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Reiner-Rubinstein/Haug single barriers with rebates and Broadie-Glasserman-Kou discrete-monitoring correction, touch ladder, smile-consistent digitals on the vanna-volga smile, Dual Currency Investment fair-APR ladder with offer audit (platform margin, implied vol paid), and a KO accumulator Monte Carlo with zero-cost strike and optional Merton jumps. Validated against Haug Table 4-13 and discrete Monte Carlo. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01FpiqUMAyo4RL5DdQHMWbwE