Teaching plan for the course unit

 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 and/or online activities 60
 -  Lecture Face-to-face 30 -  Problem-solving class Face-to-face 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

5. Portfolio optimization

*  Dynamic programming. Hamilton-Jacobi-Bellman equation. Martingale method.

5.1. Utility functions

5.2. Dynamic programming. HJB equation

5.3. Martingale method

 Teaching methods and general organization

 For safety reasons only half of the lectures will be face-to-face  lectures till the administration decide to drop this restriction. The on line lectures will consist of lectures as close as possible to lectures in the classroom, by explaining through slides the theoretical and the practical parts of the subject, via the official communications tools provide by the university like Business Skype or BB Collaborate. Face-to-face lectures will be devoted to solve doubts, questions, assessments as well as to lecture.  In the situation requires a full on line course the dynamics will be that and assessments will change accordingly

 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.   In case of full online lecturing  T will be replace by an oral exam.   Examination-based assessment The single assessment consists of a final examination with theoretical questions (30%) and problems (70%). In case of full online lecturing  single assessment will be replace by an oral exam with the same features as the written exam.