Turbocharging Derivatives — Variance, Convexity, and Everything in Between

The roots of convexity and Jensen’s Inequality

  1. σ (annualized volatility) = 10%
  2. σ = 20%

So now we can spot two main sources of convexity in derivatives:

  1. The payoff function (i.e., non-linear payoff)
  2. The underlying process dynamic, which is governed by the variance and time (the greater either one of them, the higher the value of our derivatives)

Volatility, Variance, and Additivity

  1. Black-Scholes options pricing formula expresses the fluctuation parameter in terms of annualized standard deviation (volatility)
  2. It’s easier for us to convert daily returns of asset prices to annualized volatility (i.e., 1% move to 16% vol using the “rule-of-16”), as everything grows at the rate of sqrt(t)

Let’s look at three widely used use-cases for variance in derivatives trading:

  1. Forward-Volatility trading

Creating The Ultimate Convexity in Derivatives Space



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