Module manager: Dr Jan Palczewski
Email: J.Palczewski@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2018/19
MATH2750 and (MATH2525 or MATH2540)
| MATH5320M | Discrete Time Finance |
| MATH5330M | Continuous Time Finance |
This module is approved as an Elective
Financial investments such as stocks and shares are risky: their value can go down as well as up. To compensate for the risk in a fair market, a discount is needed. This module will develop the necessary probabilistic tools to enable investors to value such assets.
To develop a general methodology based on stochastic analysis for the pricing of financial assets in risky financial markets.
By the end of this module, students should be able to:
a) describe the main instruments available in financial markets;
b) use filtrations and martingales to model any evolving state of knowledge in a fair market;
c) use appropriate stochastic methods to evaluate return rates on risky assets and also interest rates;
d) value options using the Black-Scholes theorem.
Financial investments such as stocks and shares are risky: their value can go down as well as up. To compensate for the risk in a fair market, a discount is needed.
This module will develop the necessary probabilistic tools to enable investors to value such assets.
Topics included:
1. Economic background. Markets, options, portfolios, arbitrage.
2. Discrete time stochastic processes. Conditional expectation, Markov chains, measure theory, filtrations, martingales.
3. Discrete time finance. Asset pricing in a risky market, viability, discrete Black-Scholes formula, equivalent martingale measure.
4. Continuous time stochastic processes. Brownian motion, stochastic integrals, Ito calculus, Cameron-Martin-Girsanov theorem.
5. Continuous time finance. Geometric Brownian motion, asset prices, volatility, continuous Black-Scholes theorem.
6. Modelling interest rates.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Practical | 1 | 2 | 2 |
| Private study hours | 115 | ||
| Total Contact hours | 35 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Studying and revising of course material.
Completing of assignments and assessments.
Regular problem solving assignments
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 20 |
| Total percentage (Assessment Coursework) | 20 | |
There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 30 Mins | 80 |
| Total percentage (Assessment Exams) | 80 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 07/01/2019
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