Financial Mathematics 4: Models of Local and Stochastic Volatilities

Martingales and probability changes: Girsanov theorem
  • Exponential stochastics
  • Local martingale
  • Density
  • Radon-Nikodym density
  • Change of measure in stochastic process
  • Practical workshop
  • Solving Black & Scholes via a change of probability
Models using local volatility
  • CEV model (Constant Elasticity of Variance)
  • Presentation of the notion of local volatility: the Derman model
  • Modelisation 'sticky strike' / 'sticky moneyness'
  • Trinomial tree
  • Dupire implicit diffusion
  • Dupire formula.
Volatility parameters: the Heston model
  • Neutral risk measurement
  • Cox Ingersoll Ross process (square root)
  • Fourier transformation
  • Heston neutral risk model
  • Volatility within the Heston model
  • Calibration
  • Correlation in the Heston model: issues with fixed correlation
Hybrid approach: SABR model
  • Introduction to the SABR model
  • Calibration of the SABR model
  • Practical workshop
  • Application in EXCEL of the Heston model

  • Master the problems of measuring change in a process
  • Control of local volatility models
  • Control of stochastic volatility
  • Mastering the Heston model and calibration of its parameters
  • Comprehensive and exhaustive presentation of interest rate models, their uses and their limitations
  • People interested in updating or refreshing their knowledge on the subject (Front office, Middle office, Back office, Risk Control and Audit)
  • People in contact with problems of local and stochastic volatility (Asset managers, Asset / liability managers, ...¦)
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