If the options market is likened to an unpredictable ocean, the volatility surface is a hydrological map with reefs, warm currents and storm zones marked. It does not directly tell you where to catch big fish, but it allows you to see the dangers and opportunities in different seas at a glance. When you are struggling to decide which strike price to buy for a call option before Tesla's financial report, or you don't know how to position yourself in the sideways market after Bitcoin's halving, this "topographic map" will quietly tell you: the fear and greed of the market are hidden in those undulating curves.

1. What is the volatility surface?

Imagine you are standing on the roof of CCTV building overlooking the whole city of Beijing - the volatility surface is the "God's perspective" of the options market. It uses the strike price as an east-west street, the expiration time as a north-south avenue, and the height of each skyscraper corresponds to the implied volatility of different options. For example, when Bitcoin broke through $70,000 in March 2025, the call option IV with an exercise price of $80,000 suddenly rose from the ground, like a spire breaking through the clouds, suggesting that the market is betting on a "crazy rush to the top".

The most fascinating thing about this three-dimensional surface is its "expression management". When the surface of the S&P 500 options is left-biased (the IV of put options with low strike prices is higher), it is like Houhai suddenly sinking into a basin - indicating that large funds are quietly buying "anti-fall insurance"; while the right-biased shape is like Jingshan suddenly rising into a ridge, revealing speculators' enthusiasm for the bull market. When Tesla released a humanoid robot in January this year, its option surface changed from "flat grassland" to "karst landform" within 72 hours. The IV of the call option with a strike price of $300 soared 45%, while the IV of the put option with a strike price of $250 dropped 12%. This is the "vote of confidence" cast by the market with real money.

The surface can be further broken down into new simple indicators. For example, the surface of the same time and different strike prices is an IV skewness curve. The surface of the same strike price and different time is an IV term structure curve.

2. Three practical codes of surfaces

1. “Weather forecast” in the time dimension

The curved expiration timeline hides the market's "patience index" for risk. On the eve of Bitcoin halving, the IV of near-month options was 28% higher than that of far-month options, just like fishermen who would rather buy life jackets at a high price today than stock up for next month's voyage when they see dark clouds on the horizon. Smart traders will then build a "calendar spread": sell near-month call options with high IV and buy far-month call options with low IV to earn the volatility premium in the time difference.

2. The “emotional thermometer” on the strike price axis

When the VIX index is calm, the surface of U.S. stock options often presents a perfect "smile curve" - the IV of out-of-the-money options is slightly higher than that of at-the-money contracts, just like a beach with a gentle coastline. However, during the GameStop short squeeze, the IV of a $10 put option was 30% higher than that of a $100 call option, and the surface was distorted into a hideous "ghost face". This is the "artificial tsunami" created by the large army of retail investors using option contracts.

3. Arbitrage opportunities in surface distortion

On the day when the United States approved the Bitcoin spot ETF in April 2024, a strange phenomenon occurred on the Deribit exchange: the IV of the $75,000 call option with an exercise price reached 95%, while the IV of the $60,000 put option with the same expiration date was only 68%. This is like two adjacent mountains with completely different altitudes. Institutions with a keen sense of smell immediately built a "volatility arbitrage portfolio": selling high-IV call options and buying low-IV put options, while using spot to hedge directional risks and achieve delta neutrality, making a net profit of 23% in volatility difference returns within a week.

3. Bitcoin vs. US stocks: A song of ice and fire on the surface

The curve of Bitcoin options is always more "turbulent" than that of US stocks. When the curve of S&P 500 is still fluctuating gently, the IV curve of Bitcoin may have been on a "roller coaster". In January 2025, Bitcoin was sideways at $65,000 for two weeks, but its monthly option curve showed a rare "double peak pattern": the call option with an exercise price of $70,000 and the put option with an exercise price of $58,000 both had IV peaks, just like the coexistence of volcanoes and glaciers - this is the extreme confrontation between the long and short sides at an important juncture.

In contrast, the curve of Apple options is more like a carefully trimmed Japanese garden. Even before the autumn new product launch, its curve maintained an elegant "right-leaning smile", and the IV only increased by 0.5% for every $10 increase in the strike price. This calmness stems from the rational pricing of institutional investors: they use algorithms to decompose volatility into each strike price and expiration date, just like using a compass to draw a perfect arc on the curve.

4. Basic methods of using surfaces to formulate trading strategies

Step 1: Locate the “terrestrial anomaly area”

Before the market opens each day, compare the current surface with the 20-day historical surface. When you find that the IV of a certain strike price is suddenly 2 standard deviations higher than the mean, it is like suddenly discovering a steep cliff in a plain area - it may be a trap, or it may hide gems. Before the NVIDIA GTC conference, the IV of the call option with an exercise price of $950 was 18% higher than that of the surrounding contracts. Foresighted traders made arrangements in advance and made a profit of 92% on the day when Huang Renxun demonstrated the results of the robot.

Step 2: Choose the right mountaineering equipment

In steep areas (such as out-of-the-money options with a sudden increase in IV), the buyer's strategy is used to amplify volatility leverage; in flat areas (such as at-the-money options with historically low IV), the seller's strategy is used to harvest time value. Just like in the calm period after the Bitcoin halving, selling a wide straddle combination (Iron Condor) can steadily obtain 3-5% premium income every week.

Step 3: Set up a “safe evacuation route”

When the curve shape undergoes irreversible distortion (such as a 20% surge in the VIX index in a single day), you must decisively initiate hedging. During the Silicon Valley Bank crisis in 2024, a trader immediately bought SPY out-of-the-money put options when the curve reached a historical extreme to the left. Although he paid a 5% hedging cost, he successfully avoided a subsequent 23% account drawdown.

Of course, the trend of the surface may extend or reverse. How to judge the trend of the surface and make arbitrage is a profound knowledge. We will further analyze it in the following courses.

5. Next Issue Preview

Tomorrow we will delve into the "Option Chain Interpretation"

Homework

1. Surface scanning training : Call the current Tesla option volatility surface on TradingView and mark the strike price area where IV is higher than the 30% percentile

2. Arbitrage strategy design : Assuming that the Bitcoin monthly option surface is left-skewed (put IV > call IV), design a delta-neutral arbitrage portfolio

3. Actual combat simulation : Use a virtual account of $100,000 to implement a "volatility surface regression" transaction on the Deribit platform (short distortion zone IV/long normal zone IV)