Exact Terminal Compactification for Finite-Source Quoted-Band Superhedging of Activated Bitcoin Calls

Source abstract

An exact projective compactification is established and implemented for quoted-band superhedging of activated Bitcoin calls with payoff 1{X1≥B}X2−K+. The computation is exact on the terminal half-line, conditional on a disclosed finite first-date support; no equality with a continuum of first-date states is claimed. Recession variables are identified as projective-boundary atoms, one per first-date source node, and the finite-knot inequalities with the terminal-slope rows are proved necessary as well as sufficient for the semi-infinite continuous-terminal hedge. Only quoted bid–ask bands are used: no fitted volatility surface, no mid-price substitution, and no ex post quote repair. Across 82 monthly Deribit snapshots from October 2019 to July 2026 and two maturity pairs, 161 of 164 panels are feasible. Median reductions from the constant-delta value, conditional on the disclosed finite first-date support throughout, are 6.35% for 1M/2M and 3.30% for 3M/6M, against a median relative interval width of 42.65%, so these are seller-capital savings rather than point estimates of market value. Deleting the recession rows changes no feasible value measurably, yet at the smallest terminal cutoff, it creates 125 false infeasibility classifications and 431 hedges that pass every finite-grid test while failing the omitted terminal ray. Price stability and certificate validity are, therefore, distinct properties.