Delta: From Options to Prediction Markets
Early this year, I became more serious about options trading and hired a coach who’s been doing it for 20 years. From the very first lesson, the concepts he would grill me on most were the “Greeks”. Specifically, delta and theta.
One memorable Sunday, I dialed into our call excited to show him all of the high-premium positions I had sold. His reaction was not what I expected.
Oh, premium revenue? Doesn’t matter. The thing that matters is your portfolio-level delta.
He ignored my P&L calculations and asked me “What’s your total delta right now?” before chiding me for having too high of a positive delta.
I thought he meant my biggest trade. He meant my whole book.
It’s not about the 98% of the time your strategy works. It’s about the 2% when everything goes to shit.
Delta plays a huge factor in how traders should manage their “portfolio” of positions on prediction markets like Polymarket and Kalshi. In the US, prediction market positions are regulated as a variant of futures contracts in the US. Concepts like delta are critical to understand.
Delta in the world of options
An options contract is a bet on an asset’s price at a given date in the future. It has its own price that reflects what traders think the underlying stock might do rather than what it’s doing right now.
In options, delta measures how much an option contract’s price changes for every $1 move in the underlying stock. Mathematically:
This formula captures the derivative relationship: the option’s price depends on the underlying stock’s price, and delta tells you the rate of change between them.
For example, if TSLA trades at $400 and a weekly 410 call has a delta of 0.45, that means for every $1 move in TSLA, the option’s price should change by about 45¢.
When TSLA jumps to $445 on positive news, that same call’s delta might surge to 0.70, becoming more “stock-like” ($0.70 move per $1 as opposed to a $0.45 move) as it moves closer to in-the-money. This acceleration in sensitivity is called gamma, but that could be its own article. For now, just think of it as the rate that delta changes.
Delta as a probability proxy
In options, delta is also used as a rough stand-in for the probability an option contract finishes in-the-money (ITM). More simply, the probability that the price of the asset will be within the strike price by the expiration date, and thus the contract will “hit”.
That idea comes from the Black–Scholes model, where for a long position:
Under the model’s assumptions, is a calculation that considers factors like the stock or ETF’s price, option strike price, implied volatility and time decay. ends up close to the probability of the option expiring in-the-money, with a few caveats.
So when someone says, “This Tesla 450 10/31 call has a 0.35 delta,” it also means “the market thinks that TSLA has about a 35% chance of reaching $450 by 10/31.”
Unlike theta (time decay) and other concepts that I’ll explore in future articles, the strict definition of delta (rate of change of contract relative to underlying) does not apply perfectly to prediction markets. This is because is no 1:1 option contract <> underlying asset relationship like a TSLA Call contract <> TSLA stock.
You can’t write the derivative formula because token price and probability are the same thing. However, the concept of convexity (acceleration/deceleration in the rate of change) still applies.
Delta and prediction markets
In prediction markets, small context shifts create outsized price moves, especially at 50%-50% scenarios with maximal uncertainty. Moving from a Yes of 50% to 70% is a 40% relative increase in probability; moving from 70% to 90% is only 29%. Same absolute shift, diminishing impact.
This mirrors options: if META is at $730, options contracts with a $730 strike price have the largest fluctuations in delta. Options contracts with a $800 strike price will react more sluggishly to news.
Moreover, the probability proxy maps to prediction markets perfectly. The price IS the probability: on Polymarket or Kalshi, the contract price (Yes / No token price) represents the probability that an event happens.
Prices stay between $0 and $1 because they represent probabilities. A Yes share trading at $0.55 means the market believes there’s a 55% chance the event happens. As a delta proxy, that probability quantifies the market’s view of the event’s likelihood in the same way a 0.55-delta option reflects a 55% ITM probability.
”So what?” Tactical tips for prediction markets trading
That was a lot. With that foundation, I’ll break down a few tangible, practical ways you can apply delta thinking to your prediction markets trading.
1. Be judicious with your entry prices. 50-50 markets are risky.
Statistically, an option contract has the highest “delta sensitivity” (rate of change of delta) at the money. For example, a TSLA 450 Call contract’s price is most sensitive to change when TSLA is right at 450 - a $1 swing either way determines if the option is worthless or not.
Similarly, investing in a 50-50 prediction market will have the largest rate of change of probability and thus, uncertainty. Moving from 50% → 60% is a 20% relative increase in probability and return on capital. Moving from 30% → 40% is a 33% relative increase AND return. It’s dangerous to invest in these without an edge, because your initial investment could decrease in value more rapidly. Waiting until that market is 60-40 or 65-35 market will give you outsized returns relative to the certainty.
2. Hedge prediction markets with traditional instruments
Prediction markets are a boon for institutional investors because they can finally hedge their traditional investments. They can control for global instability by betting on markets in politics, weather and world events.
As a prediction markets trader, think in the reverse way. Use traditional investments to hedge your prediction market bets. You can buy spot stocks/ETFs, buy/sell options or futures and trade the VIX to hedge event risk. For example, people betting on Kamala to win the 2024 election could have hedged with selling puts or buying long calls on the S&P or crypto ETFs. People betting on strong crypto price action in prediction markets can hedge by shorting BTC futures.
3. Think about being “delta-neutral” across your predictions market portfolio
Like we saw in the beginning of this article, your portfolio-level delta is important to keep an eye on. Betting on BTC > $140k, QQQ > $700 and 3 Fed rate cuts by EOY 2025 are all dovish-Fed, risk-on bets on the same worldview. One unpredictable world event could upend all 3 positions. Be wary of that 2% when everything goes to shit - offset optimism in one area with contrarian bets elsewhere.
Take a minute to review your net directional exposure across your predictions (and broader) portfolio. If multiple bets resolve to the same underlying outcome, you’re levered, not diversified. Right now, the world is more unpredictable than ever. Imagine the various alternate universes that could play out and try to balance your portfolio accordingly.
4. Arbitrage delta/probability mismatches between markets
This is an offshoot of points 2 and 3. Because predictions markets offer another way to express opinions on financial assets, it’s another venue to arbitrage vis-a-vis on-chain and off-chain markets.
For example, if Kalshi prices ETH >$4,500 by EOY at 65% but options deltas on ETHE imply 45%, that’s a 20 basis-point gap. As long as there’s sufficient liquidity, these delta/probability mismatches are pure edge. You could buy the underpriced NO on Kalshi and buy some ETHE end-of-Dec call options or a call spread at $45.
If Copper > $5/lb by EOY is 50% on Polymarket but CPER futures imply ~70%, you could buy YES on Polymarket and short CPER to end up in the green either way.
Prediction markets feel more like gambling than trading on public markets, but they’re all interconnected. They all involve real money, so treat them accordingly.
© 2025 Kevin D. Kim