Math96. Mathematical Finance II     

This version was revised on Mar 23, 2009.    

Lecturer:         Meifang Chu
Office:             245 Wilder
Telephone:     646-2971
Email:   meifang@dartmouth.edu 

Time and Place
Lectures: 10A=10:00-11:50 am on Tue/Thurs at Haldeman 028, Spring 2009
X-Hour: Wednesdays 3:00-3:50PM
Final Exam: Take Home due at noon June 8th.
Office Hour: TBA

Course Description and Requirements

This course is a continuation of Mathematics 86 with an emphasis on the mathematics
underlying fixed income derivatives. Topics include stochastic calculus, Radon -Nikodym derivative, change of measure (Girsanov’s theorem), the Martingale representation theorem, discrete-time and continuous-time formulation of the interest rate models, credit risk models and prepayment risk models and the valuation and risk managment of  fixed-income derivatives and credit derivatives.

Grades are determined at 75%from the homework problem sets that are due every
two weeks and 25% from a sit-in final exam. These problem sets involve deriving and
solving equations numerically, analytically and graphically. The codes can be written in any languages that students feel comfortable with. All the lecture notes, problem sets,
sample codes and additional documents will be available on the Dartmouth Blackboard.

Prerequisites: Mathematics 86 Mathematical FInance I
                          or Physics 122 in F'06 (or  P82 in S'08) on Quantitative Finance.
Dist: QDS.

(1) Syllabus (Reading: John Hull, 7th edition)        

Module
 Reading
 I. Valuation of Exotic Options in Equity, FX and Commodities H7
(a) Feynman-Kac Formulation
(b) Monte Carlo method
(c) Finite Difference method
(d) binomial tree and trinomial tree models
(e) analytic approximation to American Options
 H13
H11
H19
H26
II. Review: Stochastic Processes and Stochastic Calculus
(a) Ito Processes and Ito's Lema
(b) Poisson and Cox Processes (Jump)
(c) Levy Process
 H12
III. Review: Martingale Formulation of Risk Neutral Valuation
(a) density martingale
(b) Radon-Nikodym derivatives
(c) change of measure  and Girsanov’s theorem
H27
IV. Inerest Rate Models and Interest Rate Derivatives
(a) short-rate model
(b) lognormal forward rate model (HJM)
(c) lognormal libor rate model (BGM)
(d) tree models
(e) fixed-income derivatives: swaps, caps, floors, swaption, currency swaps,
Bermudan swaptions, bond options etc.
H4,6,30
H31

H30
H28, 32
V. Credit Risk Models and Credit Derivatives  
(a) transition probability of default and credit ratings
(b) credit events  triggered by barrier, jump/shock and credit raqting transition
(d) correlated default: Moody's model, correlated jumps and Copula model
(e) credit products: credit default swaps, credit spread options, first-N-to-default notes
     credit-linked notes  and collateralized debt obligations (CDO's).
 H22
H23
VI. Prepayment Risk Models and Mortgage Backed Securities
          (a) prepayment models
          (b) products with prepaymetn risks: mortgage-backed securities, asset-baked securities
 H31
VII. Implied Volatility and Stochastic Volatility 
(a) volatility smile in FX market
(b) volatitlity skew in equity market
(c) term structure of volatility in interest rate models
(d) stochastic volatility models
 H18
H26
VIII. Other Derivatives
          (a)  weather derivatives
        (b)  real options
        (c)  inflation-linked derivatives
        (d) catastrophe derivatives
        (e) energy derivatives
 H33

(2) Text Book   

   Options, Futures and Other Derivatives (7th Edition) (Hardcover)                                  
    by John C. Hull    *
    

3) Optional Readings

    * reserved in the Baker Library, 
 
<<<<Financial Engineering>>>>

   Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit
    by  Damiano Brigo and Fabio Mercurio

    Martingale Methods in Financial Modelling
    by Marek Musiela and Marek Rutkowski
 
  Option Pricing: Mathematical Models and Computation                               
    by Paul Wilmott, Jeff Dewynne, Sam Howison   * 

    Derivatives: The Theory and Practice of Financial Engineering                            
    by Paul Wilmott   * 
 
    Continuous-Time Finance
    by Robert Merton

   Pricing Financial Instruments: The Finite Difference Method
   by Domingo Tavella  *

<<<Stochastic Calculus>>>
   Stochastic Differential Equation (Paperback)
    by Bernt K. Oksendal 
 
   Brownian Motion and Stochastic Calculus
   by Ioannis Karatzas *

   Stochastic Calculus for Finance. I & II
    by Steven E. Shreve 

    Probability with Martingales
     by David Williams   *
  
    The Theory of Stochastic Processes
     by D.R. Cox and H.D. Miller   

     Monte Carlo Methods in Financial Engineering
     (Stochastic Modelling and Applied Probability)
     by Paul Glasserman *

    Financial Calculus
      by Baxter and Rennie *



<<<Credit Risks and Pre-Payment Risks>>>

     Credit Derivatives Pricing Models: Model, Pricing and Implementation
     by   Philipp J. Schönbucher   *
   
     Credit Risk Modeling: Theory and Applications
     by David Lando *

    Credit Risk: Pricing, Measurement and Management
     by Darrell Duffie and Kenneth J. Singleton *

    Structured Finance and Collaterized Debt Obligations:
     New Development in Cash and Synthetic Securitization
     by Janet Tavakoli *

   Structured Finance Modeling with Object-Oriented VBA
    by Evan Tick   * (ebook)

   An  Introduction to Credit Risk Modeling
     by  Bluhm, C, Overbeck, L.,Wagner, C.*

   An Introduction to Copulas (Lectures Notes in Statistics 139), Springer
    by R. B. Nelsen
   
   Basics of Mortgage-Backed Securities
   by Joseph, Hu *

    Subprime Mortgage Credit Derivatives
    by Laurie Goodman, et al *

    Salomon Smith Barney Guide to Mortgage-backed ans Asset-Backed Securities
     by Lakhbir Hayre  * (ebook)

     The Handbook of Fixed Income Securities
      by Frank Fabozzi  *

     The Handbook of Mortgage Backed Securitites
    by Frank Fabozzi  *


<<<Others>>>

     My Life as a Quant : Reflections on Physics and Finance                                            
     by Emanuel Derman    
   
     How I became a Quant: Insights from 25 of Wall Street's Elite 
     by Barry Schachter and Richard Lindsey


 
 
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             Physics Department's home page.
             Math Department's home page.