Research Note

Sources consulted for Parts 3 and 4. Numbers in brackets match the footnote markers in the body text; click any footnote to jump here, and the back-arrows below return you to the citation site.

1. textbook ↩ used in §3.1

   Hull, J. C. Options, Futures, and Other Derivatives. Pearson.

2. paper ↩ used in §3.1

   Rubinstein, M. (1994). "Implied Binomial Trees." Journal of Finance 49(3), 771–818.

3. paper ↩ used in §3.1

   Merton, R. C. (1976). "Option Pricing When Underlying Stock Returns Are Discontinuous." Journal of Financial Economics 3, 125–144.

4. paper ↩ used in §3.1

   Bates, D. (1996). "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options." Review of Financial Studies 9(1), 69–107.

5. paper ↩ used in §3.2

   Bachelier, L. (1900). Théorie de la spéculation. Annales Scientifiques de l'É.N.S. 17, 21–86.

6. book ↩ used in §3.2

   Davis, M. & Etheridge, A. (2006). Louis Bachelier's Theory of Speculation: The Origins of Modern Finance. Princeton University Press.

7. paper ↩ used in §3.3

   Heston, S. L. (1993). "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options." Review of Financial Studies 6(2), 327–343.

8. paper ↩ used in §4.1

   Jorion, P. (2000). "Risk Management Lessons from Long-Term Capital Management." European Financial Management 6(3), 277–300.

9. book ↩ used in §4.1

   Lowenstein, R. (2000). When Genius Failed: The Rise and Fall of Long-Term Capital Management. Random House.

10. book ↩ used in §4.2

    Gatheral, J. (2006). The Volatility Surface: A Practitioner's Guide. Wiley.

AI tools

Claude (Anthropic). Claude code was used for research and paper summaries as well as layout design and solution verification.

Popular accounts of LTCM widely cite "100:1" leverage at peak. Jorion (2000) puts on-balance-sheet leverage at 25–30:1 ($125B in assets on roughly $5B equity), with the higher "effective" figure coming from $1.25 trillion in notional derivative exposure. I cross-checked Jorion against the Federal Reserve History essay on LTCM and the standard Wikipedia summary; all three agreed on the 25–30:1 on-balance-sheet figure plus the trillion-dollar notional, so I used Jorion's number in §4.1 with the notional caveat called out explicitly.

Sources mostly converged: the technical claims around Heston's parameter count, Merton's jump-diffusion mechanics, and LTCM's rescue numbers were consistent across the canonical references, so the harder work turned out to be framing rather than fact-checking. The biggest surprise was discovering Bachelier developed the mathematics of Brownian motion five years before Einstein used it for pollen-grain physics — a detail the standard textbook narrative on stochastic calculus tends to drop. The hardest section to write was §4.3, because sources cannot tell you what to think; the position emerged from synthesising the earlier sections rather than from any single citation.