Visualization of financial instruments

Abstract

Until recently the visualization of financial instruments has been largely limited to two-dimensional representations of data. We have found meaningful multi-dimensional diagrams that aid in the visualization and analysis of various financial instruments. This paper focuses on the visualization of options because of the opportunity to explore the interesting inter-relationships between the determinants of option pricing. Using actual trading data, the multi-dimensional visualization of options revealed the substantial discrepancy between the theoretical and the actual pricing of options. Two ways of computing implied volatilities were compared, the conventional open-ended Black-Scholes "trial-and-error" method and a new closed-form solution method of Bharadia et al. We empirically falsify Bharadia's claim that his formula produces more moderate implied volatility than the conventional trial-and-error method. First, Bharadia's formula produces much more curvature in the volatility smile, so that his volatility is larger particularly for relatively low strike prices. Second, on some days, Bharadia's volatility smile can be empirically shown to be consistently larger than that of the trial-and- error method at all available strike prices.