Morton Model Research Articles

Individualized physiology-based digital twin model for sports performance prediction: a reinterpretation of the Margaria–Morton model

Performance in many racing sports depends on the ability of the athletes to produce and maintain the highest possible work i.e., the highest power for the duration of the race. To model this energy production in an individualized way, an adaptation and a reinterpretation (including a physiological meaning of parameters) of the three-component Margaria–Morton model were performed. The model is applied to the muscles involved in a given task. The introduction of physiological meanings was possible thanks to the measurement of physiological characteristics for a given athlete. A method for creating a digital twin was therefore proposed and applied for national-level cyclists. The twins thus created were validated by comparison with field performance, experimental observations, and literature data. Simulations of record times and 3-minute all-out tests were consistent with experimental data. Considering the literature, the model provided good estimates of the time course of muscle metabolite concentrations (e.g., lactate and phosphocreatine). It also simulated the behavior of oxygen kinetics at exercise onset and during recovery. This methodology has a wide range of applications, including prediction and optimization of the performance of individually modeled athletes.

Exploring Dynamic Asset Pricing within Bachelier’s Market Model

This paper delves into the dynamics of asset pricing within Bachelier’s market model (BMM), elucidating the representation of risky asset price dynamics and the definition of riskless assets. It highlights the fundamental differences between BMM and the Black–Scholes–Merton market model (BSMMM), including the extension of BMM to handle assets yielding a simple dividend. Our investigation further explores Bachelier’s term structure of interest rates (BTSIR), introducing a novel version of Bachelier’s Heath–Jarrow–Morton model and adapting the Hull–White interest rate model to fit BMM. This study concludes by examining the applicability of BMM in real-world scenarios, such as those involving environmental, social, and governance (ESG)-adjusted stock prices and commodity spreads.

Accounting for Dynamic Changes in the Power-Duration Relationship Improves the Accuracy of W' Balance Modeling.

This study aimed 1) to examine the accuracy with which W' reconstitution (W' REC ) is estimated by the W' balance (W' BAL ) models after a 3-min all-out cycling test (3MT), 2) to determine the effects of a 3MT on the power-duration relationship, and 3) to assess whether accounting for changes in the power-duration relationship during exercise improved estimates of W' REC . The power-duration relationship and the actual and estimated W' REC were determined for 12 data sets extracted from our laboratory database where participants had completed two 3MT separated by 1-min recovery (i.e., control [C-3MT] and fatigued [F-3MT]). Actual W' REC (6.3 ± 1.4 kJ) was significantly overestimated by the W' BAL·ODE (9.8 ± 1.3 kJ; P < 0.001) and the W' BAL·MORTON (16.9 ± 2.6 kJ; P < 0.001) models but was not significantly different to the estimate provided by the W' BAL·INT (7.5 ± 1.5 kJ; P > 0.05) model. End power (EP) was 7% lower in the F-3MT (263 ± 40 W) compared with the C-3MT (282 ± 44 W; P < 0.001), and work done above EP (WEP) was 61% lower in the F-3MT (6.3 ± 1.4 kJ) compared with the C-3MT (16.9 ± 3.2 kJ). The size of the error in the estimated W' REC was correlated with the reduction in WEP for the W' BAL·INT and W' BAL·ODE models (both r > -0.74, P < 0.01) but not the W' BAL·MORTON model ( r = -0.18, P > 0.05). Accounting for the changes in the power-duration relationship improved the accuracy of the W' BAL·ODE and W' BAL·MORTON , but they remained significantly different to actual W' REC . These findings demonstrate that the power-duration relationship is altered after a 3MT, and accounting for these changes improves the accuracy of the W' BAL·ODE and the W' BAL·MORTON , but not W' BAL·INT models. These results have important implications for the design and use of mathematical models describing the energetics of exercise performance.

Evaluation of Ground-Based Models for Estimating Surface Albedo with In-Situ Radiometric Measurements across China

Surface albedo is an essential parameter in many solar radiation applications. Although several models are available, it remains debatable whether they are applicable to other locations. Using long-term daily measurements of radiation acquired by observational networks in China, this study examined the applicability of six existing albedo models: Ineichen model (IeM), Gueymard model (GM), Dong model (DeM), Iziomon-Mayer model (IMM), Morton model (MM), and Zhou model (ZeM). The evaluation results of model performance through statistical analysis showed that among the available ground albedo models, ZeM had the best overall performance at 12 selected stations, IeM was shown to provide acceptable estimations for locations where albedo records are readily available. The statistical results of individual station have shownthat the number of input parameters is not the only key factor for determining the predictive performance of ground albedo models. In other words, a simple model has potential for accurate estimation of ground albedo with appropriate model parameters. Therefore, the simple two-parameter DeM was selected to re-calibrate with in-situ radiometric measurements, which can be adopted as a surrogate for ZeM to predict surface albedo in China.

Kernel-based collocation methods for Heath–Jarrow–Morton models with Musiela parametrization

We propose kernel-based collocation methods for numerical solutions to Heath–Jarrow–Morton models with Musiela parametrization. The methods can be seen as the Euler–Maruyama approximation of some finite-dimensional stochastic differential equations and allow us to compute the derivative prices by the usual Monte Carlo methods. We derive a bound on the rate of convergence under some decay conditions on the interpolation functions and some regularity conditions on the volatility functionals.

A NOTE ON REAL-WORLD AND RISK-NEUTRAL DYNAMICS FOR HEATH–JARROW–MORTON FRAMEWORKS

We show that for time-inhomogeneous Markovian Heath–Jarrow–Morton models driven by an infinite-dimensional Brownian motion and a Poisson random measure an equivalent change of measure exists whenever the real-world and the risk-neutral dynamics can be defined uniquely and are related via a drift and a jump condition.

An Approximate Swaption Formula in Heath–Jarrow–Morton Models

This article provides an analytical approximation formula for a swaption price when the instantaneous forward rate follows a Heath–Jarrow–Morton (HJM) model. The author’s approximation strategy, based on the chaos expansion approximation, is to replicate the probability density function of the complex quasi-Gaussian process from a simpler one, which has a semi-closed form solution. It is not restricted to the linear approximation, as is the technique proposed by the existing literature, but can be extended to higher order approximations. Moreover, computation of the approximation is fast; hence, it is suitable for calibration purposes. The author illustrates results through numerical implementation and calibration done using market data. <b>TOPICS:</b>Options, interest-rate and currency swaps, derivatives <b>Key Findings</b> • The authors approximation strategy, based on the chaos expansion approximation, is to replicate the probability density function of the complex quasi-Gaussian process from a simpler one, which has a semi-closed form solution. • It is not restricted to the liner approximation, as is the technique proposed by the existing literature, but can be extended to higher-order approximations. • Computation of the approximation is fast; hence, it is suitable for calibration purposes.

ЧЕЛОВЕК И НЕЧЕЛОВЕЧЕСКИЕ СУЩЕСТВА: ВОЗМОЖНОСТИ ВЗАИМОДЕЙСТВИЯ

The paper presents an analysis of the ways for interaction between man and non-human beings. Those ways are considered in anthropological and philosophical-ecological methodical approaches. The approaches imply rejecting the anthropocentrism as actual ontological basis of the Western cultural tradition. T. Morton models a coexistence of humans and non-human beings as a network uniting all living creatures. Human and non-human beings are now placed in a single process of coexistence and the human ends to be at the top of the natural hierarchy. One of the options to revise the system of interaction of human and non-human beings is to rely on the non-Western (Chinese) philosophical tradition. The anthropological approach to rethinking the position of human in the world is presented in E. Cohn’s project. He considers the human being in the framework of his interactions with the world of non-human often crucial for survival. Based on the semiotics by C. Pierce, Cohn postulates that all living beings are capable to represent the world around them using certain signs for that. A way to establish interspecies communication is animism and concept of perspectivism, which clarifies it. Animism is about the internal similarity of living beings, with a difference in external characteristics. Perspectivism allows to add that every living creature is able to understand the other by accepting his or her point of view, his or her perspective. Thus, the rejection of the anthropocentrism enables development of equal relations of human and non-human beings. Such equal coexistence may have a positive impact on sustainability.

Heterogeneity in the extent of linkage disequilibrium among exonic, intronic, non-coding RNA and intergenic chromosome regions.

Whole-genome sequence data enable construction of high-resolution linkage disequilibrium (LD) maps revealing the LD structure of functional elements within genic and subgenic sequences. The Malecot-Morton model defines LD map distances in linkage disequilibrium units (LDUs), analogous to the centimorgan scale of linkage maps. For whole-genome sequence-derived LD maps, we introduce the ratio of corresponding map lengths kilobases/LDU to describe the extent of LD within genome components. The extent of LD is highly variable across the genome ranging from ~38 kb for intergenic sequences to ~858 kb for centromeric regions. LD is ~16% more extensive in genic, compared with intergenic sequences, reflecting relatively increased selection and/or reduced recombination in genes. The LD profile across 18,268 autosomal genes reveals reduced extent of LD, consistent with elevated recombination, in exonic regions near the 5' end of genes but more extensive LD, compared with intronic sequences, across more centrally located exons. Genes classified as essential and genes linked to Mendelian phenotypes show more extensive LD compared with genes associated with complex traits, perhaps reflecting differences in selective pressure. Significant differences between exonic, intronic and intergenic components demonstrate that fine-scale LD structure provides important insights into genome function, which cannot be revealed by LD analysis of much lower resolution array-based genotyping and conventional linkage maps.

Interest rate model with humped volatility under the real-world measure

The purpose of this paper is to develop real-world modeling for interest rate volatility with a humped term structure. We consider humped volatility that can be parametrically characterized such that the Hull–White model is a special case. First, we analytically show estimation of the market price of risk with humped volatility. Then, using U.S. treasury yield data, we examine volatility fitting and estimate the market price of risk using the Heath–Jarrow–Morton model, Hull–White model, and humped volatility model. Comparison of the numerical results shows that the real-world humped volatility model is adequately developed.

Long-term factorization in Heath–Jarrow–Morton models

The long-term factorization decomposes the stochastic discount factor (SDF) into discounting at the rate of return on the long bond and a martingale that defines a long-term forward measure. We establish sufficient conditions for existence of the long-term factorization in HJM models. A condition on the forward rate volatility ensures existence of the long bond volatility. This yields existence of the long bond and convergence of $T$ -forward measures to the long forward measure. It contrasts with the familiar risk-neutral factorization that decomposes the SDF into discounting at the short rate and a martingale defining the risk-neutral measure.

Consistent recalibration of yield curve models

AbstractThe analytical tractability of affine (short rate) models, such as the Vasiček and the Cox–Ingersoll–Ross (CIR) models, has made them a popular choice for modeling the dynamics of interest rates. However, in order to properly account for the dynamics of real data, these models must exhibit time‐dependent or even stochastic parameters. This breaks their tractability, and modeling and simulating become an arduous task. We introduce a new class of Heath–Jarrow–Morton (HJM) models that both fit the dynamics of real market data and remain tractable. We call these models consistent recalibration (CRC) models. CRC models appear as limits of concatenations of forward rate increments, each belonging to a Hull–White extended affine factor model with possibly different parameters. That is, we construct HJM models from “tangent” affine models. We develop a theory for continuous path versions of such models and discuss their numerical implementations within the Vasiček and CIR frameworks.

The Respiratory Compensation Point is Not a Valid Surrogate for Critical Power.

It is unclear whether the respiratory compensation point (RCP) may be used as a valid surrogate for critical power (CP). Accordingly, we sought to determine the measurement agreement between the CP and the RCP obtained during incremental cycling of varying ramp slopes. Eleven recreationally active men completed three separate ramp-incremental cycling protocols, where the work rate increment was slow (SR, 15 W·min), medium (MR, 30 W·min), or fast (FR, 45 W·min). The RCP was obtained using the ventilatory equivalent for CO2 output method. The CP was determined via Morton's model for ramp-incremental exercise. The assumption that the RCP and the CP occur at equivalent external work rates was assessed by one-way repeated-measures ANOVA and by evaluating the concordance correlation coefficient (CCC) and typical error (root-mean-square error [RMSE]) for each ramp protocol, separately. The external work rate corresponding to the RCP increased with increases in the ramp-incremental slope (P < 0.05). The RCP values in MR (268 ± 37 W) and FR (292 ± 41 W), but not SR (243 ± 35 W), were different (P < 0.05) from CP (247 ± 43 W). The degree to which the relationship between the CP and the RCP approximated the line of identity was relatively poor for SR (CCC = 0.73 and RMSE = 28 W), MR (CCC = 0.63 and RMSE = 36 W), and FR (CCC = 0.42 and RMSE = 55 W). Our data confirm that the external work rate associated with the RCP is labile and that these power outputs display poor measurement agreement with the CP. Taken together, these findings indicate that the RCP does not provide an accurate estimation of CP.

Safe Space for change in the outside world of School: A Framework for running Therapeutic Groups in schools

In this paper presentation report presenter (Jill McWilliam) will give a brief overview of the framework developed with school-based facilitators and multi agency teams for use alongside the Morton model of Therapeutic Story groups. The presenter will give a brief summary of case study material to show how a child used the space in a group to express inner pre-occupations and re-engage with learning and his peers and class teacher. The case study will include an example of the profile of the child developed using the evaluation tool (Metaphors Social and Learning Resilience Score) that is then shared with the school as a means of showing changes resulting from the work and next steps with the child in school or with the family.

A Heuristic Algorithm for the Heath–Jarrow–Morton Model

Heath–Jarrow–Morton [1990, 1991, and 1992] presented a general, intuitively appealing, term structure model for pricing interest rate claims. However, in discrete time, the model results in a non-recombining tree for many general deterministic volatility structures, which can be relatively computationally expensive when the number of time steps is large. This article provides a technique that combines interpolation with sparse ad-hoc mesh generation for valuing interest rate claims in the Heath–Jarrow–Morton framework. When this approach is used, the number of nodes in the mesh is significantly reduced without sacrificing accuracy. This article shows that with proper choice of nodes, the method will converge.

The Term Structure of Interest Rates Under Heath–Jarrow–Morton Models with Fast Mean-Reverting Stochastic Volatility

This paper is a study of the term structure of interest rates based on the Heath–Jarrow–Morton (HJM) models with Hull–White volatility function. Under fast mean-reverting stochastic volatility, we obtain an analytic formula for an approximate bond price with estimated error using a Markovian transform method combined with a singular perturbation method. The stochastic volatility correction effect against time-to-maturity is revealed so that it can capture more of the complexities of the interest rate term structure.

The Long Bond, Long Forward Measure and Long-Term Factorization In Heath-Jarrow Morton Models

This paper proves existence of the long bond, long forward measure and long-term factorization of the stochastic discount factor (SDF) of Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM) models in the function space framework of Filipovic´ (2001). In particular, a sufficient condition on the weight in the Hilbert space of forward rate volatility curves is given that ensures existence of the long bond volatility process, the long bond process and the long-term factorization of the SDF into discounting at the rate of return on the long bond and a martingale component defining the long forward measure, the long-term limit of T-forward measures.

Option pricing on foreign exchange in a Markov-modulated, incomplete-market economy

In this study, we investigate the currency option pricing in a Markov-modulated, incomplete-market economy. Specifically, the dynamics of the spot foreign exchange rate and the domestic/foreign instantaneous forward interest rates are, respectively, governed by a two-factor Markov-modulated stochastic volatility model with jumps and a Markov-modulated Heath–Jarrow–Morton model. The analytical expressions are obtainable using the random Esscher transform. Numerical examples are also given.

Liquidity Premium Theory: an Empirical Support From Sukuk (Islamic Bonds) Yields and Profits Curves

The need to account for all one-period returns on bonds which are reinvested at the coupon rate and which in turn would lead to percentage increase in the investors’ wealth over a particular investment horizon led to Liquidity Premium Theory. Sukuk (Islamic bonds with profit rates instead of coupon rates) has been found to be similar to conventional bonds and has been used to achieve same objectives, especially in meeting long term needs of lenders “lid borrowers ill the capital market. Therefore, this study examines the relationship between the yields and maturities of Sukuk to see if long term investors who currently dominate Sukuk market are obtaining term premium to compensate them for the risk involved in long term lending. Using extended Heart, Jarrow and Morton (1992) model, empirical result obtained using 2001 -2009 data on Sukuk and employing MATLAB statistical tool on spot and forward profit rates indicate that there is biased expectation by the Sukuk investor:’. The biased expectation was evidence a from the shape of the Sukuk yields and credit curves plotted. This is a plausible confirmation that there is a positive spread between yields all Sukuk. A broad battery of statistical evidences from the term structure of profit rate suggests that there is support, through Sukuk holders’ expectation, for Liquidity Preference Theory.

Financial applications on multi-CPU and multi-GPU architectures

The use of high-performance computing systems to help to make the right investment decisions in financial markets is an open research field where multiple efforts have being carried out during the past few years. Specifically, the Heath---Jarrow---Morton (HJM) model has a number of features that make it well suited for implementation on massively parallel architectures. This paper presents a multi-CPU and multi-GPU implementation of the HJM model that improves both the performance and energy efficiency. The experimental results reveal that the proposed architectures achieve excellent performance improvements, as well as optimize the energy efficiency and the cost/performance ratio.