{
  "lesson": "exotic-options.md",
  "updated": "2026-09-19",
  "data_status": "All paths, contract inputs and numerical examples are hypothetical; no market observations are included.",
  "private_source_mapping": [{
    "file": "JA253.5 Notes.pdf",
    "title": "Exotic Options",
    "physical_pages": 59,
    "published": false,
    "coverage": [
      {"pages": "1-9", "use": "Contract classification, time dependence and cashflows"},
      {"pages": "10-24", "use": "Strong/weak path dependence and dimension counts"},
      {"pages": "25-30", "use": "Order, embedded decisions and pricing methods"},
      {"pages": "31-34", "use": "Barrier contract and PDE boundaries"},
      {"pages": "35-47", "use": "Integral state, hedging and arithmetic Asian PDE"},
      {"pages": "48-50", "use": "Floating-strike Asian similarity reduction"},
      {"pages": "51-59", "use": "Discrete average and lookback updating rules"}
    ]
  }],
  "public_sources": [
    {"url": "https://people.maths.ox.ac.uk/gilesm/talks/IMACS_2013.pdf#page=10", "use": "Brownian bridge crossing probability and product survival weighting; applied here to exact log GBM with constant coefficients"},
    {"url": "https://business.columbia.edu/faculty/research/continuity-correction-discrete-barrier-options", "use": "Broadie, Glasserman and Kou 1997: continuous versus discrete barrier monitoring"},
    {"url": "https://arxiv.org/abs/1106.1999", "use": "Kumar, Waikos and Chakrabarty 2011: average-strike Asian PDE reference"}
  ],
  "conventions_and_corrections": [
    "Cashflow uses C, not q; V-before equals V-after plus payment when states are otherwise unchanged. Constant cash payment need not change delta/gamma.",
    "Weak barrier path dependence still requires an alive/hit flag; no added continuous state dimension on the alive PDE domain.",
    "State dimension is distinguished from time and Brownian driver count.",
    "Finite-variation integral state remains random through S, without a new diffusion term; no V_II or V_SI terms.",
    "Hedging argument includes self-financing cash account; rebalancing costs are not omitted.",
    "V=I W(S/I,t) applies to continuous floating-strike arithmetic Asian with I>0; inception I=0 is singular.",
    "Fixing remapping with matched old/new state is a derived extension beyond page 59, not a quoted source formula.",
    "All-exotics-OTC, never-continuous, universally-prefer-PDE and automatic-Greeks-jump claims are not adopted.",
    "Sampling error, monitoring/numerical error and model error are separate; terminal averaging alone does not price early exercise.",
    "Source PDF and slide screenshots are not included in the repository or deployed website."
  ],
  "simulations": {
    "assumptions": "European call payoffs; no dividends, costs, rebates or early exercise; constant r and sigma; exact GBM date-to-date transitions under Q; independent standard Normal shocks; continuously compounded annual r; T in years; synthetic dollar units.",
    "defaults": {"S0": 100, "K": 100, "H": 130, "r": 0.03, "sigma": 0.2, "T": 1, "steps": 12, "paths": 12000, "seed": 2535},
    "asian": "Arithmetic average over jT/m, j=1,...,m; S0 excluded.",
    "barrier_discrete": "S0 and all fixing dates through T monitored; touch counts as hit.",
    "barrier_continuous": "Product of exact conditional log-GBM bridge survival probabilities, constant upper H; weighted discounted payoff SE across independent paths; no simulated hit count for continuous monitoring.",
    "uncertainty": "Sample SD with N-1 denominator, SE=SD/sqrt(N), approximate Normal 95% CI; rare-event limitations stated.",
    "rng": "Browser and Python use documented seeded generators independently; identical seeds do not imply identical paths across languages.",
    "same_endpoint": {"A": [100,110,120,110,110], "B": [100,140,90,100,110], "K": 100, "H": 130, "payoffs_A_vanilla_asian_out": [10,12.5,10], "payoffs_B_vanilla_asian_out": [10,10,0]},
    "cashflow_figure": {"coupon": 4, "coupon_time": 0.5, "principal": 100, "maturity": 1, "r": 0.03}
  },
  "assets": {
    "route": "no-image-generator",
    "brand": "QuantCorner / QuantSeras existing light book theme, purple/teal accents with optional dark theme",
    "generator": "scripts/make_exotic_options_figures.py",
    "math_source": "scripts/exotic_options_math.py",
    "files": ["assets/images/exotic-path-payoffs.svg", "assets/images/exotic-monitoring.svg", "assets/images/exotic-cashflow-jump.svg"],
    "editable_source": "Deterministic Python calculations and SVG geometry; no image-generation tool used"
  },
  "notebook": {"generator": "scripts/make_exotic_options_notebook.py", "code_cells": 9, "dependencies": "Python standard library", "source": "Canonical chapter Markdown with SHA-256; inlined Python helper functions; embedded SVG attachments"},
  "limits": "Lesson formulates PDEs and similarity reduction but does not implement a finite-difference PDE solver. Not a market-calibrated exotic pricing system."
}