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25873 Fundamentals of Derivative Security Pricing

Warning: The information on this page is indicative. The subject outline for a particular session, location and mode of offering is the authoritative source of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.

Subject handbook information prior to 2019 is available in the Archives.

UTS: Science: Mathematical and Physical Sciences
Credit points: 8 cp

Subject level:

Postgraduate

Result type: Grade and marks

There are course requisites for this subject. See access conditions.

Description

This subject introduces the basic concepts for the pricing of derivative securities from an intuitive perspective. Topics include; arbitrage pricing in continuous time, different interpretations of the arbitrage pricing condition, leading to the partial differential equation, martingale and integral evaluation viewpoints. Exotic options, American option and option pricing under stochastic volatility are also considered.

Subject learning objectives (SLOs)

Upon successful completion of this subject students should be able to:

1. Have an understanding of the assumptions and the mathematical background of derivative pricing theory in continuous time
2. The ability to implement the theoretical models of continuous time finance and to develop intuition for the underlying financial issues and aspects such as arbitrage-free derivative pricing, martingales, stochastic volatility and jump-diffusion models
3. Be able to understand available literature on derivative securities pricing
4. Be able to price derivative securities from both the partial differential equation and the martingale viewpoints

Course intended learning outcomes (CILOs)

This subject also contributes specifically to the development of following course intended learning outcomes:

  • Demonstrate mastery of high level quantitative finance technical skills necessary for professional practice (5.1)

Contribution to the development of graduate attributes

The aim of this subject is to present the various financial and mathematical concepts, techniques and intuition necessary to price derivative securities in a non-stochastic interest rate environment. This subject introduces students to the modelling of asset price dynamics in continuous time, the arbitrage pricing of derivatives in continuous time, interpretations of the arbitrage pricing condition leading to the partial differential equation, martingale and integral evaluation viewpoints. American options and option pricing under stochastic volatility and jump-diffusion dynamics will also be introduced. The focus of the subject is on the development of economic intuition behind the various concepts. Implementation of some models on the computer will also form part of the subject requirements.

This subject contributes to the development of the following graduate attributes:

  • Attitudes and values
  • Business practice oriented skills

This subject also contributes specifically to develop the following Program Learning Objectives for the Master of Quantitative Finance:

  • 4.2: Critically evaluate and apply sustainability principles to business practices in the financial sector
  • 5.1: Master quantitative finance technical skills necessary for professional practice

Teaching and learning strategies

The subject is presented in seminar format. Essential principles are presented and analysed in the lecture component and in addition students are lead through practical application exercises.

Content (topics)

  • Basic option pricing problem, concepts, and techniques in single-period model
  • Black-Scholes option pricing: hedging, risk-neutral valuation, martingale and PDE approaches
  • A general approach including numeraire approach to pricing multi-factor derivative securities and applications to exchange and/or currency options
  • The martingale interpretation of the derivative pricing equation, market prices of risk of driving factors, change of measure, and risk neutral valuation
  • Option pricing under stochastic volatility dynamics and volatility smiles
  • Exotic options and American options.

Assessment

Assessment task 1: Assignment (Group)

Objective(s):

This assessment task addresses subject learning objective(s):

1, 2, 3 and 4

Weight: 20%

Assessment task 2: Assignment (Individual)

Objective(s):

This assessment task addresses subject learning objective(s):

1, 2 and 3

Weight: 30%

Assessment task 3: Final Exam (Individual)

Objective(s):

This assessment task addresses subject learning objective(s):

1, 2, 3 and 4

This assessment task contributes to the development of course intended learning outcome(s):

5.1

Weight: 50%
Length:

Two hours, including 10 min. reading time

Minimum requirements

Students must achieve at least 50% of the subject’s total marks.

Required texts

Chiarella, C., X. He and C. Sklibosis Nikitopoulos, 2015, Derivative Security Pricing: Techniques, Methods and Applications, Springer.

References

Bjork, T. 2004, Arbitrage Theory in Continuous Time, 2nd edn., Oxford University Press.
Epps, T.W. (2000), Pricing Derivative Securities. World Scientific.
Neftci, S.N. 2000, An Introduction to the Mathematics of Financial Derivatives, 2nd edn., Academic Press.

Schlögl, E. (2014), Quantitative Finance: An Object-Oriented Approach in C++, Chapman & Hall
Shreve, S. 2004, Stochastic Calculus for Finance I: The Binomial Asset Pricing ModelContinuous Time Models, Springer.
Shreve, S. 2004, Stochastic Calculus for Finance II: Continuous Time Models, Springer