{"status":"ok","tool":"coin_history","price":"free","data":{"coin_id":"ethereum","current_price_usd":2267.105799720751,"model":"merton_jump_diffusion","days":90,"simulations":20000,"model_params":{"drift_mu":0.08,"diffusion_sigma":0.6,"jump_intensity_lambda":3.0,"jump_mean_mu_j":-0.06,"jump_vol_sigma_j":0.12},"forecast_percentiles":{"5th":1292.015,"25th":1779.0391,"50th":2207.5638,"75th":2728.3866,"95th":3710.9835},"risk_metrics":{"VaR_95":1292.015,"VaR_95_pct":-43.01,"CVaR_95":1139.489,"CVaR_95_pct":-49.74},"source":"coingecko_merton_oracle","verifiability":{"provably_fair":true,"method":"Monte Carlo seeded from the public drand randomness beacon — the seed is committed publicly each round and cannot be cherry-picked. Re-fetch the round and reproduce.","beacon":"drand-league-of-entropy","round":6602949,"randomness":"936f28c5cec184bfd394c51a9abddf959f2497b308cbc60c5da1015ffbcd8cfc","verify_round_url":"https://api.drand.sh/public/6602949","exact_params":{"mu":0.08,"sigma":0.6,"lambda_jump":3.0,"mu_j":-0.06,"sigma_j":0.12,"n_sims":20000,"days":90,"current_price":2267.105799720751,"model":"merton_jump_diffusion"},"reproduce":"rng = numpy.random.default_rng(int(randomness, 16)); Z = concat(rng.standard_normal(n_sims//2), -that) for antithetic variates; draw N=rng.poisson(lambda_jump*days/365, n_sims) and J=rng.normal(N*mu_j, sqrt(max(N,1))*sigma_j); apply the terminal Merton/GBM formula."}}}