# What’s a “Delta”?

## Delta

1. Time until the bet is over- If today is December 31st, 2022 and the price of Tesla stock is four times the price it was on January 1st, 2022 then it is very very likely that the price the following day will be at least two times the price it was at the beginning of the year (meaning I win the bet), because it is unlikely the stock goes down more than 50% overnight. So, a rational derivatives price would be very very close to \$10, say \$9.95. On the other hand, if it’s month 3 (9 months of the bet remaining) and the price is four times the price at the beginning of the year, it seems somewhat likely that the stock will be above the two times bet price by the end of the year. But, this extra 9 months introduces some uncertainty, changing the confidence of winning the bet from very very likely to somewhat likely, so a rational derivatives price would instead be somewhat close to \$10, say \$7. Note the price of the Tesla stock is the same in both cases, what has changed is the time until the bet is over, which changes the derivative price.
2. Price of the referenced asset- Regardless of the time until the end of the bet, the derivatives price will depend on the price of Tesla stock at any given moment. Suppose it’s 6 months into the bet (6 months remaining). If Tesla stock is up ten times in this 6 month period, I can be pretty confident that I will win the bet, so someone might be willing to pay me \$9 to take on this bet. If Tesla stock was down 99% from the beginning of the year, it would be very unlikely that I will win the bet so someone wouldn’t be willing to pay me anything. In fact, I’d have to pay someone almost \$10 to take the risk. Note the time to the end of the bet is the same in both cases, what has changed is the price of Tesla stock at that point in time.
3. Volatility of the referenced asset- Volatility refers to the amount up or down an asset will typically move in a defined time period. For example, gold’s volatility is usually pretty low, because the price fluctuates pretty slowly. Bitcoin’s volatility is usually pretty high, because it can double or halve in short period of time. Suppose hypothetically that Tesla stock was a very very low volatility asset and in its entire history has only ever gone up or down 2% annually. This implies the price never changes much. Then, a bet that Tesla will double is not very likely, because it doesn’t usually change price that much. So, the derivatives price of this bet would be low. On the other hand, if hypothetically Tesla stock often moves by 10% per day, it seems much more possible that Tesla could double over a year (it could do so in as little as ~7 days if it always moves up or down 10%!). So, the derivatives price of this bet would be much higher because intuitively it seems more possible that Tesla could double if given enough time.

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