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Siegel's paradox: E[S_T]·E[1/S_T] = e^(σ²T) > 1 (reciprocal-rate convexity correction)
area:fxFX & multi-currency — Garman–Kohlhagen, rate parity, quanto.FX & multi-currency — Garman–Kohlhagen, rate parity, quanto.difficulty:smallStraightforward change for someone familiar with the repoStraightforward change for someone familiar with the repogood first issueGood for newcomersGood for newcomershelp wantedExtra attention is neededExtra attention is neededstatus:readyScoped enough for a contributor to pick upScoped enough for a contributor to pick uptype:proofLean theorem, proof repair, or theorem generalizationLean theorem, proof repair, or theorem generalizationStatus: Open.#109 In raphaelrrcoelho/formal-mathfin;Covered & uncovered interest-rate parity F = S·e^((r_d−r_f)T)
area:fxFX & multi-currency — Garman–Kohlhagen, rate parity, quanto.FX & multi-currency — Garman–Kohlhagen, rate parity, quanto.difficulty:smallStraightforward change for someone familiar with the repoStraightforward change for someone familiar with the repogood first issueGood for newcomersGood for newcomershelp wantedExtra attention is neededExtra attention is neededstatus:readyScoped enough for a contributor to pick upScoped enough for a contributor to pick uptype:proofLean theorem, proof repair, or theorem generalizationLean theorem, proof repair, or theorem generalizationStatus: Open.#108 In raphaelrrcoelho/formal-mathfin;Glosten–Milgrom adverse-selection bid–ask spread from Bayesian quotes
area:executionOptimal execution & market microstructure — Almgren–Chriss, Kyle, market impact.Optimal execution & market microstructure — Almgren–Chriss, Kyle, market impact.difficulty:mediumRequires repo context, Lean fluency, or careful validationRequires repo context, Lean fluency, or careful validationhelp wantedExtra attention is neededExtra attention is neededstatus:readyScoped enough for a contributor to pick upScoped enough for a contributor to pick uptype:proofLean theorem, proof repair, or theorem generalizationLean theorem, proof repair, or theorem generalizationStatus: Open.#107 In raphaelrrcoelho/formal-mathfin;Kyle (1985) single-period equilibrium price impact λ = σ_v/(2σ_u)
area:executionOptimal execution & market microstructure — Almgren–Chriss, Kyle, market impact.Optimal execution & market microstructure — Almgren–Chriss, Kyle, market impact.difficulty:mediumRequires repo context, Lean fluency, or careful validationRequires repo context, Lean fluency, or careful validationstatus:readyScoped enough for a contributor to pick upScoped enough for a contributor to pick uptype:researchOpen investigation where the path is not yet clearOpen investigation where the path is not yet clearStatus: Open.#106 In raphaelrrcoelho/formal-mathfin;Raw-SVI total-variance slice: non-negativity, convexity, and linear wings b(1∓ρ)
area:stoch-volStochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.Stochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.difficulty:mediumRequires repo context, Lean fluency, or careful validationRequires repo context, Lean fluency, or careful validationstatus:readyScoped enough for a contributor to pick upScoped enough for a contributor to pick uptype:proofLean theorem, proof repair, or theorem generalizationLean theorem, proof repair, or theorem generalizationStatus: Open.#105 In raphaelrrcoelho/formal-mathfin;Calendar-spread no-arbitrage: European call non-decreasing in maturity (total variance w=σ²T monotone)
area:stoch-volStochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.Stochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.difficulty:mediumRequires repo context, Lean fluency, or careful validationRequires repo context, Lean fluency, or careful validationhelp wantedExtra attention is neededExtra attention is neededstatus:readyScoped enough for a contributor to pick upScoped enough for a contributor to pick uptype:proofLean theorem, proof repair, or theorem generalizationLean theorem, proof repair, or theorem generalizationStatus: Open.#104 In raphaelrrcoelho/formal-mathfin;Model-free implied variance / VIX static replication as the 1/K² OTM-option strip
area:stoch-volStochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.Stochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.difficulty:mediumRequires repo context, Lean fluency, or careful validationRequires repo context, Lean fluency, or careful validationhelp wantedExtra attention is neededExtra attention is neededstatus:readyScoped enough for a contributor to pick upScoped enough for a contributor to pick uptype:proofLean theorem, proof repair, or theorem generalizationLean theorem, proof repair, or theorem generalizationStatus: Open.#103 In raphaelrrcoelho/formal-mathfin;CEV European call closed form (non-central chi-squared)
area:stoch-volStochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.Stochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.difficulty:hardRequires deep domain knowledge or upstream coordinationRequires deep domain knowledge or upstream coordinationstatus:blocked-upstreamBlocked on Mathlib, BrownianMotion, or another external projectBlocked on Mathlib, BrownianMotion, or another external projecttype:researchOpen investigation where the path is not yet clearOpen investigation where the path is not yet clearStatus: Open.#102 In raphaelrrcoelho/formal-mathfin;Dupire local-volatility formula σ_loc² = (∂_T C + rK∂_K C)/(½K²∂²_K C)
area:stoch-volStochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.Stochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.difficulty:hardRequires deep domain knowledge or upstream coordinationRequires deep domain knowledge or upstream coordinationstatus:blocked-designBlocked on a modeling, theorem-shape, or architecture decisionBlocked on a modeling, theorem-shape, or architecture decisiontype:researchOpen investigation where the path is not yet clearOpen investigation where the path is not yet clearStatus: Open.#101 In raphaelrrcoelho/formal-mathfin;SABR Hagan asymptotic implied volatility (ATM leading order + O(T²) error bound)
area:stoch-volStochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.Stochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.difficulty:hardRequires deep domain knowledge or upstream coordinationRequires deep domain knowledge or upstream coordinationstatus:blocked-designBlocked on a modeling, theorem-shape, or architecture decisionBlocked on a modeling, theorem-shape, or architecture decisiontype:researchOpen investigation where the path is not yet clearOpen investigation where the path is not yet clearStatus: Open.#100 In raphaelrrcoelho/formal-mathfin;Heston characteristic function: verify C, D solve the Heston Riccati ODEs
area:stoch-volStochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.Stochastic & local volatility — Heston, SABR, Dupire, variance swaps, vol surface.difficulty:hardRequires deep domain knowledge or upstream coordinationRequires deep domain knowledge or upstream coordinationstatus:blocked-designBlocked on a modeling, theorem-shape, or architecture decisionBlocked on a modeling, theorem-shape, or architecture decisiontype:researchOpen investigation where the path is not yet clearOpen investigation where the path is not yet clearStatus: Open.#99 In raphaelrrcoelho/formal-mathfin;Basic unilateral CVA = (1−R)·∫₀ᵀ EE(u)·e^(−ru)·h(u)·S(u) du
area:creditCredit risk — structural + reduced-form default, CDS, correlation, XVA.Credit risk — structural + reduced-form default, CDS, correlation, XVA.difficulty:mediumRequires repo context, Lean fluency, or careful validationRequires repo context, Lean fluency, or careful validationstatus:readyScoped enough for a contributor to pick upScoped enough for a contributor to pick uptype:proofLean theorem, proof repair, or theorem generalizationLean theorem, proof repair, or theorem generalizationStatus: Open.#98 In raphaelrrcoelho/formal-mathfin;