- Rules of Thumb
- Average move vs 1 SD Move
- Delta vs ITM Probability
- Butterflies, Straddles and 50d Options
- Variance Drain
- Variance Equations
- Vol Drag
- Index Correlation
- Vol Regime Evidence
- Monte Carlo Simulation
- Probability Density Functions

**Notes & Ideas**

**Books**

Rating | Title | Author | Status | Subtitle | Tagline | Takeaway | Type | Dojo Topic | Date | Pages | Recommend | Cover | Arena | My Notes & Ideas (Files) | Notes? | Project | URL |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

4 ββββ | Positional Option Trading | Euan Sinclair | Read | Textbook | September 20, 2020 | 198 | |||||||||||

Trading Volatility: Correlation, Term Structure and Skew | Colin Bennett | Reading | Trading volatility, correlation, term structure and skew | Textbook | March 28, 2021 |

**Other Media**

Satus | Future Value | Name | Author | Category | Notes | P.A.R.A. | Projects | Goal Outcomes | Notes & Ideas | Tags | Theme | URL | Value Goals | Dojo | Created | Updated | Arena | Description | Full Title | Last Highlighted | Last Synced | Link | Subtopics | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Read | 5 βββββ | Lessons from the 50d Option | Kris Adbelmessih | Jul 7, 2020 12:19 AM | Mar 18, 2021 1:26 PM | |||||||||||||||||||

To Read | Spot-Vol Dynamics: SPX Options | Timothy Klassen | Jan 14, 2020 7:27 PM | Jan 12, 2021 9:16 PM | ||||||||||||||||||||

Read | 4 ββββ | Know Your Weapon - Black Scholes! | Haug | White Paper | Source | Investing | Sep 28, 2020 3:46 PM | Sep 28, 2020 7:24 PM | ||||||||||||||||

Read | 3 βββ | Toy Skew Model Thread | @Mephisto731 | Tweets | Source | Oct 6, 2020 2:06 PM | Nov 15, 2020 2:49 PM | |||||||||||||||||

Read | 4 ββββ | Correlation Primer and Pitfalls | Shay Allen Hill | Dec 26, 2020 8:27 PM | Jan 12, 2021 9:15 PM | |||||||||||||||||||

Read | 5 βββββ | Liquidity Cascades | Corey Newfound Research | Dec 21, 2020 3:54 PM | Jan 12, 2021 9:12 PM | |||||||||||||||||||

Read | 3 βββ | 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 | ||||||||||||||||

Read | 4 ββββ | Option-implied probability distributions, part 2 Β· Reasonable Deviations | Source | Mar 18, 2021 1:22 PM | Mar 18, 2021 1:27 PM | |||||||||||||||||||

Read | 3 βββ | 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 | ||||||||||||||||||||

Read | 5 βββββ | Volatility Clusters - | Breaking the Market | Article | Source | Trading | Jul 12, 2021 4:23 PM | Jul 18, 2021 12:25 PM | ||||||||||||||||

Read | 4 ββββ | Long Vol: It's Always Different | Article | Source | Jul 4, 2021 12:16 AM | Jul 18, 2021 12:27 PM | ||||||||||||||||||

Read | 3 βββ | 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:
- 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). Whatβs the relationship between d2 and d1?

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 itβs vol is βlowβ.β

**Butterflies, Straddles and 50d Options**

Interesting Observations About Options

- 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 βbodyβ 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 βsquished to the leftβ 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 β .5 * variance.
- The mode is S β 1.5*variance.

### Variance Equations

## Vol Drag

**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

# Vol Regime Evidence

# Monte Carlo Simulation

Here, for your notes -Doc

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 β repoX))*dt) + X(t)*volX*W1*sqrt(dt)

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

This is the most simple way. Donβt worry about the exponentials.

# Probability Density Functions

- The