# Financial Modeling

## Winter 2018, PSTAT 223B

## M-W 9:30-10:45, HSSB 1207

**Jean-Pierre Fouque**

fouque at pstat.ucsb.edu
**Office Hours: W 11am-12pm South Hall 5504 or by appointment**

## Agenda:

**Midterm 1: Wednesday February 14**

**Midterm 2: Wednesday March 14**

**Week 1 (classes cancelled due to final exams of Fall quarter): **

**January 8: ** No class.
**January 10: ** No class
**Week 2: **

**January 15: ** Holiday.
**January 17: ** One period models. Arbitrage. Replication. Risk-neutral valuation.
**Week 3: **

**January 22: ** Multi-period models.
**January 24: ** Black-Scholes model. Self-financing portfolios and no-arbitrage pricing (Chapters 6 and 7).
**HW1 due Monday February 5: p. 63-64: 4.2 and 4.5, p. 80-82: 5.5, 5.8, 5.10, 5.11, p. 91: 6.1**
**Week 4: **

**January 29: ** Black-Scholes formula. Breeden-Litzenberger formula. Carr-Madan formula. Implied volatility.
**HW2 due Monday February 12: p. 113: 7.2, 7.4, 7.5 and p. 134-136: 9.1, 9.2, 9.3, 9.10**
**January 31: ** Breeden-Litzenberger formula. Carr-Madan formula. Local volatility models and Dupire formula.
**Week 5: **

**February 5: ** Local volatility models and Dupire formula.
**HW3 due Wednesday February 21: p. 281: 18.1-4**
**February 7: ** Stochastic volatility models.
**Week 6: **

**February 12: ** Stochastic volatility models continued.
**February 14: ** **Midterm 1**** open books/notes.**
**Week 7: **

**February 19: ** Holiday.
**February 21: ** Dividends. Bonds and Interest Rates.
**HW4 due Monday February 26: p. 246: 16.6 and 16.8. Read Section 16.1**
**Week 8: **

**February 26: ** Bonds and Interest Rates (continued).
**HW5 due Monday March 5: p. 386: 24.1-5 and p. 287: 24.7**
**February 28: ** Forward rates, HJM model.
**Week 9: **

**March 5: Bond options. Forward measure.**
**March 7: Poisson processes, intensities , by Michael Zhang.**
**Week 10: **

**March 12: Credit risk, default modeling (structural and intensity-based).**
**March 14: ** **Midterm 2**** open books/notes.**
**Course Outline**

An introduction to stochastic models in finance with applications to valuation and hedging of derivatives in equity, fixed income, and credit markets, and to portfolio allocation.
**Prerequisites:**

PSTAT 213 A-B-C Introduction to Probability Theory and Stochastic Processes (or equivalent)

PSTAT 223A Stochastic Calculus and Applications (or equivalent)

__TEXT__:

Arbitrage Theory in Continuous Time by Tomas Bjork, 3rd ed, Oxford 2009