Read on Twitter
Options Myth:
When the market is volatile, options are worth more b.c options are more likely to expire in the money.
Yes, it’s true that options gain value in periods of high market volatility. However, the reason is more subtle than the commonly explained reason above.
1/
When the market is volatile, options are worth more b.c options are more likely to expire in the money.
Yes, it’s true that options gain value in periods of high market volatility. However, the reason is more subtle than the commonly explained reason above.
1/
To see why that's flawed, consider an "at the money" option.
An example is a call option w/ a strike price of $420 on Tesla stock. Assume Tesla's current price is also $420.
The call gives its holder the right to buy Tesla stock at $420, no matter how high Tesla gets.
2/
An example is a call option w/ a strike price of $420 on Tesla stock. Assume Tesla's current price is also $420.
The call gives its holder the right to buy Tesla stock at $420, no matter how high Tesla gets.
2/
The call's owner profits more as the price of Tesla goes up.
Tesla has a ~50% chance of going down and a ~50% chance of going up*. So, the option has a ~50% chance of expiring "in the money," no matter how volatile Tesla is.
3/
*Black-Scholes' Brownian motion assumption
Tesla has a ~50% chance of going down and a ~50% chance of going up*. So, the option has a ~50% chance of expiring "in the money," no matter how volatile Tesla is.
3/
*Black-Scholes' Brownian motion assumption
So, if Tesla's stock price experiences a period of higher (implied) volatility, the option's probability of expiring in the money hasn't changed.
Yet the option's value should go up.
Why?
4/
Yet the option's value should go up.
Why?
4/
The correct answer lies in the extremes - the option is now more likely to take extremely large values at expiry, but is no more likely to be worthless.
If Tesla's volatility goes up, Tesla stock is more likely to take very large values or really small values.
5/
If Tesla's volatility goes up, Tesla stock is more likely to take very large values or really small values.
5/
Very large values at expiry are a jackpot for our call option. The higher the value, the higher the price of the option.
Very small values mean that the option will not be exercised, and will have a value of $0, no matter how low the Tesla stock crashes.
6/
Very small values mean that the option will not be exercised, and will have a value of $0, no matter how low the Tesla stock crashes.
6/
Options have asymmetric upside and are positively impacted by increasingly good events but not negatively impacted by increasingly bad events.
More vol makes an option more likely to hit larger "jackpots" and pay out a lot, but more vol doesn't make a loss more likely. Fun!
7/
More vol makes an option more likely to hit larger "jackpots" and pay out a lot, but more vol doesn't make a loss more likely. Fun!
7/
This asymmetric upside is what we mean when we say that an option has "convexity." The idea of "convexity" informs much of the theory and practical knowledge around options pricing and hedging.
Options are valuable because of their convexity! :D
8/
Options are valuable because of their convexity! :D
8/
If y'all have any more questions about options, let me know & it might feature in a tweetstorm in the future!
9/9
9/9
