volatility-modeling

" This paper identifies what appears to be the first explicit formula for Black–Scholes implied volatility, resolving a 50-year-old problem in option pricing. The key observa tion is that the call price can be written as a survival probability of an inverse Gaussian distribution." https://arxiv.org/pdf/2604.24480 Statistics: Posted by Collector — 39 minutes ago

I've been trying to learn options math and am getting hung up on a basic misunderstanding. From what I have gathered, to get a single day volatility from annualized volatility, you would do something like this - var dailyVol = impliedVol / sqrt(1.0 / 365); My assumption would then be that if I want to find an "x sigma" daily move to the upside or downside, I would do the following - var newPrice …

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalized shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literat…

We introduce a multi-scale stress accumulation framework for identifying regimes of elevated future volatility in financial time series. The model constructs a binary stress signal based on extreme return events and aggregates it using exponential weighting across fast, intermediate, and slow temporal scales. To ensure adaptability across changing market conditions, stress regimes are defined usi…

I use QLIKE as loss function to evaluate the forecasting performance of a RV realized volatility model. QLIKE = log $h$ + $\frac{\hat{\sigma}^2}{h}$ where $h$ is volatility forecast and $\hat{\sigma}^2$ is the ex post value of volatility (realized volatility computed with intraday returns). If I proxy volatility with log(RV), what are $h$ and $\hat{\sigma}^2$ in the QLIKE? The forecast and ex pos…

I want to calculate implied volatility of american option of a short term interest rate future. Let's take for example a put option for a SOFR future with $K=95, price=0.105, T=0.750685, underlying=95.505$ I currently use as a first approximation the implied vol by using finding implied vol using the Bachelier model (used to price European options from my understanding). The undiscounted price fo…

This video traces the evolution of volatility modeling from Black-Scholes to modern surface calibration, covering SVI parametric models, Dupire local volatility, and the Heston stochastic volatility framework with practical derivative pricing applications. 🎥 Video Tutorial • 📈 Options Strategy 🎥 Watch Video: https://youtu.be/EjaO4UaVLJA Topics: quantitative finance, investment analysis, financ…

A comprehensive masterclass exploring the evolution from Black-Scholes to modern volatility surfaces. Master SVI parametric models, Dupire local volatility, Heston stochastic volatility, hybrid LSV architectures, rough volatility frontiers, and deep learning applications for derivative pricing. 📊 Deep Research • 📈 Options Strategy Topics: quantitative finance, investment analysis, financial edu…

I'm trying to replicate how Bloomberg's OVML prices options. My guess is whenever I'm solving for IV, I'm passing a premium that's too cheap, that's why the IV I solve overcompensates. This is probably because I'm discounting the premium improperly. Same goes with the Premium being cheaper than the actual deal. Here's the sample deal I'm trying to validate my pricer with using OVML. # Sample Deal…

In this article, we develop a novel large volatility matrix estimation procedure for analyzing global financial markets. Practitioners often use lower-frequency data, such as weekly or monthly returns, to address the issue of different trading hours in the international financial market. However, this approach can lead to inefficiency due to information loss. To mitigate this problem, our propose…

Exploring the microstructural foundations of order flow, market impact, and volatility through a unified mathematical framework. Based on breakthrough research by Muhle-Karbe et al., this deep dive reveals how a single structural statistic binds together long memory, square-root scaling, and rough volatility. 📊 Deep Research Topics: quantitative finance, investment analysis, financial education…

So I'm learning about volatility smiles and volatility surfaces from Hull's Options, Futures and Other Derivatives . On p. 459, there is the following table (Table 20.2) of a volatility surface: Maturity 0.90 0.95 1.00 1.05 1.10 1 month 14.2 13.0 12.0 13.1 14.5 3 month 14.0 13.0 12.0 13.1 14.2 6 month 14.1 13.3 12.5 13.4 14.3 1 year 14.7 14.0 13.5 14.0 14.8 2 year 15.0 14.4 14.0 14.5 15.1 5 year …

Author: Chainika Thakar (Originally written By Punit Nandi) Before be jump into the blog! Checkout our new video on Intraday Implied Volatility: What Python + Options Data Reveal. This video focuses on building that foundation by working directly with intraday options data using Python. We move beyond charts to show how minute-level Bank Nifty data is structured, cleaned, and prepared for analysi…

Introduction If you’ve been trading anything other than cash over the past eighteen months, you’ve noticed something peculiar: periods of calm tend to persist, but so do periods of chaos. A quiet Tuesday in January rarely suddenly explodes into volatility on Wednesday—market turbulence comes in clusters. This isn’t market inefficiency; it’s a fundamental stylized fact … Continue reading "Volatili…

Volatility tests market conviction and tokenization sees growing appetite. This Week – Matt Howell at T. Rowe Price discusses recent market “warning shocks” that have tested conviction and shifted cross-asset […]

We are in a period of uncertainty. Volatility has been in the headlines since the announcement of new trade policies early in April, bringing heightened uncertainty and challenging trading environments across major markets. In April, we’ve seen Liquidity in key futures markets drop sharply—E-mini S&P 500s are trading at levels not seen since the 2020 COVID selloff, and quote sizes in 10-yea…

By Manusha Rao You may have noticed that markets sometimes remain calm for weeks and then swing wildly for a few days. That’s volatility in action. It measures how much prices move—and it’s a big deal in trading and investing because it reflects risk. But here’s the catch: estimating volatility isn't straightforward. A 2% drop often sparks more headlines than a 2% gain. That’s asymmetric volatili…

In this series on volatility forecasting, I previously detailed the Heterogeneous AutoRegressive (HAR) volatility forecasting model that has become the workhorse of the volatility forecasting literature1 since its introduction by Corsi2. I will now describe an extension of that model due to Bollerslev et al.3, called the Heterogeneous Exponential (HExp) volatility forecasting model, in which the …

In The Local Volatility Surface (2008), Emanuel Derman analyzes the dynamics of the local volatility smile. He observes that, in a negatively skewed market, the evolution of the index is characterized by lower local volatility as the index level increases and higher local volatility as the index level decreases. This behavior causes the local volatility smile to shift in the opposite direction of…

Volatility is an important aspect in the financial market. It refers to how much and how quickly an asset price changes over time. A higher period of volatility means that an asset is changing quickly. For example, if a stock opens at $10 and rises to $13, and falls back to $9 in a single […] The post What is Volatility in Stocks (and All Other Assets)? appeared first on Real Trading .