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

Financial Instruments 2A



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).

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
  • Swaptions

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?


HULL J. : Options, Futures and Other Derivatives, 6th edition, PRENTICE HALL, 2005.
LAMBERTON D et LAPEYRE B : Introduction au calcul stochastique appliqué à la finance, ELLIPSES
PORTAIT R et PONCET P : Finance de marché, Dalloz, 2008.