Statistics 390/Mathematical Finance 345
Stochastic Calculus and Finance I
Wednesday evenings, 6:00-9:00 PM
Eckhart Hall, 1st Floor, Room 133
Instructor
Steven LALLEY
Eckhart Hall 118
702.9890
E-mail: lalley@galton.uchicago.edu
Office Hour: THURSDAY 2:00 - 3:00
Course Assistants
Hae K. IM
E-mail: haky@galton.uchicago.edu
Zhengyuan ZHU
E-mail: zhu@galton.uchicago.edu
This course is an
introduction to stochastic calculus as it is relevant to the pricing
and hedging of options and other derivative securities. It is offered
in collaboration by the Department of Statistics and the master's
program in Mathematical Finance. The main objectives of the course are
(1) to provide a working knowledge of the Ito stochastic calculus, and
(2) to show how it is used to obtain arbitrage prices and hedging strategies
for various financial derivative securities, including forwards, European
contingent claims, barrier options, and simple foreign currency options.
The course has a
sequel in Winter quarter, Statistics 391/Mathematical Finance 346.
Stat 390-391 are part of the Statistics and
Finance program. Math Fin 345-346 are part of the Master's program in Financial
Mathematics.
Topics to be Covered:
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Discrete Pricing Models
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Discrete Multiperiod Models
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Binomial Trees
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Risk Neutral Measures
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Discrete Martingales
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Continuous Stochastic Calculus
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Wiener Process (Brownian Motion)
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Ito Integral and Ito Formula
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Girsanov Formula
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Continuous--Time Martingales
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Martingale Representation Theorem
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Ito Processes and PDEs
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Black--Scholes Theory
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Arbitrage Pricing
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Black--Scholes Formulae
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Risk Neutral Measures
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Numeraire Invariance
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Market Completeness
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Extensions of the Black-Sholes theory
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Barrier Options
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Currency Options
There will be weekly homework assignments, and midterm and final exams.
The course assistants will conduct weekly help sessions on Friday
afternoons.
Exams:
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Midterm: October 24
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Final: Finals Week (to be announced)
Prerequisites:
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Stat 390: consent of instructor (enforced)
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Math 345: enrollment in the Financial Mathematics Program
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both: The preparatory
course offered in September, or equivalent
Texts:
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Course Notes: will be posted
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Recommended Books:
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S. Neftci .
Introduction to the Mathematics of Financial Derivatives
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J. C. Hull . Options, Futures, and Other Derivatives
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Darrell Duffie (1996). Dynamic Asset Pricing Theory (2nd or later
edition). Princeton U. Press.
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J. M. Steele . Stochastic Calculus and Financial Applications
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P. Billingsley . Probability and Measure
September 2001