​BitMEX Alpha: Arbitrage between Polymarket and Options

原作者：BitMEX

Welcome back to our weekly analysis of options investment strategies. Today, we will share a unique trading opportunity that stems from a significant difference in Bitcoin prediction probabilities between the BitMEX options market and prediction platform Polymarket.

The last out-of-the-money Bitcoin call option with a strike price of $120,000 (expiring on December 27) on BitMEX shows that the risk-neutral probability of Bitcoin reaching this price is about 8%. However, participants on the Polymarket platform have priced the probability of Bitcoin reaching $120,000 before December 31 at about 17%. This significant difference may bring arbitrage opportunities for savvy traders.

In this article, we take a closer look at this price mismatch, detail how the 8% probability is calculated, propose a trading strategy to exploit this discrepancy, and highlight key risks — specifically when even a slight increase in Bitcoin could result in a loss.

Let’s start with the detailed analysis.

Differences between BTC options implied probability and Polymarket

Polymarket prediction markets show a 17% probability of BTC reaching $120,000 by December 31 — more than double the options-implied probability of 8%.

The calculation process of 8% implied probability in BitMEX options market:

Lets do a quick calculation using the Black-Scholes model (omitting some intermediate steps):

• Spot Price(S): $97,500

• Exercise Price(K): $120,000

• Remaining term (T): about 16 days, or 0.0438 years

• Risk-free rate (r): 4.5%

• Implied volatility (σ): 72.4%

By calculating the parameter d 2, we can get the risk-neutral probability N(d 2)

Final result:

N(d 2)≈ 0.08, or 8%

This suggests that the options market (which is typically more mature and closer to fair risk-neutral pricing) assesses the probability of Bitcoin breaking $120,000 much lower than the sentiment-driven pricing in the prediction market. This difference creates an opportunity for arbitrage.

Arbitrage strategy: short Polymarket and buy out-of-the-money call options

If you agree with the more conservative 8% probability assessment of the options market, then the 17% pricing on Polymarket may be too optimistic. Here is the specific strategy:

1. Sell the Yes contract on Polymarket (17%): If Bitcoin does not reach $120,000 before December 31, you will receive the entire premium proceeds.

2. Buy a $120,000 Bitcoin call option (expiring on December 27): This option is priced closer to the 8% probability assessment and can provide hedging protection when Bitcoin breaks through $120,000 before December 27. If Bitcoin rises sharply, the option gains can offset Polymarkets losses.

Strategic advantages:

• You are essentially betting that Polymarket is overestimating the likelihood of Bitcoin breaking $120,000, while using that discrepancy to buy relatively cheap out-of-the-money call options.

• Call options act as a hedging tool, providing protection if the price of Bitcoin surges.

Specific operation method

Example analysis:

• Assume that a $120,000 call option on BitMEX costs $654.

• Short the Yes contract on Polymarket at $0.18. To cover the $654 option cost, you need to short approximately 3,633 Polymarket contracts (approximately $654).

Scenario Analysis and Revenue Structure

1. Scenario 1: Bitcoin does not reach $120,000 before December 31

○ The call option expires at zero ($654 loss)

○ Polymarket Yes contract is not triggered, you keep the $654 profit
Net result: roughly unchanged

2. Scenario 2: Bitcoin breaks through $120,000 before December 27 Assuming Bitcoin reaches $130,000 at the expiration date on December 27

○ Call option: Intrinsic value = 130,000 – 120,000 = $10,000 gain

○ Polymarket: Event occurred, $3,633 to be paid ($1 per contract)
Net Profit: 10,000 – 3,633 = 6,367 USD, a significant profit

3. Main Risk: Bitcoin Only Slightly Surpasses $120,000 Assume that Bitcoin reaches $121,000 on December 27. At this point the event is likely to occur before December 31 and the Polymarket Yes contract will settle at $1.

○ Call option profit: 121,000 – 120,000 = 1,000 USD

○ Polymarket payment: $3,633
Net loss: 1,000 – 3,633 = -2,633 USD

This is a key risk point: if Bitcoin only slightly exceeds $120,000, your option gain is limited, but you still have to pay the full $3,633 Polymarket payout. Since we are trying to fully offset the option cost by shorting a large number of Polymarket contracts, the fixed Polymarket payout may far exceed the small option gain. In short, a small breakout of Bitcoin (only slightly exceeding $120,000) will result in a large net loss.

Risk Warning

• Expiration mismatch: The option expires on December 27, while the Polymarket contract lasts until December 31. Bitcoin may not break $120,000 until after the option expires, at which point you will lose the option hedge protection.

• Non-linear payoff structure: The most dangerous area is just above $120,000. If Bitcoin fails to break through the strike price significantly, the fixed $1 payout per Polymarket contract may far exceed your small option profit.

• Difference between risk-neutral and actual probabilities: Option markets use risk-neutral probabilities, while polymarkets may reflect market sentiment. This difference may persist or widen.

• 市場 liquidity and execution risk: Spreads, slippage and position size are all important. Large transactions may affect market prices and undermine the initial strategy settings.

• The magnitude of the breakout is critical: only a significant breakout above $120,000 would be necessary for options gains to significantly outweigh Polymarket’s losses.

總結

This strategy targets the 8% probability difference between the options market and the prediction market, which is 17%. On the surface, it looks tempting: short a potentially overvalued contract on Polymarket, while hedging with relatively cheap out-of-the-money call options.

However, the risks cannot be ignored. If Bitcoin breaks through $120,000 modestly, the option gains may not be enough to offset the huge Polymarket payout, resulting in a large loss. This strategy requires careful consideration of various ratios, payoff structures, and target prices. If you do not have a strong belief that Bitcoin is either well below $120,000 or breaking through significantly, you may be stuck in a costly middle ground.

Please trade with caution, control your positions appropriately, and always pay attention to the maturity mismatch and yield curve shape before deciding whether to deploy this strategy.

This article is sourced from the internet: ​BitMEX Alpha: Arbitrage between Polymarket and Options

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