START ROGUETRADER DD THREAD: GEX, VEX, & Option Arbitrage (15): We calculate the Total Gamma Exposure(GEX) for each option’s strike by multiplying each option’s gamma, for all calls & puts, by Open Interest. (1/15) $SPX $SPY $VIX 💻📕🔥🔥🔥
After that we multiply them by 100 as the each option represents 100 shares. For puts we multiply each by -1 as their gamma is negative. (2/15)
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GEX = Option's Gamma for Each Strike * Open Interest * 100 multiplier (multiply puts by -1 since gamma is negative). Then sum all gamma with same strikes together. This gives GEX for each strike. Dealers flip long to short, at zero gamma. (3/15) $SPX $SPY 🩸
When dealers are short gamma, they are buying up shares of stock to delta hedge. And when long gamma, they are shorting down shares of stock. (4/15)
At Zero Gamma: Implied vol is going up. This is where dealers change from long gamma to short gamma. And delta hedge. Which is why these levels are vital; as they generate new equilibriums in the market for the stock. (5/15)
$SPY $SPX 💨
$SPY $SPX 💨
Vanna Exposure (VEX) is second order Greek Vanna, using implied vol as a means to dictate where option deltas head towards. Vanna is change in option’s delta for a change in implied volatility. Focuses on change in delta for a 1% move in implied vol. (6/15) $SPX 🔥
Where GEX looks for spotting changes in dealer’s book based on changes in spot price, VEX looks to spot changes based on implied volatility. Positive VEX means dealers add liquidity, negative means they strip it away. (7/15) $SPX $SPY 👀
Example: assume VEX is 77,300.19. If $SPX drops 1 point from 3,788.19 to 3,787.19 (-0.00026398%), implied vol then rises 0.002638% (-0.00026398% * -10). Using -10x factor. Dealers are then buying $77,300,190 of $SPX to re hedge delta. (8/15) 📐
Helps to understand intrinsic impact of not just gamma & GEX, but also implied vol and Vanna. All are tied together. And all impact option chains in different ways. All matter at end of day when pricing options. (9/15)
$SPY $SPX 💻
$SPY $SPX 💻
If an option violates price bounds, an arb opp. can theoretically exist. General notion is that no option should sell for less than exercised value.
For Calls : Call Value > Stock Price – Strike Price $SPX $QQQ (10/15)
For Calls : Call Value > Stock Price – Strike Price $SPX $QQQ (10/15)
Means, for example, a call with a strike of say $20, at a spot price of $30, should never sell for less than $10. If it did, arbitrage is possible, as you can simply buy call for less than $10, and exercise at expiration to make $10. (11/15) $SPY $SPX 📕
One can tighten bounds using present value. Assume risk free rate of 10%.
PV stock = $20/1.10 = $18.18
Lower bound call = $30 - $18.18 = $11.82 (12/15)
$SPY $SPX ☘️
PV stock = $20/1.10 = $18.18
Lower bound call = $30 - $18.18 = $11.82 (12/15)
$SPY $SPX ☘️
Call then needs to trade higher than $11.82. And if it trades less than that, one can buy call, sell short a share of stock for $30, and invest proceeds at risk free rate of 10%. (13/15)
$SPX $SPY 💨
$SPX $SPY 💨
Then, in future: If stock > $20: Collect proceeds from riskless trade, exercise option (buy at $20) to cover short. Lock in difference. (14/15)
If stock < $20: Collect proceeds from risk free trade, buy a share in market (> $20),pocket difference. Essentially, investing nothing today & guaranteed positive payout in future. Other ways to derive this possible, but this is main idea. END DD THREAD. (15/15)
$SPY $SPX 📕🔥
$SPY $SPX 📕🔥
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