### Stochastic Models in Finance (IE 432)

2023 Fall
Faculty of Engineering and Natural Sciences
Industrial Engineering(IE)
3
6
Semih Onur Sezer sezer@sabanciuniv.edu,
English
IE303
Formal lecture
Discussion based learning

### CONTENT

The objective of the course is to introduce basic stochastic models and techniques used in mathematical finance. The first half of the course is dedicated to discrete-time models, the other half to their continuous-time counterparts. The topics covered include pricing and hedging in binomial models and Black-Sholes models, fundamental theorems of asset pricing, martingales, Brownian motion, stochastic integration, Itô rule. Depending on the progress in class, we also briefly discuss SDE?s as they appear in continuous-time models.

### OBJECTIVE

- To introduce the basic stochastic models and techniques used in mathematical finance
- To teach pricing and hedging in binomial models and Black-Sholes models

### LEARNING OUTCOMES

• Upon completing this course, students should be able to: Price different instruments in both discrete time binomial models and continuous time Black-Scholes model
• Find hedging strategies in different pricing problems
• Compute expectations related to random walk and Brownian motion
• Apply Ito rule and use it in different problems

### PROGRAMME OUTCOMES

1. Understand the world, their country, their society, as well as themselves and have awareness of ethical problems, social rights, values and responsibility to the self and to others. 1

2. Understand different disciplines from natural and social sciences to mathematics and art, and develop interdisciplinary approaches in thinking and practice. 3

3. Think critically, follow innovations and developments in science and technology, demonstrate personal and organizational entrepreneurship and engage in life-long learning in various subjects; have the ability to continue to educate him/herself. 2

4. Communicate effectively in Turkish and English by oral, written, graphical and technological means. 1

5. Take individual and team responsibility, function effectively and respectively as an individual and a member or a leader of a team; and have the skills to work effectively in multi-disciplinary teams. 1

1. Possess sufficient knowledge of mathematics, science and program-specific engineering topics; use theoretical and applied knowledge of these areas in complex engineering problems. 4

2. Identify, define, formulate and solve complex engineering problems; choose and apply suitable analysis and modeling methods for this purpose. 3

3. Develop, choose and use modern techniques and tools that are needed for analysis and solution of complex problems faced in engineering applications; possess knowledge of standards used in engineering applications; use information technologies effectively. 3

4. Have the ability to design a complex system, process, instrument or a product under realistic constraints and conditions, with the goal of fulfilling specified needs; apply modern design techniques for this purpose. 1

5. Design and conduct experiments, collect data, analyze and interpret the results to investigate complex engineering problems or program-specific research areas. 1

6. Possess knowledge of business practices such as project management, risk management and change management; awareness on innovation; knowledge of sustainable development. 1

7. Possess knowledge of impact of engineering solutions in a global, economic, environmental, health and societal context; knowledge of contemporary issues; awareness on legal outcomes of engineering solutions; knowledge of behavior according to ethical principles, understanding of professional and ethical responsibility. 1

8. Have the ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. 1

1. Applying fundamental and advanced knowledge of natural sciences as well as engineering principles to develop and design new materials and establish the relation between internal structure and physical properties using experimental, computational and theoretical tools. 1

2. Merging the existing knowledge on physical properties, design limits and fabrication methods in materials selection for a particular application or to resolve material performance related problems. 1

3. Predicting and understanding the behavior of a material under use in a specific environment knowing the internal structure or vice versa. 1

1. Formulate and analyze problems in complex manufacturing and service systems by comprehending and applying the basic tools of industrial engineering such as modeling and optimization, stochastics, statistics. 4

2. Design and develop appropriate analytical solution strategies for problems in integrated production and service systems involving human capital, materials, information, equipment, and energy. 1

3. Implement solution strategies on a computer platform for decision-support purposes by employing effective computational and experimental tools. 1

### ASSESSMENT METHODS and CRITERIA

 Percentage (%) Final 55 Midterm 45