Financial Calculus

Program Type:

Thesis

Non Thesis

Course Code:

FE 501

Semester:

Spring

P:

3

Lab:

0

Credits:

3

ECTS:

10

Course Language:

English

Course Objectives:

The aim of the course is to provide students with the ability to understand mathematical models used in financial analysis and to apply them in solving real-life financial problems.

Course Content:

From Random Motion to Brownian Motion, quadratic variations and volatility, stochastic integrals, martingale property, Ito formula, Geometric Brownian Motion, solution of Black-Scholes equation, stochastic differential equations, Feynman-Kac Theorem, Cox-Ingersoll-Ross and Vasicek Models, Girsanov Theorem and risk-free measurements, Heath-Jarrow-Morton Model, currency exchange instruments.

Teaching Methods:

1: Lecture, 2: Question-Answer, 3: Discussion, 4: Simulation, 5: Case Study

Assessment Methods:

A: Testing, B: Presentation C: Homework, D: Project, E: Laboratory

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Programme Learning Outcomes	Teaching Methods	Assessment Methods


Study of stochastic processes	1,2,3	1,2,3	A, B, C, D
Applications of the Ito integral for stochastic analysis and Wiener and Poisson processes	1,2,3	1,2,3	A, B, C, D
Solution of stochastic differential equations for Wiener process and finance applications of CIR, MOU and BUX models	1, 5	1,2,3	A, B, C, D
Girsanov's theorem, Fokker-Planck equations and their applications in finance	1, 5	1,2,3	A, B, C, D
Feynman-Kac theorem and its applications in finance	1, 2, 5	1,2,3	A, B, C, D

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1	Introduction
2	Probability Theory
3	Markov and Chebyshev inequalities, Central Limit Theorem
4	Gaussian processes
5	Wiener processes, Kolmogorov continuity criterion
6	Poisson process, Telegraph process, Unified Poisson process
7	Wiener-Ito integral, Ito lemma for Wiener and Poisson processes
8	Ito isometries, Poisson integral, Martingale and Semi-Martingale
9	Midterm
10	Stochastic differential equations for the Wiener process
11	CIR, MOU and BUX models in finance
12	Girsanov theorem, Fokker-Planck equations and their applications in finance
13	Feynman-Kac theorem and its applications in finance
14	Stochastic differential equations for the jump process and Merton's model
15	Final Exam	All Content

Recommended Sources

RECOMMENDED SOURCES

Textbook

G. Ünal : Lecture Notes

Additional Resources

M. Baxter and A.Rennie, Financial Calculus, CUP (2003).

A.G. Malliaris, Stochastic Methods in Economics and Finance, Elsevier (1999).

S. Neftçi, An introduction to Financial derivatives AP 2nd ed.

S.E. Shreve, Stochastic calculus for Finance Vol 1 and 2 Springer (2004)

B. Oksendal, Introduction to stochastic differential equations 5th edition

2003

Springer ,L. C. Evans, An Introduction to stochastic differential

equations Berkeley Lecture Notes 2005.

Material Sharing

MATERIAL SHARING
Documents			Guidelines and additional examples for Lecture Topics and Homework Assignments
Assignments			Homework assignments
Exams			Midterm Exam and Final Exam

Assessment

ASSESSMENT
IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-Term	1	60
Class Performance	10	40

	Total	100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		50
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		50
	Total	100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAMME
No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	It uses the knowledge and skills it has internalized in the fields of Economics, Finance, Statistics and Computer Science in interdisciplinary studies and produces different fields of application.			X
2	With the awareness of lifelong learning and questioning, it follows national and international publications; It is expected to expand the limit of knowledge with scientific articles by reaching the level of preparing works in accordance with academic rules.			X
3	Designs, implements, solves and interprets analytical, modeling and empirical research; This way it makes predictions.				X
4	When he is involved in business life, he is expected to blend his knowledge in different fields with his differences and competencies and reflect them to his individual career.		X
5	With his English proficiency, he follows the knowledge and developments in his field at an international level and communicates with his colleagues.			X
6	Uses computer software and information and communication technologies required by related fields at an advanced level.		X

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (Including the exam week: 15x Total course hours/week)	16	3	48
Hours for off-the-classroom study (Pre-study, practice, review/week)	16	5	80
Homework	10	6	60
Mid-term	1	20	20
Final	1	40	40
Total Work Load			248
Total Work Load / 25 (h)			9.92
ECTS Credit of the Course			10

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