We employ a Bayesian modelling technique for high dimensional cointegration estimation to construct low volatility portfolios from a large number of stocks. The proposed Bayesian framework effectively identifies sparse and important cointegration rel...
Anyone who follows the stock market knows that some days market indexes and stock prices move up, and other days they move down. This is called volatility. The more dramatic the swings, the higher …
Volatility is the oscillation of prices between high and low values from an asset's average market performance. Since there is no uniformity in price range, it represents risky behavior.
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state...
I’m interested in hearing from people who traded options or volatility professionally (market making, prop desks, hedge funds, structured products). When a strategy or framework stopped working in ...
The CBOE Volatility Index has gone through some wild swings lately, but generally I see an upwards trend since the start of this year (purple line in the image). What are everyone’s thoughts on this...
VOLATILITY meaning: 1. the quality or state of being likely to change suddenly, especially by becoming worse: 2. the…. Learn more.
We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following a diffusion with stochastic volatility. In the current financial market especially, it is important to include stochas...
In my journey of discovering financial mathematics, I have been working on a coding project/dashboard with an emphasis on volatility modeling It pulls data from yFinance and uses some basic ARCH mod...
Feb 12, 2026 · Volatility shows how much a security or market index’s returns fluctuate over time, indicating how widely prices move around their average. It's often calculated from the standard …
Decentralized finance (DeFi) lacks centralized oversight, often resulting in heightened volatility. In contrast, centralized finance (CeFi) offers a more stable environment with institutional safeguards. Institutional backing can play a stabilizing r...
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic function. We pr...
In the paper written by Klibanov et al, it proposes a novel method to calculate implied volatility of a European stock options as a solution to ill-posed inverse problem for the Black-Scholes equation. In addition, it proposes a trading strategy base...
In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finan...
VOLATILITY meaning: 1. the quality or state of being likely to change suddenly, especially by becoming worse: 2. the…. Learn more.
Chicago Board Options Exchange's CBOE Volatility Index, a popular measure of the stock market's expectation of volatility based on S&P 500 index options. It
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Feb 12, 2026 · Volatility shows how much a security or market index’s returns fluctuate over time, indicating how widely prices move around their average. It's often calculated from the standard …
The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called ``square-root impact law'', which states that impact grows as the square-root of trad...
This study uses the GARCH (1,1) model to examine the impact of COVID-19 cases (log value) on the volatility of the Exchange rate return of Bangladeshi taka (BDT) over the US dollar (USD), Japanese Yen (JPY), and Swedish Krona (SEK). The result shows...
Option pricing based on Black-Scholes processes, Monte-Carlo simulations with Geometric Brownian Motion, historical volatility, implied volatility, Greeks hedging (⭐ 316)
What kind of implied volatility extrapolation is appropriate? Roger Lee proved that the Black-Scholes implied variance can not grow faster than linearly in log-moneyness. This paper investigates what happens in the Bachelier (or Normal) implied volat...
In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than the close fo...
The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around volatility, tryi...
We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results established in Jose...
We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrin...
An advanced memory forensics framework (⭐ 7972)
Diebold & Yilmaz method, DCC-Garch method on composite indicies. 2009-2019 (⭐ 23)
We study a multivariate autoregressive stochastic volatility model for the first 3 principal components (level, slope, curvature) of 10 series of zero-coupon Treasury bond rates with maturities from 1 to 10 years. We fit this model using monthly data...
In the field of quantitative finance, volatility models, such as ARCH, GARCH, FIGARCH, SV, EWMA, play the key role in risk and portfolio management. Meanwhile, factor investing is more and more famous since mid of 20 century. CAPM, Fama French three...
This article describes condensation of the elements and use of condensation temperatures (Tcond) to interpret the volatility trend of the Earth. Major points are: (1) a listing of updated 50% Tcond for all natural elements and Pu at 1e-2 to 1e-8 bar...
Recent research has documented a significant rise in the volatility (e.g., expected squared change) of individual incomes in the U.S. since the 1970s. Existing measures of this trend abstract from individual heterogeneity, effectively estimating an...
This study examines how institutional differences and external crises shape volatility dynamics in emerging Asian stock markets. Using daily stock index returns for Indonesia, Malaysia, and the Philippines from 2010 to 2024, we estimate EGARCH(1,1) a...
Volatility clustering is an important characteristic that has a significant effect on the behavior of stock markets. However, designing robust models for accurate prediction of future volatilities of stock prices is a very challenging research proble...
In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it might be p...
We test various volatility models using the Bitcoin spot price series. Our models include HIST, EMA ARCH, GARCH, and EGARCH, models. Both of our in-sample-fit and out-of-sample-forecast results suggest that GARCH and EGARCH models perform much better...
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper addresses t...
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised. Connections with t...
The short maturity limit $T\to 0$ for the implied volatility of an Asian option in the Black-Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note we derive the subleading $O(...