Related papers: The Simple Yield Curve Models
We explain the main concepts of Prospect Theory and Cumulative Prospect Theory within the framework of rational dynamic asset pricing theory. We derive option pricing formulas when asset returns are altered with a generalized Prospect…
Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to…
The money supply is endogenous if the monetary policy strategy is the so called Inflation and Interest Rate Targeting, IRT. With that and perfect credibility, the theory of the price level and inflation only needs the Fisher equation, but…
By considering the three dimensional Heisenberg group $\mathbb{H}_1$ as a flat model of pseudo-hermitian manifolds, the authors in [8] derived the Frenet-Serret formulas for curves in $\mathbb{H}_1$. In this notes we show three applications…
The Stable Reduction Theorem guarantees that any smooth, projective, geometrically irreducible curve of genus $g \geq 2$ over a discretely valued field admits a unique stable model after a finite field extension. Computing this model is a…
We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model…
There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King (1997), Clarida et al. (1999),…
A heat kernel approach is proposed for the development of a general, flexible, and mathematically tractable asset pricing framework in finite time. The pricing kernel, giving rise to the price system in an incomplete market, is modelled by…
For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers. Our results extend Maddocks' and Sachkov's rigidity…
This paper fills the limited statistical understanding of Shapley values as a variable importance measure from a nonparametric (or smoothing) perspective. We introduce population-level \textit{Shapley curves} to measure the true variable…
The valuation process that economic agents undergo for investments with uncertain payoff typically depends on their statistical views on possible future outcomes, their attitudes toward risk, and, of course, the payoff structure itself.…
The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…
A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein--Uhlenbeck processes such that the related bond…
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…
The slow-roll approximation is the usual starting point to study the constraints imposed on the inflaton potential parameters by the observational data. We show that, for a potential exhibiting at least two extrema and giving rise to a…
Let $M$ be a von Neumann algebra and let $(N_t)_{t\in[0,T]}$ be an increasing family of abelian von Neumann subalgebras encoding a (classical) information flow. Fix a faithful normal state $\varphi_\rho$ and a filtration of normal…
We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a…
Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually…
We consider a rough differential equation with a non-linear damping drift term: \begin{align*} dY(t) = - |Y|^{m-1} Y(t) dt + \sigma(Y(t)) dX(t), \end{align*} where $X$ is a branched rough path of arbitrary regularity $\alpha >0$, $m>1$ and…
The SABR model is a benchmark stochastic volatility model in interest rate markets, which has received much attention in the past decade. Its popularity arose from a tractable asymptotic expansion for implied volatility, derived by heat…