ENSAE Paris - École d'ingénieurs pour l'économie, la data science, la finance et l'actuariat

Instruments Financiers 3A


The objective of the course is to present financial instruments in two aspects:

  • A qualitative and descriptive aspect in which the instruments are presented not as an abstract representation but in their role within economic processes. The "users" of these instruments will be evoked (companies, banks, central banks). The market mechanisms involving these instruments will be described.
  • A quantitative aspect intended to give students the necessary basis for the manipulation, evaluation (by AOA/replication) and sensitivity analysis(s) of standard financial instruments (cash products, firm derivatives, optional derivatives).

Main Learning Outcomes: At the end of this course, students should be able to :

  •  Manipulate the different interest rate conventions, perform profitability calculations, build an amortization table.
  • Evaluate a bond, calculate its rate of return, analyze it in duration and sensitivity.
  • Bootstrap a zero-coupon curve from the quotation of market instruments (bonds or euribor derivatives)
  • Understand, manipulate and evaluate interest rate derivatives such as FRAs, Euribor futures and interest rate swaps; understand the mechanisms and use of optional derivatives such as caps/floors and swaptions.
  • Master the different properties of European options ("calls" and "puts"), their valuation principle by replication, their sensitivity to market factors ("Greek")
  • Understand the Black Scholes model, know how to use it to evaluate European options, know its limits and master the concept of volatility smile.
  • Master the principle of delta-neutral hedging of options and understand the nature of the residual risks involved in such management.



Actuarial calculation reminders
Notion of interest rates, capitalization and discounting, present value
Interest rate agreements: simple and compound interest, pre- and post-accounting
Amortizable loans: construction of amortization tables

Bond calculation
Determinants of the price of a bond: interest rate risk and credit risk
Actuarial rate of return on a bond
Analysis in duration / sensitivity / convexity

The yield curve
Interbank curve, bonds: which curve to use according to the context?
Interest of the ZC curve, stripping of the ZC curve from market instruments
Choice of the yield curve, default issues (CVA)

Firm interest rate derivatives 
Interbank market reference rates: EONIA and EURIBORs
Short-term derivatives: FRAs and futures on EURIBOR
Swaps (IRS): the different use cases
Swap rates and IRS quotation, role of market-makers in the IRS market
Valuation of a swap, value based on the swap rate
Sensitivity of a swap to interest rate risk, use for hedging purposes

Introductions to Rate Options: Mechanisms and Uses
Caps & floors

Introduction to vanilla options
What is an option? Payoff of a call/put and exercise strategies
Option vs. forward/future contract
Examples of the use of option-based strategies: investment, hedging, etc.

Valuation assumptions and initial properties
Lack of opportunity for arbitration
Call-put parity and convexity inequality
What factors determine the price of an option?
Introduction to sensitivities: Delta, Gamma, Vega, Theta and Rho

Evaluation of a call in the binomial model
Presentation of the binomial model (1 period, two states of the world)
The price of an option as the value of the hedging portfolio
Concept of risk-neutral probability

The Black & Scholes model
Intuitive presentation of model assumptions
The Black & Scholes formula
Intrinsic Value and Time Value, Historical Volatility vs. Implied Volatility
Introduction to the volatility smile/skew problem

Coverage of options
Delta and gamma of an option, delta-neutral coverage of an option
The trader's P&L: gamma vs. theta
From covering an option to managing an option book

Introduction to exotic options
The main exotic risks
Illustration with examples (binary option, forward start, quanto...)
Beyond Black & Scholes: which model for which type of risk?