Continuous Time Finance  Spring '05, Carr/Dupire
Syllabus
References/Additional Materials:

FTAP:
 J.M.Harrison and D.M. Kreps: Martingales and arbitrage in multiperiod securities markets. J. Econ. Theory 20 (1979) 381–408
 J.M.Harrison and S.R. Pliska: Martingales and stochastic integrals in the theory
of continuous trading. Stoch. Proc. &Appl. 11 (1981) 215–260
Change of Numeraire:
 Geman, H., El Karoui, N. and Rochet, J.C.: Changes of numeraire,
changes of probability measures and pricing of options. J. Appl. Probab. 32 (1995) 443458
Numeraire Portfolio:
 Long, J. B. (1990). The Numeraire Portfolio.
Journal of Financial Economics 26, 2969.
Local Volatility / Smile:
 Bruno Dupire/ Pricing With a Smile
General:
 Peter Carr/
Derivative Pricing  the Classic Collection
Special Announcements:
 Final Exam to be held in class on April 27th, not during the general final exam period.
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 Homework 3 is due by Wednesday, April 27.
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Review Session: Monday, April 25, 46pm, 6th Floor Warren Weaver.

Additional Review Session: Tuesday, April 26, 78pm, 6th Floor Warren Weaver.
Lecture Notes:
 Lecture 2.1: Binomial Hedging
 Lecture 2.2: Poisson Hedging
 Lecture 4: Replicating Risky Bonds
 Lecture 5: Black's Model With Default
Slides:
 Slides 2.1: Binomial Hedging
 Slides 2.2: Poisson Hedging
 Slides 3: Review of Stochatic Calculus
 Slides 4: Replicating Risky Bonds
 Slides 5.1: Black's Model with Default
 Slides 5.2: Merton's Jump Diffusion Model
 Slides 6: Choice of Numeraire
 Slides 7: Modeling Volatility (pdf format)
 Slides 7: Modeling Volatility (ppt format)
 Slides 8: Robust Dynamic Spanning
 Slides 9: More On Volatility
 Slides 10.1: Intro to Interest Rate Models
 Slides 10.2: The Vasicek Model
 Slides 10.3: The HullWhite Model
 Slides 11: Volatility Expansion
 Slides 12: The BGM Model
 Slides 13.1: Forward Measure and the HoLee Model
Homework:
 Homework 1
 Solutions to Homework 1
 Homework 2
 Homework 3
Homework 1 Tips:
 In problem 1b, is there a context where borrowing cash is necessary to take advantage of a mispriced call?
 In problem 2b, the Chairman of the NYSE only flips the coin once a day for ALL of the companies.
 In part 2 (questions 48), focus on equation 7 in lecture 2.2.
 In part 3, questions 11 and 12, the "behavior" of a random variable includes more than just its expected value (how much more?).
Homework 2 Corrections/Tips:
 In (1), should be 1 (tau > T)