jmholzer / probabilistic

Generate probability curves for the future price of publicly traded securities using options chain data.
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Future feature: generating IV smile using delta instead of strike price #5

Open tyrneh opened 1 year ago

tyrneh commented 1 year ago

Summary:

Source: (page 53 of link) To convert a call price function into the relevant volatility smile (and vice versa) involves transforming both axes in a non-linear way. We convert option prices into implied volatilities. The implied volatility is the volatility of the underlying asset price implied by the Black-Scholes (1973) model and is a non-linear transformation of the option price. A conventional volatility smile plots implied volatility against the strike price, but such smiles can vary in smoothness from day to day, making consistent interpolation problematic. We choose to interpolate implied volatilities across deltas rather than strikes, as illustrated in Chart 5. The delta of an option is the rate of change of the option price with respect to the underlying asset price and is a non-linear transformation of the strike price. These ‘delta smiles’ have a more stable degree of smoothness from day to day. The interpolation across the delta smile as in Chart 5 is done using a smoothing spline, which is a flexible non-parametric technique. A smoothing spline is a piecewise cubic polynomial, the smoothness of which is controlled by a single parameter, the smoothness parameter. Because we interpolate across delta space we can hold the smoothing parameter constant from day to day. This means that changes in pdfs from day to day reflect changes in the underlying data, and not in the estimation technique.