Teaching plan for the course unit

 

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General information

 

Course unit name: Quantitative Finance

Course unit code: 568193

Academic year: 2018-2019

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%)