Options trading part 3: Gamma/curvature risk

As the underlying moves, the delta moves because of Gamma.

Gamma introduction by CME
Greeks introduction

“Gamma Γ” is also known as the convexity of the delta.

Γ” is the symbol used to represent “gamma.”

delta Δ * dollar change in underlying = option value change in $0.5 Δ * $1 = option value change $0.5
old delta + gamma = new delta
0.5 + 0.02 = 0.52

Gamma measures the “speed” at which an option’s delta will change in reaction to a move in the underlying asset. Positive gamma means that the option contract will become more and more valuable at an increasing rate as the underlying asset goes up in value.

delta Δ * dollar change in underlying = option value change in $
0.52Δ * $1 = $0.52
$48.50 + $0.52 = $49.02

Tesla's share price increased from $700 to $702, which is an increase of 0.285%

Our “call option” value increased from $48 to $49.02, which is an increase of ~2.1%

Delta value convention

“delta” of a call option falls within a range of 0 to 100 Δ

“delta” of a put option falls within a range of -100 to 0 Δ

The underlying contract (ie spot) always has a delta of 1 or, using this convention, a delta of 100 Δ.

Calculate Gamma

  • old delta
  • new delta
  • old price
  • new price
Using delta convention.
So instead of 0.5Δ, we say 50 Δ
( old delta Δ - new delta Δ ) / (old price - new price) = gamma Γ( 0.5 − 0.52 ) /( 700 − 701) = 0.02 Γ

Quantify gamma Γ

An “at the money” call option typically has a delta of 0.5Δ or 50%.
3% gamma Γ

Since gamma refers to the rate of change in an option’s delta, it can be thought of as a measure of an option’s exposure to realized volatility.

Long Gamma

prise rises → delta from -1Δ to -0.08Δ (less negative)

Gamma graph

Maximum “gamma Γ” at “strike price.”
Gamma Γ starts at a slow rate.
“gamma Γ” gradually increases as the underlying (i.e., spot) approaches the strike price.
Maximum “gamma Γ” is reached at the “strike price.”
Tails off

Short Gamma

0.5 * 100 = 50 shares
-0.5 * 100 = -50 shares
Short-selling “at the money” call option
+50 (buy shares)
______
+50 shares
The call option is delta is -0.7Δ which is equal to -70 shares short50 - 70 = 20 shares short (delta -0.2Δ)
( old delta Δ - new delta Δ ) / (old price - new price) = gamma Γ
(-0.5 − −0.7) / (300-350) = -0.004 Γ
+50 (buy shares)
+20 (buy shares)
___
+70 shares
The call option is delta is -0.5Δ which is equal to -50 shares short70 - 50 = 20 shares long (delta 0.2Δ)
( old delta Δ - new delta Δ ) / (old price - new price) = gamma Γ
(-0.5 - -0.7) / (300 - 350) = -0.004 Γ

When you short options and you want to delta hedge, ironically you end up

Buying high

Selling low 😆

“Why would somebody choose to sell options contracts short?”

Why not constantly buy options and use delta hedging to make lucrative trades?”

Buying options contracts has a drawback.

This is referred to as “Time decay” or “theta”

FTX MOVE Contracts

If you short an FTX MOVE contract, you are “short-gamma,”

if you long an FTX MOVE contract, you’re “long-gamma.”

Your delta: 0.771
Your gamma: 0.00014
Your theta: -159.92 (time decay will erode the value)
To delta hedge: short 0.771 BTC
Adjust your short when delta changes
Your delta: -0.771
Your gamma: -0.00014
Your theta: +159.92 (time decay will work in your favor)
To delta hedge: long 0.771 BTC
Adjust your long when delta changes
https://pro.gvol.io/ftx-move

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Gamma & Convexity

Understanding the dynamic connection between “delta” and “gamma” unlocks the full potential of options trading.

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0.06 * $30730 = $1843.8
Linear vs. Non-linear (Convex)
PNL call option position if it would expire today
PNL if BTC hits $50k

Buying options contracts has a drawback.

This is referred to as “Time decay” or “theta”

Moving 40 days closer to expiration.
Options trading part 1: remember that gap between the convex curve is the “time value.”

Convexity bonus video

Trading platform: Delta exchange

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Looking for options trading parts 1 and 2?

Final words

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