CALTECH                                          

 BEM 105 Options; Course Web page: SYLLABUS                                                                                               

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Syllabus
Homeworks and Exams
Readings



SYLLABUS:

Instructor: Jaksa  Cvitanic, 137 Baxter,  x1784, cvitanic@hss.caltech.edu
Office Hours: Monday 3:30-4:00PM or by appointment.
T.A.s:
 Serkan Kucuksenel  • serkank@hss.caltech.edu • (626) 395-4052 • 8a Baxter Hall
Michael Alton  • mralton@hss.caltech.edu • (626) 395-4093 • 250 Baxter Hall

Class meetings:  Mo,Wed 2:00-3:25PM,  24 BBB


Prerequisites: A basic knowledge of  probability/statistics.
Some exposure to stochastic processes and partial differential equations is
helpful, but not mandatory.

Grading:  60% homeworks, equally weighted.  40%  final exam.  For those taking the course on Pass/Fail: you must pass the final and you must receive 25% of the grade for each homework to pass the course.
Penalty for late submission of homework: 10% per day. Penalty for late submission of final: 33% per day.

Collaboration policy:  Discussions of class material are allowed; on homeworks fellow students can give hints - but please report them; no collaboration allowed on final. Homeworks and final are open-book, open-notes, but you are not allowed to consult others.

COURSE MATERIAL:  The required textbook is

J. Cvitanic and F. Zapatero: Introduction to the Economics and Mathematics of Financial Markets

There are many good more advanced books on the subject, such as

S. Shreve: Stochastic Calculus for Finance II : Continuous-Time Models     
T. Bjork:  Arbitrage Theory in Continuous Time  

 
Content and Goals:
 
This is an  introductory course on options and other financial derivative securities, and their
applications to risk management.We will start with discrete-time models, but most
of the course will be in the framework of continuous-time, Brownian Motion driven models.
A basic introduction to Stochastic, Ito Calculus will be given. The benchmark model will be the
Black-Scholes-Merton pricing model, but we will also cover more general models, such as
stochastic volatility models. We will discuss both the Partial Differential Equations approach, and the
Probabilistic approach. We will also cover modeling of interest rates and fixed income risk management.

 

Topics (tentative; subject to change)

(Numbers in square brackets refer to date - approximately; numbers in parentheses refer to chapters/sections in the textbook.)

  1. [1/4]  Main  ideas: hedging and no-arbitrage; Financial Markets; options (1, 9.2)
  2. [1/9] Interest rates and dividend yields ( 2)
  3. [1/11&18] Model probabilities and state price probabilities (aka Equivalent Martingale Measure or risk-neutral probabilities): binomial model (3.1, 3.2, 3.6.1, 3.6.2, 3.6.4, 3.6.5, 6.3.1, 6.3.2, 6.3.3, 6.3.4, 6.3.5, 6.4, 7.1.1)
  4. [1/23] Forward  and futures contracts (6.2, 6.3.9, 9.1)
  5. [1/25] Bounds on options prices (6.1)
  6. [1/30 & 2/1] Stochastic Calculus (3.3 except 3.3.6, 3.3.7)
  7. [2/6] The Black-Scholes(-Merton) model (3.3.6, 3.6.6, 7.2, 7.9)
  8. [2/8] More on  Black-Scholes model (3.6.3, 3.6.6, 6.3.6, 6.3.7, 6.3.8, 7.1.2, 7.6.1)
  9. [2/13] American options; dividends; exotic options (7.3, 7.4, 7.5)
  10. [2/15 & 2/22] Portfolio risk; Hedging (5.2, 9.3, 11.2)
  11. [2/27] Stochastic volatility (7.2.4, 7.6.3, 7.6.4, 7.8)
  12. [3/1] Interest rate models  (3.4.2, 8.2.1, 8.2.2)
  13. [3/6] Forward rate models: Heath-Jarrow-Morton (8.2.3)
  14. [3/8] Risk management with bonds (10)