Garch And Stochastic Volatility Option Pricing


To give an understanding of GARCH and Stochastic Volatility Option Pricing.  A reasonable quant knowledge is assumed.



- Black-Scholes model

      Implied volatility vs. historical volatility
      Volatility smile


- The GARCH option pricing model

      Data generating vs. risk-neutral price dynamics
      Foreign currency option pricing


- Numerical methods for the GARCH option pricing model

      Volatility smile
      Monte Carlo simulations
      Markov chain approximation
      Lattice construction
      Analytical approximation
      Neural network approximation


- Tackling volatility smile using GARCH

      Put-call parity regression
      FTSE 100 index options


The general properties of the GARCH option pricing model

      Skewness and kurtosis
      Risk premium and stationary volatility


Utilize volatility smile in application

      Pricing exotic options
      GARCH delta and vega hedging
      Risk-neutral probabilities


Option pricing under stochastic volatility

      Pricing exotic options
      Diffusion limit of the GARCH model
      Diffusion limit of the GARCH option pricing model
      Numerical performance



- Final Thoughts and Conclusion

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