15.450 金融量化分析 (Analytics of Finance)

MIT Course 15 · Finance · 金融学 · 课号 15.450

TL;DR

• 运用随机微积分、偏微分方程与数值算法构建连续时间资产定价与动态对冲模型。
• 蒙特卡洛模拟与有限差分法在美式期权、奇异衍生品与结构化产品定价中的工程化实现。
• 基于历史模拟与极值理论的在险价值（VaR）与预期亏损（CVaR）全面风险管理体系。

课程简介 / Description

This course covers the key quantitative methods of finance: financial econometrics and statistical inference for financial applications; dynamic optimization; Monte Carlo simulation; stochastic (Itô) calculus. These techniques, along with their computer implementation, are covered in depth. Application areas include portfolio management, risk management, derivatives, and proprietary trading.

讲义 / Lecture Notes

• 1
  • Arbitrage-free pricing models
  • (PDF - 1.1MB)
• 2
  • Stochastic calculus and option pricing
  • Code: Quadratic variation simulation
  • (PDF)
  • (M)
• 3
  • Simulation methods
  • Code: Black-Scholes model Monte Carlo illustration
  • Code: Black-Scholes with a jump Monte Carlo (PS1, Q2)
  • Code: Monte Carlo with control variates, stochastic volatility model
  • (PDF)
  • (M)
  • (M)
  • (M)
• 4
  • Dynamic portfolio choice I: Static approach to dynamic portfolio choice
  • (PDF)
• 5
  • Dynamic portfolio choice II: Dynamic programming
  • (PDF)
• 6
  • Dynamic portfolio choice III: Numerical approximations in dynamic programming
  • Code: Numerical DP solution
  • (PDF)
  • (M)
• 7
  • Parameter estimation
  • (PDF)
• 8
  • Standard errors and tests
  • (PDF)
• 9
  • Small-sample inference and bootstrap
  • (PDF)
• 10
  • Volatility models
  • (PDF)
• 11
  • Review: Arbitrage-free pricing and stochastic calculus
  • (PDF)
• 12
  • Review: DP and econometrics
  • (PDF)
  • The following handouts and slides were used to supplement lecture materials.
  • Crossing probabilities of the Brownian motion (PDF)
  • Key points: Derivatives and Monte Carlo (PDF)
  • Dynamic programming: Justification of the principle of optimality (PDF)
  • Examples of dynamic programming problems (PDF)

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