stotastic

With the stock market freaking out and all, I figured I should take a look at how volatility was being priced in the option market. The CBOE generously provides snapshots of market data for anyone interested to download. By using this data, we can calculate the markets ‘implied volatility’, or level of ‘freaking out’. For those not familiar with the concept of implied volatility, essentially we can take the prices of options in the market and back out the volatility implied by those prices using the Black-Scholes formula. Its been shown over and over again that the assumptions of the Black-Scholes model don’t hold up to empirical data; but its an easy calculation to perform, and so implied volatility is a widely used metric. Anyway, below is my Black-Scholes option pricing function and the function used to back out implied volatility (written in R of course). Since implied volatility can only be found numerically, I used the Bisection Method to calculate it since it was easy to implement, but there are faster methods out there.

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