Volatility: Trading and Managing Risk

 

An excellent primer on volatility trading covering first principles right through to the cutting edge in models. I came away with the knowledge to put into practice many of the models applying techniques taught in the course.

Christopher Fong - Portfolio Manager, Ontario Teachers' Pension Plan
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Course Outline

The course starts by analysing the role of volatility in the current financial markets including the causes and impact of volatility smiles on a variety of financial products. This leads into sessions on the application of a range of volatility derivatives such as volatility futures and options, tradeable volatility products such as VXX, and volatility swaps. The final part of the programme covers the treatment of volatility in the more popular stochastic volatility models used in the industry such as SABR and Heston and provides insights into the most relevant approaches to modelling volatility under current market conditions.

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Who The Course is For

  • Derivative traders
  • Quants
  • Fund managers, fund of funds
  • Structured product teams
  • Private wealth managers
  • Risk managers and regulators
  • Finance directors
  • Research analysts
  • Bank and corporate treasury managers

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Prior Knowledge

Basic econometrics and Black-Scholes. Participants will also need to be competent users of Excel.


This program is eligible for 24 Continuing Education credit hours from the CFA Institute. If you are a CFA Institute member, CE credit for your participation in this program will be automatically recorded in your CE Diary.


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Day One

Black-Scholes Revisit

  • 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
  • Models with jumps

Local Vol

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

Workshop – Calibrating local vol 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

  • The Heston equation
  • Derivation and the Heston fundamental PDE
  • The role of market price of risk
  • Problem with a complex root
  • Derivation through Fourier transform and characteristic function
  • Volatility surface sensitivities to Heston parameters
  • Gatherial’s equations 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 use it to price a Barrier option

SABR and the Vol 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
  • 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
  • Options on realised variance

Workshop - Finding a risk neutral distribution of volatility

Day Three

Market Models of Volatility

Part I - Using Copula: Correlation and Dispersion

  • Volatility surfaces revisited – extrapolation and interpolation
  • Combining risk neutral distributions with a copula
  • Using a Gaussian copula as an alternative to Local Volatility
  • Using volatility smiles and copulae for pricing basket options
  • Correlation and dispersion trading

Workshop – Using a copula to price a basket option

Part II – Bergomi and Market Models

  • Market models of VIX options
  • Arbitrage between VIX options and S&P options
  • Bergomi’s consistent variance curve
  • Dynamics for forward volatility

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

Course review and conclusions

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