FINM 345/STAT 390 Stochastic Calculus, Autumn 2009
Floyd B. Hanson, Visiting Professor Email: [email protected] Master of Science in Financial Mathematics Program University of Chicago
Lecture 1, Corrected Post-Lecture
7:30-9:30 pm, 28 September 2009,
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Lecture 1 Homework: Stochastic Jump and Diusion Processes (Due by Lecture 2 in Chalk FINM345 Digital Dropbox) You must show your work, code and/or worksheet for full credit. There are 10 points per qu
CNETzhengh HW1
Zheng Hong October 5, 2009
Contents
1 Gaussian Process from Zero Mean, Unit Variance Wiener Process 2 2 Simple Poisson Process with Non Unit Amplitude 3 Wiener and Poisson Tables Partial Justication 4 Integral of Wiener Dierential Squared 5
FinM 345/Stat 390 Stochastic Calculus, Autumn 2009
Floyd B. Hanson, Visiting Professor Email: [email protected] Master of Science in Financial Mathematics Program University of Chicago
Lecture 2 (Corrected October 6, 2009)
6:30-9:30 pm, 05 October 2009
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Lecture 2 Homework: Stochastic Jump and Diusion Processes (Due by Lecture 3 in Chalk FINM345 Digital Dropbox) You must show your work, code and/or worksheet for full credit. There are 10 points per qu
CNETzhengh HW2
Zheng Hong October 12, 2009
Contents
1 Problem 1 2 Problem 2 3 Problem 3 4 Problem 4 5 Problem 5 6 Problem 6 7 Problem 7 2 3 4 5 7 8 9
1
1
Problem 1
(a) Proof: E [W 3 (t)|W (s), s
3
t] t]
2
= E [(W (t) W (s) + W (s)3 |W (s), s
3
use the dep
FINM 345/Stat 390 Stochastic Calculus, Autumn 2009
Floyd B. Hanson, Visiting Professor Email: [email protected] Master of Science in Financial Mathematics Program University of Chicago
Lecture 3 (from Singapore) Diffusion Stochastic Calculus
6:30-9:30
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Lecture 3 Homework: Stochastic Jump and Diusion Processes (Due by Lecture 4 in Chalk FINM345 Digital Dropbox) You must show your work, code and/or worksheet for full credit. There are 10 points per qu
FinM 345/Stat 390 Stochastic Calculus, Autumn 2009
Floyd B. Hanson, Visiting Professor Email: [email protected] Master of Science in Financial Mathematics Program University of Chicago
Lecture 4 (from Singapore) Jump & Jump-Diffusion Stochastic Calculu
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Lecture 4 Homework: Stochastic Jump and Jump-Diusion Processes (Due by Lecture 5 in Chalk FINM345 Assignment Submenu) cfw_Note dropping the Digital Dropbox You must show your work, code and/or workshe
CNETzhengh HW4
Zheng Hong October 26, 2009
Contents
1 Inverse Problem for Poisson Integral 2 Solution to a Jump SDE 3 Solution to another Jump SDE 4 Find Coecients Transformable 2 2 2 3
1
1
If
t 0
Inverse Problem for Poisson Integral
X (s)dP (s) = ecP (t)
FinM 345/Stat 390 Stochastic Calculus, Autumn 2009
Floyd B. Hanson, Visiting Professor Email: [email protected] Master of Science in Financial Mathematics Program University of Chicago
Lecture 5 (from Chicago) More Jump-Diffusion Calculus, Simple and C
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Lecture 5 Homework (HW5) : Simple and Compound Jump-Diusions Stochastic Calculus (Due by Lecture 6 in Chalk FINM345 Assignment Submenu) cfw_Note: Dropped the Digital Dropbox You must show your work, c
CNETzhengh HW5
Zheng Hong November 2, 2009
Contents
1 Theorem Proof 2 Simulate for linear simple jump-diusion 3 log-double-uniform jump distribution 4 log-normally distributed jump amplitude case 2 3 4 4
1
1
Theorem Proof
(a) Proof: Let ti = t0 + i t for
FinM 345/Stat 390 Stochastic Calculus, Autumn 2009
Floyd B. Hanson, Visiting Professor Email: [email protected] Master of Science in Financial Mathematics Program University of Chicago
Lecture 6 (Corrected Post-Lecture) More Compound Jump-Diffusion Cal
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Lecture 6 Homework (HW6): Marked Jump-Diusions Stochastic Calculus Continued (Due by Lecture 7 in Chalk FINM345 Assignment Submenu) cfw_Note: Dropped the Digital Dropbox You must show your work, code
CNETzhengh HW6
Zheng Hong November 9, 2009
Contents
1 Simulate X(t) for the log-normally distributed jump amplitude case 2 Ito mean square limit 3 Expectation of Mark Deviation Sums 4 Variance of X(t) for Linear SDE. 2 2 3 3
1
1
Simulate X(t) for the log-
FinM 345/Stat 390 Stochastic Calculus, Autumn 2009
Floyd B. Hanson, Visiting Professor Email: [email protected] Master of Science in Financial Mathematics Program University of Chicago
Lecture 7 (from Chicago) Distributions and Financial Applications
6
CNETzhengh HW7
Zheng Hong November 16, 2009
Contents
1 Simulate the Normal-Uniform Hybrid Mark 2 correlated diusion dierentials 3 the Black-Sholes PDE problem 4 The Greeks (Sensitivity Coecients) 5 Black-Scholes European Option Pricing 2 2 3 3 4
1
1
Simul
FinM 345/Stat 390 Stochastic Calculus, Autumn 2009
Floyd B. Hanson, Visiting Professor Email: [email protected] Master of Science in Financial Mathematics Program University of Chicago
Lecture 8 (from Chicago) More Merton BS+ Option Pricing and Jump-di
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Lecture 8 Homework (HW8): More Merton Option Pricing and JD Financial Applications (Due by Lecture 8 in Chalk FINM345 Assignment Submenu) cfw_Note: Dropped the Digital Dropbox You must show your work,
CNETzhengh HW8
Zheng Hong November 23, 2009
Contents
1 Computation Using Mertons (1976) Jump-Diusion Model for European Options 2 Jump-Diusion Monte Carlo Option Pricing 3 log-return compound process 4 Jump-Diusion European Option Prices are Bigger Than B
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Lecture 9 Homework (HW9): Stochastic Volatility (Due by Lecture 10 in Chalk FINM345 Assignment Submenu) cfw_Note: Dropped the Digital Dropbox You must show your work, code and/or worksheet for full cr
CNETzhengh HW9
Zheng Hong November 30, 2009
Contents
1 mean-reverting, square-root diusion 2 Simulate a solution to the SV-SDE 2 2
1
1
mean-reverting, square-root diusion
t Set X (t) = V0 + 0.5 0 ev (s)/2 (v dWv )(s) Then, dX (t) = 0.5ev (t)/2 v (t)dWv (
FINM345/STAT390 Stochastic Calculus
Hanson
Autumn 2009
Take-Home Final Examination: Due by 6:30pm CST Monday 07 December 2009 (7:30pm EST at UBS; 7:30am Tuesday 08 Dec. in Singapore) in Chalk FINM345 Assignment Submenu You must show your work, code and/or
CNETzhengh nal exam
Zheng Hong December 7, 2009
Contents
1 JD SDE Transformations 2 Stochastic Calculus Example from Forward Contracts 3 Stock-Variance Covariance 4 Very Heuristic Model of American Option Smooth Contact to Put Payo Function 3 5 7 9
5 RGW