相关论文: A new measure of risk using Fourier analysis

We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose…

Measuring risk is at the center of modern financial risk management. As the world economy is becoming more complex and standard modeling assumptions are violated, the advanced artificial intelligence solutions may provide the right tools to…

To reject the Efficient Market Hypothesis a set of 5 technical indicators and 23 fundamental indicators was identified to establish the possibility of generating excess returns on the stock market. Leveraging these data points and various…

We propose a new method of measuring the third and fourth moments of return distribution based on quadratic variation method when the return process is assumed to have zero drift. The realized third and fourth moments variations computed…

Managing a portfolio to a risk model can tilt the portfolio toward weaknesses of the model. As a result, the optimized portfolio acquires downside exposure to uncertainty in the model itself, what we call "second order risk." We propose a…

We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \levy dynamic. The price of the option is described by a partial integro-differential equation…

Nowadays, when crashes and crises are rather frequent events, an effective monitoring system for the international financial market is needed. Modern nonlinear methods, such as Recurrence Quantification Analysis (RQA), demonstrate the…

In this paper, we propose the Fourier Discrepancy Function, a new discrepancy to compare discrete probability measures. We show that this discrepancy takes into account the geometry of the underlying space. We prove that the Fourier…

In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of…

A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked…

This paper proposes a dynamic process of portfolio risk measurement to address potential information loss. The proposed model takes advantage of financial big data to incorporate out-of-target-portfolio information that may be missed when…

If two signals are phase synchronous then the respective Fourier component at each spectral band should exhibit certain properties. In a pair of artificially generated phase synchronous signals the phase difference at each frequency band…

We provide an alternative method for analysis of multifractal properties of time series. The new approach takes into account the behaviour of the whole multifractal profile of the generalized Hurst exponent $h(q)$ for all moment orders $q$,…

We propose a new set of stylized facts quantifying the structure of financial markets. The key idea is to study the combined structure of both investment strategies and prices in order to open a qualitatively new level of understanding of…

This paper develops a continuous-time filtering framework for estimating a hazard rate subject to an unobservable change-point. This framework naturally arises in both financial and insurance applications, where the default intensity of a…

Given a Fourier transformable measure in two dimensions, we find a formula for the intensity of its Fourier transform along circles. In particular, we obtain a formula for the diffraction measure along a circle in terms of the…

The discrepancy between realized volatility and the market's view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast's ability to predict…

This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $ S=(S_{t})_{t\geq0} $ is given by \[…

A method is presented for investigating the periodic signal content of time series in which a number of signals is present, such as arising from the observation of multiperiodic oscillating stars in observational asteroseismology. Standard…

As financial instruments grow in complexity more and more information is neglected by risk optimization practices. This brings down a curtain of opacity on the origination of risk, that has been one of the main culprits in the 2007-2008…