At month 0, you buy a PUT struck at your debt level — downside insurance. Each month, as debt drops from repayment, the model prices selling the held PUT and buying a cheaper one at the new, lower strike. If the net roll profit after slippage exceeds $20, the roll executes. The price difference is your roll savings.

11 monthly checkpoints (months 1–11). At month 12, the final PUT expires. The Debt vs Strike chart in the path explorer shows this visually.

Black-Scholes, European cash-settled PUTs. Inputs: spot, strike (= 103% of debt, snapped up to exchange grid), time to expiry, IV from SVI surface. Risk-free rate = 0 (crypto convention). BS is used because Deribit uses it for mark pricing — theoretical and market prices are directly comparable.

Deribit historical options trades, ~1.4M data points over 700+ days. SVI parameterization per day across 5 tenor buckets (short / 90d / 180d / 270d / 365d), 26 moneyness points (0.4–2.9).

Min quote thresholds: 6/bucket (short tenors), 12/bucket (180d+). Sparse buckets forward-filled up to 60 days. IV is the most sensitive input to PUT pricing — a full surface captures the smile/skew that a single ATM vol would miss.

GBM calibrated from ~3 years of Binance BTCUSDT hourly candles, resampled to daily log returns. Daily resolution (dt = 1/365).

Regime-matched IV: For forward months, the model picks the historical IV surface whose 7-day trailing return best matches the simulated path — so options are priced with IV realistic for the current regime, not a stale snapshot.

GBM is the simplest model that captures drift + vol. It does not model regime shifts, jumps, or stochastic vol.

Bitmor hedges every BTC-backed loan with a PUT option. If a borrower defaults at any point, the protocol liquidates by selling the BTC collateral and the PUT. The coverage ratio checks whether those two assets cover the outstanding debt plus a 3% liquidator fee. The PUT itself is struck 3% above the debt level to maintain a collateralisation buffer.

This backtest asks: has there been a single day in history where coverage dropped below 1.0? It originates a loan on every calendar day from April 2021 through March 2025 (~1,460 loans), then replays the actual BTC price path for the full 12-month term. No Monte Carlo, no randomness.

Each loan uses the same parameters as the Monte Carlo simulation: 30% down payment, 70% LTV, 10% APR accrual, 15% APR for conservative payment sizing, 12-month term. The PUT is struck 3% above the debt level, snapped up to the nearest Deribit-listed strike — ensuring a minimum collateralisation buffer.

Debt accrues daily. Monthly payments are deducted at 30-day boundaries. At each monthly checkpoint, the model attempts a PUT rolldown: sell the held PUT, buy a cheaper one struck 3% above the new (lower) debt level. The roll executes only if profitable after slippage.

For each of the 360 days in a loan's life, the model computes:

The PUT is valued using Black-Scholes with the actual SVI implied volatility surface for that calendar date. IV lookup uses nearest-neighbor matching on tenor and moneyness. If the exact date is missing (weekends), the nearest available surface date is used.

The same SVI surface used for roll-down research: daily Deribit data from April 2021 to March 2026, parameterized across 5 tenor buckets and 26 moneyness points. Black-Scholes, European cash-settled PUTs, risk-free rate = 0.

No regime matching is needed here. Since the backtest replays historical dates, it uses the actual IV surface for that exact day.

Same model as roll-down research: flat 0.8% half-spread through 30% OTM, then quadratic ramp to 5% at 50% OTM. Calibrated to live Deribit BTC put orderbooks. Slippage is subtracted from PUT MTM before computing coverage, and applied to both legs of a roll.