IV
Implied Volatility (IV) refers to the market’s expectations of future price fluctuations of an underlying asset. Unlike historical volatility, which can be derived from past prices, IV is a “forward-looking” metric inferred from current option prices.

In simpler terms:
IV reflects the market’s confidence or fear about future price movement as expressed through “option pricing”.

More precisely:

• IV is a key input variable in option pricing models such as Black-Scholes.
• Since the market price of an option is known, and other parameters (spot price, strike price, risk-free rate, and time to maturity) are also known,
• We can “reverse-engineer” the volatility value that makes the model price match the market price.
• This reverse-solved volatility is known as “Implied Volatility”.

Example:

• Suppose BTC is currently trading at $105,000.
• A BTC call option is priced at $2,000 on the market.
• Plugging this into the Black-Scholes model, you find that to match the $2,000 price, the implied volatility must be 65%.
• Therefore, the IV of this option is 65%.

Key features:

Key takeaway:
Implied volatility represents “future expectations” embedded in an option’s price — it reflects how the market is currently pricing in potential future volatility of the underlying asset, rather than past performance.

How Implied Volatility Affects Delta

The impact of Implied Volatility (IV) on Delta is a critical but often overlooked aspect of options pricing. Here’s a breakdown:

When IV increases

• Out-of-the-money Options (OTM): Delta increases (moves closer to 0.5 or -0.5)
• In-the-money Options (ITM): Delta decreases (also moves closer to 0.5 or -0.5)
• Delta distribution flattens and clusters around 0.5

Underlying logic:

1.Delta measures how sensitive an option’s price is to changes in the underlying price

• Specifically, Delta indicates how much the option price is expected to change when the underlying asset’s price moves by 1 unit.

2.Implied volatility reflects the market’s expectation of future price fluctuations

• When volatility increases, it means the market anticipates greater price swings in the future. As a result, option prices rise—particularly out-of-the-money (OTM) options, which tend to gain more in value.

Higher volatility increases the probability of an option becoming in-the-money.

• For example, if an out-of-the-money call option sees a rise in implied volatility, its chance of reaching the strike price increases → the option becomes more “in-the-money–like” → Delta rises.
• Similarly, for an in-the-money call option, higher volatility introduces more uncertainty about it staying in the money → Delta decreases and moves closer to 0.5.

Example - Call Option:

In Summary:
Rising IV increases Delta for OTM options and decreases Delta for ITM options — causing all Deltas to converge toward 0.5.

How Time Affects Delta

In crypto options trading, Delta measures how sensitive an option’s price is to changes in the BTC spot price:

• Call Options (Calls): Delta ranges from 0 to 1
• Put Options (Puts): Delta ranges from -1 to 0

Delta is not only influenced by the underlying price but also highly sensitive to time to maturity.

Impact of Time to Maturity:

For far-dated options (options with a longer time to maturity):

• Given BTC’s high volatility, far-dated options have a wider possible price path.
• Even if the option is currently out-of-the-money (e.g., BTC is trading at $104,000 while the strike price of a call option is $110,000), the market still believes there’s a reasonable chance the price might rise above the strike before expiration.
• As a result, the Delta of such OTM options does not drop too low—it typically stays around 0.25 to 0.35;
• Likewise, for ITM options, the Delta doesn’t approach 1 as closely.

Conclusion: Deltas appear more “neutral”, hovering closer to 0.5, reflecting greater uncertainty.

For near-term options (those close to maturity):

• When very little time remains until expiry, the window for price movement becomes significantly narrower.
• If the option is still out-of-the-money (e.g. BTC is at $104,000 and the strike price is $110,000), there is very little chance it will become in-the-money before maturity.
• Delta drops sharply (e.g., 0.01~0.05).
• Conversely, if BTC is at $104,000 and the strike price is $90,000 (deep in-the-money), it’s almost guaranteed the option will remain in-the-money at expiry. In this case, the Delta is very high, nearing 1.

Conclusion: The Delta of near-expiry options becomes much more polarized—either very close to 0 or very close to 1. This reflects an “all or nothing” characteristic.

Key takeaway:
In BTC options trading, the shorter the time to maturity, the more “extreme” the Delta values become—either nearing 0 or 1. The longer the time to expire, the more “neutral” the Delta becomes, typically trending toward 0.5 due to the increased uncertainty about future price movements.