- 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 | Euan Sinclair | Read | Textbook | September 20, 2020 | 198 | ||||||||||||

5 βββββ | The Second Leg Down | Hari Krishnan | Read | There are Ways to be long vol without bleeding too kuch | Textbook | February 4, 2023 | 189 |

**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 | Kris Adbelmessih | Jul 7, 2020 12:19 AM | Mar 18, 2021 1:26 PM | ||||||||||||||||||||

To Read | Timothy Klassen | Jan 14, 2020 7:27 PM | Jan 12, 2021 9:16 PM | |||||||||||||||||||||

Read | 4 ββββ | Haug | White Paper | Source | Investing | Sep 28, 2020 3:46 PM | Sep 28, 2020 7:24 PM | |||||||||||||||||

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

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

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

Read | 3 βββ | Harel Jacobson | Article | Types of Realized Vol Models | Source | Nov 15, 2020 10:15 PM | Mar 18, 2021 1:26 PM | |||||||||||||||||

Read | 4 ββββ | Source | Mar 18, 2021 1:22 PM | Mar 18, 2021 1:27 PM | ||||||||||||||||||||

Read | 3 βββ | Jan 20, 2021 1:12 AM | Mar 18, 2021 1:27 PM | |||||||||||||||||||||

Just Saving | Bookmark | Mar 18, 2021 10:21 AM | Mar 18, 2021 1:27 PM | |||||||||||||||||||||

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

Read | 4 ββββ | Article | Source | Jul 4, 2021 12:16 AM | Jul 18, 2021 12:27 PM | |||||||||||||||||||

Read | 3 βββ | 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)

$\color{white} Avg = \sigma * \underbrace{\sqrt{2/\pi}}_{\text{.798}}$

**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?

$D2 = D1 - \sigma\sqrt{t}$ 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 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