Continuous Time Finance - Spring '05, Carr/Dupire


References/Additional Materials:


J.M.Harrison and D.M. Kreps: Martingales and arbitrage in multiperiod securities markets. J. Econ. Theory 20 (1979) 381408
J.M.Harrison and S.R. Pliska: Martingales and stochastic integrals in the theory of continuous trading. Stoch. Proc. &Appl. 11 (1981) 215260

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) 443--458

Numeraire Portfolio:

Long, J. B. (1990). The Numeraire Portfolio. Journal of Financial Economics 26, 29-69.

Local Volatility / Smile:

Bruno Dupire/ Pricing With a Smile


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.
Homework 3 is due by Wednesday, April 27.

Review Session: Monday, April 25, 4-6pm, 6th Floor Warren Weaver.

Additional Review Session: Tuesday, April 26, 7-8pm, 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 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 Hull-White Model
Slides 11: Volatility Expansion
Slides 12: The BGM Model
Slides 13.1: Forward Measure and the Ho-Lee Model


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 4-8), 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)