 Teaching plan for the course unit

 Close  General information

Course unit name: Quantitative Finance

Course unit code: 568193

Coordinator: Jose Manuel Corcuera Valverde

Department: Department of Mathematics and Computer Science

Credits: 6

Single program: S

 Estimated learning time Total number of hours 150

 Face-to-face learning activities 60
 -  Lecture 30 -  Problem-solving class 30
 Independent learning 90

 Recommendations

 It is recommended that students have taken the subject Stochastic Calculus.

 Learning objectives
 Referring to knowledge — To know the theory of modelling financial markets, in discrete and continuous time, under the hypothesis of no arbitrage (NA).    — To be able to calculate pricing and hedging financial derivative under NA.    — To know and be able to derive the well-known formula of Black-Scholes and to be aware of its importance.   — To know interest rate models under NA.       — To know how to manage credit risk under NA.

 Teaching blocks

1. Financial derivatives: Discrete time models

1.1. Investment strategies; Admissible strategies and arbitrage; Martingales and opportunities of arbitrage; First fundamental theorem

1.2. Complete markets and option pricing; Second fundamental theorem

1.3. The Cox-Ross-Rubinstein model

1.4. American options; The optimal stopping problem; Application to American options

2. Financial derivatives: Continuous-time models

2.1. The Black-Scholes model; Pricing and hedging

2.2. Multidimensional Black-Scholes model with continuous dividends

2.3. Currency options

2.4. Stochastic volatility

3. Interest rates models

3.1. Interest rates; Bonds with coupons, swaps, caps and floors

3.2. A general framework for short rates; Options on bonds; Short rate models; Affine models

3.3. Forward rate models; The Heath-Jarrow-Morton condition

3.4. Change of numéraire; The forward measure

3.5. Market models

3.6. Forwards and Futures

4. Credit risk models

4.1. Structural approach

4.2. Reduce form approaches: Hazard process approach and intensity-based approach

 Official assessment of learning outcomes

 The final grade will be calculated as follows: 0,7*P+0,3*T, where   — T is the mark obtained in two  partial written exams containing theory and exercises;   — P is the mark obtained by solving a list of problems and some practical exercises done in class     Examination-based assessment The single assessment consists of a final examination with theoretical questions (30%) and problems (70%)