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This paper examines algorithms implemented in MATLAB that can be used to solve systems of Black-Scholes equations for implied volatility and implied risk-free rate. These algorithms were run on a dataset of almost 400,000 call options traded between 2003 and 2012. After adjusting for volatility skew, the options are re-priced using these model-implied parameters in the Black-Scholes equation. ... read moreMoneyness, time to expiration and the size of the bid-ask spread, are then examined to explain why market prices and model prices differ over time. This paper finds that call options far from expiration usually have Black-Scholes prices that exceed market prices, while those with large bid-ask spreads have, on average, market prices that exceed model prices. This paper also finds that, given recent developments in financial markets, including increased volatility and investor risk aversion, the Black-Scholes model may no longer accurately price call options.read less
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