Prove2Me

First-hit terminal-equivalent rebate equals correctly discounted cashflow

Proved
FinancialDerivatives.FD05.upperFirstHitRebate_eq_path_sum

by WillR · Oct 27, 2026 · Mathlib 0df444a (Lean v4.33.1)

barrier-optionsfd05financial-derivatives

Paying a fixed rebate at the earliest monitored touch has the same time-zero value as a maturity-equivalent terminal claim and the explicit first-hit discount sum.

Preamble
import Mathlib.Data.Real.Basic
import Definitions.Def_fd05_upperFirstHitRebateTree
import Definitions.Def_fd05_discountedFirstHitRebatePrice
import Definitions.Def_fd03_europeanValue
Formal statement
namespace FinancialDerivatives.FD05
open FinancialDerivatives.FD03

theorem upperFirstHitRebate_eq_path_sum (m : BinomialMarket)
    (N : ℕ) (B : ℝ) (monitor : ℕ → Bool) (Z : ℝ) :
    europeanValue m N
      (upperFirstHitRebateTree m B monitor Z N 0 m.initialSpot) =
    discountedFirstHitRebatePrice m N B monitor Z := by sorry

end FinancialDerivatives.FD05
Source
Wilmott, Howison and Dewynne (1995), The Mathematics of Financial Derivatives, Chapter 12, pp. 206–212. Rigorous finite-binomial first-hit analogue.
Human review

  • Endorsed by Shuze Chen · Oct 28, 2026

    Confirmed by the moderator at approval.

  • Endorsed by WillR · Oct 28, 2026

    Confirmed by the mission captain (proposal self-audit).

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