem Modeling zero-coupon Treasury rates with VIX for volatility.
method Multivariate autoregressive stochastic volatility model, proving stability and Law of Large Numbers.
result VIX accurately models zero-coupon Treasury rates and returns.
We introduce a bond portfolio management theory based on foundations similar to those of stock portfolio management. A general continuous-time zero-coupon market is considered. The problem of optimal portfolios of zero-coupon bonds is solved for general utility functions, under a condition of no-arbitrage in the zero-c…
Paper shows how to hedge zero coupon bonds with less capital, useful for investors and planners.
problem Hedging zero coupon bonds requires significant initial capital, which is costly.
method Derive a hedging strategy that invests in risky securities and fixed income as maturity approaches.
result Less expensive hedging strategy for zero coupon bonds is possible, reducing capital requirements.
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.
Paper presents a new model for derivatives pricing using zero-coupon rates.
problem Exact volatility calibration of swaption matrices and structured products pricing.
method Model uses a dual-term structure with long-term zero-coupon rates driven by Brownian motion.
result Numerical scheme developed for model implementation and examples provided.
Unified framework matches equity and bond yields.
problem Inconsistency in pricing zero-coupon bonds and equity markets.
method Unified term structure of interest rates framework using put-call parity.
result Option-implied yield curves closely match treasury par yield curves.
This paper uses advanced math to price special insurance bonds.
problem Pricing zero-coupon CAT bonds with complex trigger events.
method Develops two models using enlargement of filtration theory.
result Derives closed-form prices for zero-coupon CAT bonds.
We analyze analytic approximation formulae for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a volatility nonlinearly depending on the interest rate itself. We derive the order of accuracy of the analytical approximation due to Choi and Wir…
Study proposes framework for cyber bonds to compensate cyber attack losses.
problem Cyber risk treatment in finance industry.
method Developed a framework, used publicly available data to determine loss distribution parameters, numerically simulated bond price and characteristics, considered two coupon calculation approaches.
result Numerical simulations of cyber bond price, yield, and characteristics.
Formula calculates bond prices between payments.
problem No new bond pricing formula available.
method Closed-form formula derivation.
result Formula accurately calculates bond prices.
The paper introduces a stochastic deflator for financial derivatives pricing.
problem Pricing financial derivatives under economic and financial risk factors.
method Implement a stochastic deflator with five factors: interest rates, market risk, stock prices, default intensities, and convenience yields.
result The deflator approach is reliable for pricing financial derivatives.
The paper modifies interest rate models to better fit current economic conditions.
problem Current interest rate models do not accurately reflect the Fed's policy and market conditions.
method Proposes a modified Black-Karasinski model (Stochastic Verhulst model) for better economic environment representation.
result The Verhulst model's dynamics are well-suited for current economic conditions and Fed actions.
Study on numerical analysis for corporate bonds using a unified 2 factor model.
problem Develop a numerical method to solve a unified 2 factor model for corporate bonds with fixed discrete coupons.
method Used explicit finite difference scheme to analyze stability and compute bond prices.
result Found conditions for the explicit finite difference scheme to be stable and computed bond prices, credit spread, and duration.
Paper proposes an analytical pricing model for puttable bonds with credit risk.
problem Analytical pricing of puttable bonds with credit risk.
method Developed a 2-factor structural PDE model and derived analytical pricing formula under specific conditions.
result Derived analytical pricing formula for puttable bonds with credit risk.
Polynomial models explain bond prices using polynomial state processes.
problem Modeling interest rates with tractable polynomial expressions.
method Classify and characterize polynomial term structure models.
result Explicit characterization of feasible parameters for bounded factor processes.
Modeling longevity bonds with a Vasicek model for better risk management.
problem Managing future uncertainty related to population longevity.
method Developed a state-space Vasicek model for zero-coupon longevity bonds.
result Unobserved instantaneous interest rate shows mean reverting behavior.
The study uses machine learning to predict CAT bond coupons based on climate data.
problem Predicting CAT bond coupons using climate data.
method Combining climate indicators with machine learning models (random forest, gradient boosting, etc.).
result Extremely randomized trees achieved the lowest RMSE in predicting CAT bond coupons.
Study analyzes bond traders' views on equity market dynamics.
problem Understanding temporal shifts in equity market parameters.
method Utilizes Black-Derman-Toy model and zero-coupon bond pricing.
result Discovers correlations between risk-neutral probability and market variables.
Revisits Jarrow & Turnbull model for credit and liquidity risk.
problem Modeling credit and liquidity risk in financial markets.
method Uses foreign exchange analogy and partially observable exchange rate.
result Derives tractable term structure models and explicit valuation formulae.
Framework for pricing and replicating barrier-style claims on asset price and volatility.
problem Pricing and replicating barrier-style claims on price and volatility.
method Assumes no arbitrage, frictionless markets, zero interest rates. Models risky asset as strictly positive continuous semimartingale with independent volatility process.
result Shows how to price and replicate barrier-style claims using the underlying asset, zero-coupon bonds, and European calls/puts.
New inflation model captures correlations and skew in interest rates.
problem Modeling inflation with market correlations and skew.
method Multi-factor volatility structure with parametric correlation calibration, leveraging single-factor Gaussian model.
result Captures market volatility skew with a single process, simplifying model calibration.
PDE models value non callable defaultable bonds under JDCEV model.
problem Valuation of non callable defaultable bonds using PDEs.
method Two PDE problems solved using Crank-Nicolson semi-Lagrangian method and bi-quadratic Lagrange finite elements.
result Agreement between PDE approach and Monte Carlo, asymptotic methods.
The paper shows real market exists free lunches with vanishing risks.
problem The hypothesis of no free lunches with vanishing risk in real markets.
method Accurately hedged extreme-maturity zero-coupon bond.
result FLVRs naturally exist in the real market.
New framework analyzes why more negative samples improve self-supervised learning performance.
problem Inconsistency between theoretical degradation and empirical improvement of downstream supervised tasks with more negative samples.
method Coupon collector's problem framework to analyze self-supervised representation learning with more negative samples.
result Bound can implicitly incorporate supervised loss in self-supervised loss by increasing negative samples.
Investors choose between bonds and savings accounts based on utility maximization.
problem Determining the optimal investment strategy in a stochastic interest rate environment.
method Analyzes utility maximization under two investment scenarios using affine term structure models.
result Bond indifference prices are found to be the roots of integral expressions.
This study benchmarks AI agents for personalized retail promotions using simulations.
problem Optimizing coupon targeting for sparse customer purchase events.
method Comprehensive simulations of customer shopping behaviors; training RL agents on batch data.
result Contextual bandit and deep RL methods outperform static policies in sparse reward environments.
In this paper, a finite-state mean-reverting model for the short-rate, based on the continuous time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and the special symmetric cases. Its limiting relationship to the Vasicek model will be examined wit…
Develops a bi-variate stochastic framework to model mortality and interest rates with long-range dependence.
problem Captures long-range dependence and instantaneous correlation in mortality and interest rates.
method Mixed fractional Brownian motions, analytical solutions, risk-neutral measure, sequential parameter estimation.
result Explicit pricing of zero-coupon bonds and extreme mortality bonds, practical implications for pricing and risk management.
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.
A new method reduces Monte Carlo variance for financial payoffs.
problem Reducing variance in Monte Carlo estimators for financial payoffs.
method Path-dependent importance sampling using neural networks.
result Significant variance reduction (2-9 times) for various financial payoffs.
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…
In this paper we compare two classical one-factor diffusion models which are used to model the term structure of interest rates. One of them is based on the Wiener-Bachelier process while the second one is based on the Ornstein-Uhlenbeck process. We show essential differences between the prices of European call options…
The paper defines arbitrage-free prices for cash flows and forward contracts using Choquet theory.
problem Defining fair prices for financial instruments in markets with asymmetric exchangeability.
method Choquet representation theory applied to non-probability measures.
result Arbitrage-free prices can be represented as integrals of bond prices with respect to exchangeability measures.
The well-known theorem of Dybvig, Ingersoll and Ross shows that the long zero-coupon rate can never fall. This result, which, although undoubtedly correct, has been regarded by many as surprising, stems from the implicit assumption that the long-term discount function has an exponential tail. We revisit the problem in …
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In…
A new formula for pricing illiquid corporate bonds.
problem Pricing bonds with limited liquidity in the market.
method Option approach with reduced-form interest and credit risk modeling.
result A simple closed formula for illiquid corporate coupon bond prices.
Paper offers fast, accurate pricing for long-dated contracts using real-world probability measure.
problem Inaccurate pricing of long-dated contracts in insurance and pension funds.
method Applies RMQ and JRMQ algorithms under real-world measure, using benchmark approach.
result Prices are less expensive than risk-neutral valuation, highlighting departure from traditional methods.
We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black-Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose …
We construct Zero-Coupon Bond markets driven by a cylindrical Brownian motion in which the notion of generalized portfolio has important flaws: There exist bounded smooth random variables with generalized hedging portfolios for which the price of their risky part is +∞ at each time. For these generalized portfol…
New models for bandit problems with fidelity rewards are introduced and analyzed.
problem Fidelity rewards in bandit problems to incentivize loyalty.
method Two models (loyalty-points and subscription) for fidelity rewards; stochastic and adversarial settings considered.
result Sublinear regret bounds for some models, worst case lower bounds for others.