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Derivatives

Notes & Ideas
Books

My Bookshelf

RatingTitleAuthorStatusSubtitleTaglineTakeawayTypeDojo TopicDatePagesRecommendCoverArenaMy Notes & Ideas (Files)Notes?ProjectURL
4 ⭐⭐⭐⭐
Euan Sinclair
Textbook
September 20, 2020
198
Trading Volatility: Correlation, Term Structure and Skew
Colin Bennett
Trading volatility, correlation, term structure and skew
Textbook
March 28, 2021
5 ⭐⭐⭐⭐⭐
The Second Leg Down
Hari Krishnan
There are Ways to be long vol without bleeding too kuch
Textbook
February 4, 2023
189

Other Media

The Media Locker

5 ⭐⭐⭐⭐⭐
Lessons from the 50d Option
Jul 7, 2020 12:19 AM
Mar 18, 2021 1:26 PM
📰
Spot-Vol Dynamics: SPX Options
Timothy Klassen
Jan 14, 2020 7:27 PM
Jan 12, 2021 9:16 PM
4 ⭐⭐⭐⭐
Know Your Weapon - Black Scholes!
Haug
White Paper
Source
Investing
Sep 28, 2020 3:46 PM
Sep 28, 2020 7:24 PM
3 ⭐⭐⭐
@Mephisto731
Tweets
Source
Oct 6, 2020 2:06 PM
Nov 15, 2020 2:49 PM
4 ⭐⭐⭐⭐
Correlation Primer and Pitfalls
Shay Allen Hill
Dec 26, 2020 8:27 PM
Jan 12, 2021 9:15 PM
5 ⭐⭐⭐⭐⭐
Corey Newfound Research
Dec 21, 2020 3:54 PM
Jan 12, 2021 9:12 PM
3 ⭐⭐⭐
The Realized Volatility Puzzle
Harel Jacobson
Article
Types of Realized Vol Models
Source
Nov 15, 2020 10:15 PM
Mar 18, 2021 1:26 PM
4 ⭐⭐⭐⭐
Option-implied probability distributions, part 2 · Reasonable Deviations
Source
Mar 18, 2021 1:22 PM
Mar 18, 2021 1:27 PM
3 ⭐⭐⭐
What is the difference between implied volatility and local volatility? - Quora
Jan 20, 2021 1:12 AM
Mar 18, 2021 1:27 PM
Just Saving
Godot Finance Working Papers
Bookmark
Mar 18, 2021 10:21 AM
Mar 18, 2021 1:27 PM
5 ⭐⭐⭐⭐⭐
Volatility Clusters -
Breaking the Market
Article
Source
Jul 12, 2021 4:23 PM
Jul 18, 2021 12:25 PM
4 ⭐⭐⭐⭐
Long Vol: It's Always Different
Article
Source
Jul 4, 2021 12:16 AM
Jul 18, 2021 12:27 PM
3 ⭐⭐⭐
Flirting with Models: Benn Eifert
Moontower
Podcast
May 16, 2021 4:41 PM
May 30, 2021 11:54 AM

Rules of Thumb

Average move vs 1 SD Move

• Doc: Probability Density Function (PDF) of a normal distribution follows 1/2pi* some stuff. To get log normal you have to transform but pi remains.
• So if you know what the sigma is, you can find the average move using the PDF:
• $\color{white} Avg = \sigma * \underbrace{\sqrt{2/\pi}}_{\text{.798}}$

• Related, ATM Straddle in dollars is spot price * .8 * vol * sqrt(252/days of straddle)

Delta vs ITM Probability

In Black Scholes: The term for delta is N(d1). The term for the probability of finishing in the money is N(d2). What’s the relationship between d2 and d1?

$D2 = D1 - \sigma\sqrt{t}$ The math defines the relationship we figured out intuitively:

The higher the volatility the more delta and probability will diverge!

Delta and probability are only similar when an option is near expiration or when it’s vol is “low”.”

• Even in a continuous distribution, the higher the volatility, the more positively skewed the distribution, the further OTM the 50d call strike lives.
• The cheapest straddle will occur at the median outcome or the ATM strike (should be 50d strikes?)
• The most expensive butterfly will have its “body” near the theoretical mode. This makes sense since a butterfly which is just a spread of 2 vertical spreads is a pure bet on the distribution. If you chart the price of all the butterflies equidistantly across strikes you will have drawn the probability density function implied by the options market

Variance Drain

• The higher the variance, the lower the median and mode! The distribution gets “squished to the left” as the probability the stock declines increases in exchange for a longer right tail like we saw during the dotcom days.
• The median expected stock price is S – .5 * variance.
• The mode is S – 1.5*variance.

Variance Equations

Variance Equation Cheat Sheet

Vol Drag

Geo Return = Arithmetic Return - 1/2 * Vol squared

Index Correlation

• The average cross-correlation of stocks in an index can be approximated by the ratio of index variance to average weighted stock variance.
• Assume index vol 17, avg stock vol 33
• Using our estimates (.17^2) / (.33^2) = .27 which is in the ballpark of where long term average SP500 index correlations have realized
• Although option folks know how spikey that number can be, especially on short measures

Monte Carlo Simulation

If X and Y are correlated (retunrs) and you want to simulate with Monte Carlo, say.

Given X(t) and Y(t), pick 2 independent standard normal variables W1 & W2

X(t+dt) = X(t)*(1 + (r – repoX))*dt) + X(t)*volX*W1*sqrt(dt)

Y(t + dt) = Y(t)*( 1 + (r – repoY))*dt) + Y(t)*volY*(W1*rho + W2*sqrt(1 – rho^2))*sqrt(dt)

This is the most simple way. Don’t worry about the exponentials.

Probability Density Functions

• The
Rebalancing Portfolio of Long Vol
macrocephalopod (@macrocephalopod) Tweeted: I thought about power perpetuals a bit more and I really like the design. If price of the underlying goes S to S’ and back to S, price of the power perp also round-trips (unlike a leveraged token, which has a lower price in this scenario because it rebalances to higher leverage)
Ben Eofert Hedge Ratio
ben eiffert volga
Select content from the quant and vol community
Think Like a Market Maker — Understanding Implied Volatility | by Harel Jacobson | Mar, 2022 | Medium
Notes on The Laws Of Trading
Moontower on Gamma - Party at the Moontower
Weighting dispersion
The Gamma Of Levered ETFs - Party at the Moontower
Variance and VIX Formulas
Moontower Quant Codex