Kalshi S&P 8000 Probability Arbitrage Visualizer

Presets:

Market & Option Parameters S&P 500 Index

S&P 500 Spot Price ($) 6,100

Target Threshold ($) 8,000

Days Remaining to Expiration 148 days

Kalshi Contract Probability (%) 70.0%

Risk-Free Rate (SOFR/Yield) 4.50%

Implied Drift 48.50% Req. Annualized μ

Implied Volatility 28.40% Model Equivalent σ

Synthetic Hedge Delta 0.320 ETF Shares / Contract

Fair Contract Delta 0.280 Model Fair Value

Monte Carlo Price Path Trajectories

2,000 Lognormal Simulated Paths

Terminal Price Density & Fair Value Arbitrage

Market vs Black-Scholes Lognormal

Market Mispricing Analysis

At a market price of 70.0%, Kalshi's binary contract implies an extreme required S&P 500 drift of 48.50% annualized. Standard baseline lognormal pricing puts the hit probability closer to 28.0%.

Arbitrage Verdict: Kalshi binary contract is OVERPRICED by 42.0% relative to baseline index volatility.

Delta Neutral Overlay

To build a synthetic hedge against a short Kalshi binary position, hold 0.320 index ETF shares per contract unit. This offsets local spot move sensitivity.

Binary Contract Yield: 42.86%

Index Target Required Gain: 31.15%

Quantitative Model Framework

Uses Geometric Brownian Motion (GBM) with Monte Carlo path sampling (2,000 iterations). Binary payoff assumes cash-or-nothing call pricing via standard Black-Scholes Gaussian cumulative distributions ($d_2$).

dx(t) = μ x(t) dt + σ x(t) dW(t)