DE数值分析+衍生品交易实务+金融工程)来源： 梁恩奇的日志在这里一个学期结束了, 把我的课堂笔记以及觉得有用的课件放在Dropbox给大家分享一下, 供有兴趣的同学学习和讨论. 国内的朋友, 你懂的.------------------------------------------------------------------------------------------------------------------------------------
Numerical Analysis of Stochastic ODEs (Comp. Meth. Quant. Fin. I: Monte Carlo Methods)讲解随机微分方程的蒙特卡洛实现与误差分析，包括强估计和弱估计等，开始会有很多概率论方面的介绍，对于概率论基础不好的同学（如我）是一个不错的开始。
Topics0. Review of probability
1. Pseudo random numbers
2. Monte Carlo methods
3 Stochastic Processes and Ito calculus
4. Stochastic differential equations
5. Strong approximations
6. Weak approximation
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CMQF 2011 Lecture Notes(print)
http://dl.dropbox.com/u/41977237/CMQF%202011%20Lecture%20Notes%28print%29.pdf
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Comp. Meth. Quant. Fin. II: PDE Methods 这门课是上一门的补充, 难度也上去了一些, 主讲有限差分和有限元法的实现与误差分析, 模型有BSM, LV, SV, Levy; 涉及到vanilla/American/Asian/Barrier/Compound/multi-asset等的实现.
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PDE
http://dl.dropbox.com/u/41977237/PDE.pdf
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Mathematical Foundations for Finance Topics
- Financial market models in finite discrete time
- Absence of arbitrage and martingale measures
- Valuation and hedging in complete markets
- Basic facts about Brownian motion
- Stochastic integration
- stochastic calculus: Ito's formula, Girsanov transformation, Ito's representation theorem
- Black-Scholes formula
这门课...上到最后很变态, 不是课程难, 而是练习很变态.. 不说了...
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Mathematical Foundation for Finance Lecture Note(print)
http://dl.dropbox.com/u/41977237/Mathematical%20Foundation%20for%20Finance%20Lecture%20Note%28print%29.pdf
MFF_exercises_questions
http://dl.dropbox.com/u/41977237/MFF_exercises_questions.pdf
MFF_exercises_solutions
http://dl.dropbox.com/u/41977237/MFF_exercises_solutions.pdf
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Equity Derivatives Trading in Practice 这是一个在Credit Suisse的交易员讲的课, 挺切合实际的, 对于想做衍生品交易的同学是一个不错的入门教程, 我也从中获益良多. 课程站在卖方的角度, 从交易的基本原理例如各种Greeks/skew的交易策略, P/L equation, Gamma trading等出发, 涉及各种vanilla/exotic/multi-asset derivatives与structure products的交易策略与定价分析, 主流的定价模型如BSM/LV/SV/JD/IIM都会涉及到. 后期也有一些不需要很多数学基础.
看完之后例如你会知道几年前挺火的Accumulator的long position, 你会long delta+short dividends+short vega+long skew, 自然在sell-off就比较惨了.
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Equity Derivatives Trading
http://dl.dropbox.com/u/41977237/Equity%20Derivatives%20Trading.pdf
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Financial Engineering 正如大部分FE的课程一样, 课程涉及Non-arbitrage argument, binomial, BSM, implied volatility, static-hedging, local volatility, stochastic volatility(Heston), jump-diffusion model, 以及各种Levy与time-change; 还有一些产品如variance swap, American/Asian/Barrier options的定价, 但都还是在market complete的条件下的. 课程的教授是一家买方HF的老板, 会有不少practical的观点, 但是有些观点例如对Local vol dynamic的意见我不能完全认同.
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Financial Engineering
http://dl.dropbox.com/u/41977237/Financial%20Engineering.pdf
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