A Quantum Model of Implied Volatility

Abstract

The quantum implied volatility (QIV) model is a minimalistic model of an implied volatility surface. It is derived by assuming that the implied volatility is the volatility which, when used as input to the Black-Scholes model, will produce the correct option price under a previously derived quantum model of asset price. In its base form, the model uses only two parameters to simulate a volatility surface over different strikes and expirations. Results can be improved by adding additional parameters, such as a drift term. The method is illustrated using data from the S&P 500 index, as well as individual stocks.