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We present two explicit rational formulae for Bachelier, or normal, implied volatility. The formulae take the option price, forward, strike, and expiry as inputs and return the implied normal volatility without iteration. They follow the…
The observed frequency shifts of the high-degree solar fundamental mode are explained using a simple geometrical optics approximation. The predicted fractional frequency shift is proportional to the mean squared velocity of the convection…
Value at risk (VaR) is a risk measure that has been widely implemented by financial institutions. This paper measures the correlation among asset price changes implied from VaR calculation. Empirical results using US and UK equity indexes…
This paper presents a factor analysis model for symbolic data, focusing on the particular case of interval-valued variables. The proposed method describes the correlation structure among the measured interval-valued variables in terms of a…
We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the…
Discount is the difference between the face value of a bond and its present value. I propose an arbitrage-free dynamic framework for discount models, which provides an alternative to the Heath--Jarrow--Morton framework for forward rates. I…
We introduce the concept of forward rank-dependent performance processes, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of…
The frequency response function (FRF) is an established way to describe the outcome of experiments in posture control literature. The FRF is an empirical transfer function between an input stimulus and the induced body segment sway profile,…
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model…
Statistical and multiscaling characteristics of WTI Crude Oil prices expressed in US dollar in relation to the most traded currencies as well as to gold futures and to the E-mini S$\&$P500 futures prices on 5 min intra-day recordings in the…
In the new field of financial systemic risk, the network of interbank counterparty relationships can be described as a directed random graph. In "cascade models" of systemic risk, this "skeleton" acts as the medium through which financial…
In the analysis of commodity futures, it is commonly assumed that futures prices are driven by two latent factors: short-term fluctuations and long-term equilibrium price levels. In this study, we extend this framework by introducing a…
Communication is now a standard tool in the central bank's monetary policy toolkit. Theoretically, communication provides the central bank an opportunity to guide public expectations, and it has been shown empirically that central bank…
Financial price changes obey two universal properties: they follow a power law and they tend to be clustered in time. The second regularity, known as volatility clustering, entails some predictability in the price changes: while their sign…
This paper investigates a novel behavioral feature of recursive preferences: aversion to risks that persist over time, or simply \textit{correlation aversion}. Greater persistence provides information about future consumption but reduces…
We develop an exchange rate target zone model with finite exit time and non-Gaussian tails. We show how the tails are a consequence of time-varying investor risk aversion, which generates mean-preserving spreads in the fundamental…
Empirical rate-and-state friction laws are widely used in geophysics and engineering to simulate interface slip. They postulate that the friction coefficient depends on the local slip rate and a state variable that reflects the history of…
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
Forward-backward correlation in pp collisions is studied in an approach that emphasizes the partonic scattering angles and circumvents the intractable problem related to the transverse momenta that are low. Assuming the back-to-back…
We study the behavior of U.S. markets both before and after U.S. Federal Open Market Committee (FOMC) meetings, and show that the announcement of a U.S. Federal Reserve rate change causes a financial shock, where the dynamics after the…