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Hypotheses

LTC/BCH Copula Mispricing-Index Pair Reversion: Enter When One Fork's Daily Return Is Jointly Extreme vs the Other (MI<0.05 / MI>0.95 on a Monthly-Refit Archimedean Copula), Exit at MI Normalisation or 5-Day Clock, Flat ~90% (Binance USD-M 1D, two legs, long-short)

Restated from first principles, not ported, from the copula pairs-trading method in the QuantConnect write-up (itself after Stander, Marais & Botha 2013). A pair trade on the two legacy Bitcoin-fork 'payment coin'…

Hypothesis

Restated from first principles, not ported, from the copula pairs-trading method in the QuantConnect write-up (itself after Stander, Marais & Botha 2013). A pair trade on the two legacy Bitcoin-fork 'payment coin' perps LTCUSDT.BINANCE and BCHUSDT.BINANCE. Both are driven by the same retail and BTC-beta flows and share a sector narrative, so their daily log returns have high rank dependence (Kendall tau is typically about 0.6-0.7) and fat joint tails that a Gaussian z-score of the spread misdescribes. That tail……Show moreShow less

Restated from first principles, not ported, from the copula pairs-trading method in the QuantConnect write-up (itself after Stander, Marais & Botha 2013). A pair trade on the two legacy Bitcoin-fork 'payment coin' perps LTCUSDT.BINANCE and BCHUSDT.BINANCE. Both are driven by the same retail and BTC-beta flows and share a sector narrative, so their daily log returns have high rank dependence (Kendall tau is typically about 0.6-0.7) and fat joint tails that a Gaussian z-score of the spread misdescribes. That tail structure is what the copula models. On the first daily bar of each UTC month, the strategy uses the trailing 365 daily log returns of both legs. It (1) builds each leg's empirical CDF as a sorted numpy array; (2) computes Kendall tau; (3) derives theta for Clayton, Gumbel and Frank from tau (closed forms, plus a 1-D Frank root-solve); (4) picks the family with the lowest AIC; and (5) estimates the hedge ratio beta = OLS slope of r_BCH on r_LTC. Each day, today's returns map to u = ECDF_LTC(r_LTC) and v = ECDF_BCH(r_BCH), clipped to [0.005, 0.995]. The two mispricing indexes are MI_{LTC|BCH} = dC/dv and MI_{BCH|LTC} = dC/du from the fitted copula's closed-form conditional distributions. The pair is fixed and declared up front, not picked by a max-tau scan over a typed list (L151). The economic reason for this pair: the two coins share a lineage and a holder base, neither has its own supplementary edge, and together they are a small, unused slice of the corpus (BTC/ETH hold most of it). Venue is Binance USD-M because shorting a leg is required and both legs have daily history from January 2020 (about 2,400 bars; the OKX LTC series is only days old). IMPLEMENTATION NOTE, because recent runs died at the 300s sandbox limit: the refit happens only once per month on a 365-element buffer, and the per-bar work is two bisect lookups plus one closed-form evaluation, so it is O(log n). Never rebuild the ECDF or rescan history inside on_bar. Risk: each leg is sized to 25% of equity notional (beta-weighted, 1x leverage, 50% gross). A hard stop closes both legs if pair PnL reaches -4% of the gross pair notional.

Analysis

Pairs Trading-Copula vs Cointegration

Backtest and paper results are hypothetical. Trading involves risk of loss.