Impact of cross sectional Factors on Implied and realized volatility of equity options 🧵

Reference paper Link - papers.ssrn.com/sol3/papers.cf… Stock Characteristics and Implied Volatility

Beta:

Implied volatility increases with beta, suggesting that market participants view high-beta stocks as riskier.

Important point on Delta Hedging that every Volatility trader should consider🧵

Do read Trading Volatility by Colin Bennett, if you are want to learn more about Vol trading

Subscribe to our Youtube Channel - youtube.com/@QuantInsider Delta Hedging and Matching Maturity

To hedge an option's delta effectively, use a forward with the same maturity. Using different maturities or stock introduces dividend risk, as forwards exclude interim dividend benefits.

This distinction helps prevent potential miscalculations in P&L.

Carry Trade 101 🧵

Subscribe to our Youtube Channel - youtube.com/@QuantInsider 1/12

Core Idea

“Borrow low, lend high.” A carry trade earns the yield differential (carry) between two assets or currencies after financing costs.

Implementing the Kelly Criterion in Continuous-Time 🧵

Subscribe to our Youtube Channel for more content of Quantitative Finance - youtube.com/@QuantInsider 1. Market set-up

Consider a money–market account earning a constant short rate r and mmm risky assets whose (ex-dividend) prices follow an Itô diffusion

Traders still talk about “Black-Scholes” vol, but almost nobody pushes the textbook equation into production to value real positions. Here’s why. 🧵 Textbook Assumptions and How the Real World Breaks Them

Constant volatility

Implied volatility is anything but constant. In 2024, 1-month ATM SPX vol averaged 15 %, while 20-delta puts printed 24 %—a 60 % “smile” markup.

Must know 18 Options and other Derivatives related Bloomberg function keys 🧵

Core Options Functions

OMON (Option Monitor)

The Option Monitor (OMON) function on Bloomberg provides real-time pricing, market data, and derived data for call and put options. It also allows you to analyze options and export data to Excel.

• Usage: Enter [Ticker] [EQUITY] OMON

OSA (Option Scenario Analysis)

Generates profit/loss tables and graphs by allowing you to input various option and underlying stock positions.

OV (Option Valuation)

• Provides pricing, volatility, and Greek data using models like Black‑Scholes, Trinomial, Roll‑Geske, etc.

The OV function on Bloomberg helps you value options by providing price and volatility data. You can use the OV function to calculate the OPM value for a loaded option

OVX (Exotic Option Valuation)
• Values exotic option types (e.g., chooser, binary, lookback) once the underlying is loaded.
The OVX function on Bloomberg is used to value

OPX function on the Bloomberg terminal helps traders analyze options expirations. It allows users to view options by expiration date, and sort them by volume and strike value. II. Supplementary Analytics Functions

DES (Description)
• Provides detailed descriptive information on a selected option.

QRM (Trade Recap)
• Shows a recap of recent trades for the option.

TSM (Trade Summary Matrix)
• Displays a matrix summarizing recent trade data.

GIP (Intraday Price Graph)
• Plots an intraday graph for the option.

GPO (Bar Chart)
• Generates a bar chart view of option pricing data.

Volatility and Correlation Analysis (VCA)
The Volatility and Correlation Analysis (VCA) tool on the Bloomberg Terminal can be used to analyze skew for major stock indexes. This tool allows users to analyze volatility across various securities.

HIVG (Historical Implied Volatility Graph)
• Graphs historical trends in the option’s implied volatility.

Mathematical Solution for Hedging When Implied Volatility is Stochastic 🧵

Implied volatility is a crucial factor in the pricing and hedging of options. Unlike historical volatility, implied volatility is derived from market prices of options and reflects the market's expectations of future volatility. When implied volatility is stochastic, meaning it changes unpredictably over time, hedging strategies become more complex.

When implied volatility is stochastic, traditional hedging techniques must be expanded to account for the additional risk factor.

Here's a detailed explanation of the mathematical approach to hedging under stochastic implied volatility conditions, primarily focusing on delta and vega hedging.

Directional Options trading by creating delta exposure is not as simple as it seems.

Let’s break this down step by step for a clear understanding.🧵

(Do Subscribe to our Youtube channel - ) for more content of Quant trading and Research. youtube.com/@QuantInsider Why Black-Scholes Delta Isn't Always Accurate?

The Black-Scholes model, a common tool in option pricing, assumes a smooth and constant volatility across all strike prices and maturities. However, in real-world markets:

Detailed overview of different Methods for "Change Point Detection" for identifying changes in market regimes, volatility shifts, or other significant events.🧵

Statistical Tests: 1.Cumulative Sum (CUSUM):
(Subscribe to our Youtube channel - ) youtube.com/@QuantInsider Use Case: Quickly detects shifts in mean returns or volatility. Ideal for simple, real-time signals where efficiency is key.

Why 0.50 Delta ≠ ATM? 🧵

A common misconception is that an at-the-money (ATM) option always has a delta of 0.50. However, this isn't always the case due to factors like the distribution of potential asset returns and the skewness of that distribution. In the Black-Scholes model:

Delta for a Call Option:

Here:

S: Current stock price
K: Strike price
T: Time to expiration
r: Risk-free interest rate
σ: Volatility

Volatility traders have Vega exposure, and the magnitude of this exposure determines the slope of their P&L. In contrast, for directional traders, the P&L slope is driven by their Delta exposure.

So understanding the sources of Vega convexity is crucial for vol traders 🧵 Volatility Smile and Term Structure:

Implied volatility typically varies across strike prices (volatility smile/skew) and maturities (term structure). These variations introduce nonlinearities in Vega, especially for options further out-of-the-money or near their expirations.

Impact of cross sectional Factors on Implied and realized volatility of equity options 🧵

Reference paper Link - papers.ssrn.com/sol3/papers.cf… Stock Characteristics and Implied Volatility

Beta:

Implied volatility increases with beta, suggesting that market participants view high-beta stocks as riskier.

Should hedging affect how we look at volatility? 🧵

Hedging and volatility are intrinsically linked, such that the notion of volatility becomes meaningless without considering the act of hedging itself.

Reference - Derivatives Models on Models by Espen Gaarder Haug The derivatives market is a fundamental, "primitive" concept in finance.

This contrasts with traditional views that treat probability distributions and statistical expectations as primary tools for understanding and predicting market behavior.

Discrete Dynamic Delta Hedging under Geometric Brownian Motion: A Practical Implementation (With Python code) 🧵

This thread explores the effectiveness of discrete dynamic delta hedging under GBM

Like retweet and comment "Dynamic Hedging" to receive the code Dynamic delta hedging is a fundamental strategy used by option traders to mitigate the risk associated with movements in the underlying asset's price.

Important point on Delta Hedging that every Volatility trader should consider🧵

Do read Trading Volatility by Colin Bennett, if you are want to learn more about Vol trading Delta Hedging and Matching Maturity

To hedge an option's delta effectively, use a forward with the same maturity. Using different maturities or stock introduces dividend risk, as forwards exclude interim dividend benefits.

Detailed Thread on Option Pricing with Deep Learning

Original paper link -

Like, Retweet and comment "OPDL", to receive the code for the Deep Learning for Option Pricing cs230.stanford.edu/projects_fall_… In the paper Three neural network models are discussed
1)MLP1.
2)MLP2.
3)LSTM.

Capitalizing on market inefficiencies by trading Post-Earnings Announcement Drift (PEAD) Strategy, with Python code Implementation

Thread🧵 Post-Earnings Announcement Drift (PEAD) strategy exploits the phenomenon where stock prices tend to drift in the direction of an earnings surprise for several weeks or months following an earnings announcement

8 Must-read for books HFT (High-Frequency Trading) from strategies to high-performance computing, low latency, market-micro structure, liquidity, and trading systems. 🧵 "High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems" by Irene Aldridge 

A comprehensive introduction to HFT, covering the basics of market microstructure, order types, execution algorithms, and backtesting.

A Detailed Breakdown of High-Frequency Trading Strategy: Order Book Skew Reversion Strategy 🧵with Python code Implementation

Shared by @christinaqi

Like, Retweet and comment "Done", to receive the code for the strategy Key Terminology

Feature (Predictor): An independent variable believed to have predictive value regarding future price movements. In machine learning, these are known as features; in statistics or econometrics, they are called predictors or regressors.

Statistical Arbitrage for Volatility with Options

This strategy seeks to capitalize on inefficiencies between the implied volatility (IV) priced into options and the realized volatility experienced by the underlying asset.

Here's a detailed Thread 🧵 Exploiting Market Inefficiencies:

Beyond the Black-Scholes Model While the Black-Scholes model provides a theoretical framework, statistical arbitrage goes beyond it by capturing market inefficiencies.

Detailed Breakdown of Term Structure Trading: 🧵 1. Overview of Term Structure Trading:
Term structure trading focuses on the dynamics of implied volatility (σimp) surfaces across different maturities (T).