Why Gamma still matters for Monte Carlo Variance Reduction?
Today we look at how combining variance reduction methods like antithetic, delta and gamma-based control variates can help to substantially reduce the standard error around your theoretical option price during monte carlo simulations.
This can explain not only how combining variates that are correlated with an option payoff can reduce standard error on estimates of option values, but also why market making firms are so concerned about hedging sensitivies or option risks that are second order or higher. By hedging different sensitivities, the variance around expected PnL can massively reduce!
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00:00 Intro
03:29 Normal Monte Carlo Estimation
04:06 Antithetic Variates
04:57 Delta-based Control Variates
07:42 Gamma-based Control Variates
10:25 Combined Antithetic and Delta-based Variates
13:38 Combined Antithetic, Delta and Gamma-based Variates
15:55 Trade-off between Standard Error and Computation Time
17:17 Why Gamma still matters?
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