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Volatility: Trading and Managing Risk

Day One

 Black-Scholes Revisited

  • A quick revision of Black-Scholes and Ito lemma
  • Black-Scholes Greeks
  • Black-Scholes implied volatility and implied risk neutral distributions
  • Examples of derivatives sensitive to the whole volatility surface
  • Motivation for alternatives to Black-Scholes and stochastic volatility  

Local Volatility

  • Is Local Volatility a stochastic volatility model?
  • Calculating a Local Volatility
  • Implementing Local Volatility models
  • Local Volatility as a conditional expectation of instantaneous volatility
  • Weaknesses of Local Volatility models

Workshop: Calibrating local volatility and pricing a Barrier option

Trading on Realised Volatility

  • Volatility Skew and Smile
  • The Greeks
  • Trading Skew and Kurtosis
  • Trading Implied Volatility
  • Variance Swaps and Volatility Swaps

Workshop: Fitting a volatility surface and pricing a variance swap

Day Two

Heston and the Volatility Surface

  • Looking at volatility dynamics in the real world
  • The Heston equation
  • The role of market price of volatility risk
  • Volatility surface sensitivities to Heston parameters
  • Linking Heston parameters to Black-Scholes implied volatilities
  • Implication of the Heston volatility surface dynamics
  • Simulating the Heston process

Workshop: Simulating the Heston dynamics and using it to price a Barrier option

SABR and the Volatility Surface

  • SABR: Stochastic Alpha, Beta and Rho
  • SABR calibration
  • SABR parameters and the volatility surface
  • Sticky strike versus sticky moneyness
  • SABR in interest rate modelling and LMM-SABR

Trading on Volatility Indices

  • Volatility indices – VIX and VSTOXX
  • Volatility as an Asset Class – VXX and VXZ
  • Incorporating Volatility into an Investment Portfolio
  • Futures and Options on Volatility Indices
  • The need for a stochastic volatility model
  • Hedging Volatility Indices

Workshop: Finding a risk neutral distribution of volatility

Day Three

Market Models of Volatility

  • Volatility surfaces revisited – extrapolation and interpolation
  • Combining risk neutral distributions with a copula
  • Using volatility smiles and copulae for pricing basket and spread options
  • Dispersion trading
  • Market models of volatility options
  • Arbitrage between volatility options and S&P options

Workshop: Relating VIX options and variance swaps

 Hedging Volatility Exposure

  • Hedging volatility exposure of a book of exotic options
  • Static versus Dynamic Hedging
  • Impact of Model choice
  • Smile risk
  • Understanding greeks
  • Vega convexity

Workshop: Finding the best vega hedge

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