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Implementing Fundamental Quantitative Techniques

Day One

Bootstrapping Yield Curves

  • The form of the discount function
  • Methods of interpolation
  • OIS, Libor and N-way curve building
  • Maximum smoothness
  • Cubic splines in detail
  • Interpolation and the forward curve

Workshop: Interpolation, forward curves and pricing

Curve Building Techniques for Use with Limited Data

  • Applying multiple regression to bond data
  • Finding a functional form for the yield curve
  • Basis splines and other approximating functions
  • Econometric issues
  • Extension to credit and inflation curve building

Workshop: Building a bond market yield curve


Day Two

Principal Components and Yield Curve Hedging

  • Review of single and two-factor duration
  • Principal components
  • Using principal components with B-splines to derive hedging factors
  • Bond arbitrage and portfolio immunisation

Workshop: Portfolio Immunisation

Modelling Movements in Asset Prices: Monte Carlo Simulation

  • Asset prices represented by Brownian motion
  • Monte Carlo simulation
  • Random number generation
  • Control variate and antithetic variable techniques
  • Low discrepancy sequences
  • Multiple dimensions and stochastic volatility
  • Simulating SABR processes

Workshop: Building and Running a Monte Carlo Simulation


Day Three

Modelling Movements in Asset Prices: Trees

  • Alternative futures
  • Probabilities and pseudo probabilities
  • The binomial tree
  • Trinomial trees
  • Trees and Monte Carlo
  • Risk neutral valuation
  • Valuing standard options

Workshop: Building a binomial tree for pricing and hedging

Using Trees for Pricing Derivatives

  • Early exercise and Bermudan structures
  • Deriving the “Greeks”
  • Modifications for Smile and Skew

Modelling Asset Prices in Continuous Time

  • Some basic stochastic calculus and Ito's Lemma
  • Normal and lognormal distributions
  • Applying the Black-Scholes analysis
  • Finite difference techniques for continuous time problems

Workshop: Comparing binomial trees and Monte Carlo techniques



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