Volatility (Realised vs Implied)
Realised volatility comes from past price moves; implied volatility is the market’s quote for future uncertainty.
Realised volatility is computed from historical returns, for example as the annualised standard deviation over a recent window.
Implied volatility is the σ that, plugged into Black–Scholes, matches the current market price of an option.
They differ because markets embed risk premia, jump risk, and supply–demand imbalances for options into implied volatility.
In calm periods, realised volatility can sit well below implied; in stress, both can spike, but not necessarily by the same amount or timing.
Realised volatility σrealised comes from past price moves; you estimate it from a return series. Implied volatility σimplied is the input to a pricing model (here Black–Scholes) that makes the model price match the market option price.
The upper panel is the realised volatility engine: take daily returns rₜ, compute their sample standard deviation, and annualise it. Moving the “Target path volatility” slider stretches or compresses these bars; σrealised follows.
The lower panel is the option pricing engine: feed a volatility σ into Black–Scholes and read off C(σ). Marking σrealised and σimplied on the same curve shows how far the market’s volatility input can sit from what actually happened in the path. That gap is where volatility risk premium, jump risk and order-flow effects live in practice.