# Coursebooks 2018-2019

Vacat .

English

#### Remarque

Only for MA3. Special schedule: see the IF website http://sfi.epfl.ch/mfe/study-plan

#### Summary

The course covers a wide range of advanced topics in derivatives pricing

#### Content

Models with stochastic volatility and jumps, pricing of vanilla options by Fourier inversion techniques, numerical methods including pricing of American-style options by simulation and finite difference, exotic derivatives (such as barrier options and cliquets), volatility derivatives (such as variance swaps, volatility swaps, and options on volatility), and term structure modeling with unspanned stochastic volatility.

#### Keywords

Derivatives, stochastic volatility, jumps, numerical methods

#### Learning Prerequisites

##### Required courses

• Derivatives
• Introduction to finance
• Investments
• Stochastic calculus I
• Stochastic calculus II

#### Learning Outcomes

By the end of the course, the student must be able to:
• Describe properties of asset returns and implied volatility surfaces
• Compare and contrast different methods for modeling implied volatility surfaces including stochastic volatility, local volatility, and jumps
• Derive the characteristic function of log stock prices in settings with stochastic volatility and jumps; discuss and implement the pricing of European put and call options by Fourier inversion techniques
• Implement an implied binomial tree and explain the formula for local volatility
• Design efficient simulation schemes for pricing options with path-dependent payoffs and early exercise features
• Implement simple finite difference schemes
• Explain the decomposition of structured products into their underlying option components; understand the model risk associated with pricing and hedging exotic derivatives and structured products
• Demonstrate the model-independent pricing of variance swaps; explain empirical results about volatility risk premiums
• Examine the properties of term structure models with unspanned stochastic volatility (USV) and explain the concept of USV in interest rate and commodity markets

#### Transversal skills

• Assess one's own level of skill acquisition, and plan their on-going learning goals.
• Take feedback (critique) and respond in an appropriate manner.

#### Teaching methods

Lectures and exercises

#### Assessment methods

40% combined weight on assignments given during the course

60% final exam - closed-book

#### Supervision

 Office hours Yes Assistants Yes Forum Yes

#### Resources

No

##### Bibliography

The main textbook for the course is
Jim Gatheral, The Volatility Surface, Wiley, 2006.

In addition, a number of journal articles will be used.

### Reference week

MoTuWeThFr
8-9
9-10 EXTRANEF_126
10-11
11-12 EXTRANEF_126
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German