Distribuições preditiva e implícita para ativos financeiros - Oliveira, Natália Lombardi de (Universidade Federal de São Carlos, 2017)
We present two different approaches to obtain a probability density function for the stock?s future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula.
Predictive and implied distributions of a stock price
Keywords: Volatilidade implícita; Smile da volatilidade; Função densidade de probabilidade implícita; Função densidade de probabilidade preditiva; Modelo autorregressivo Bayesiano; Implied volatility; Volatility smile; Implied probability density function; Predictive probability density function; Autorregressive Bayesian model; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA