Modelling the Implied Volatility Surface: Does Market Efficiency Matter? An Application to MIB30 Index Options

Abstract

We analyze the volatility surface vs. moneyness and time to expiration implied by MIBO options written on the MIB30, the most important Italian stock index. We specify and fit a number of models of the implied volatility surface and find that it has a rich and interesting structure that strongly departs from a constant volatility, Black-Scholes benchmark. This result is robust to alternative econometric approaches, including generalized least squares approaches that take into account both the panel structure of the data and the likely presence of heteroskedasticity and serial correlation in the random disturbances. Finally we show that the degree of pricing efficiency of this options market can strongly condition the results of the econometric analysis and therefore our understanding of the pricing mechanism underlying observed MIBO option prices. Applications to value-at-risk and portfolio choice calculations illustrate the importance of using arbitrage-free data only.

Semi-parametric forecasts of the implied volatility surface using regression trees

“…They exclude thinly traded options, options that violate at least one basic no-arbitrage condition, options with fewer than six trading days to maturity or more than one year, options with moneyness smaller than 0.9 and larger than 1.1, and finally contracts with a price lower than three-eighths of a dollar. Cassesse and Guidolin (2006) investigate the pricing efficiency in a bid-ask spread and transaction cost framework. They find a frictionless data set by dropping 51 percent of the original observations.…”

A CNN Based System for Predicting the Implied Volatility and Option Prices

“…Traditional parametric methods are typically based on some overly idealized assumptions including non-arbitrage conditions, lognormality, or sample-path continuity. Also, previous studies on estimating option prices mainly depend on historical transaction records without considering the performance of concurrent options [30]. In fact, several options are traded at the same moment and affect each other simultaneously.…”

“…And we also used convolutional neural networks to estimate option prices based on different input sets. In practice, several options were traded at the same time which may interact with the pricing of relevant options [30]. It is of great necessity to consider such real-time interference among different options.…”

Pricing commodity futures options in the Schwartz multi factor model with stochastic volatility: An asymptotic method

“…This has the advantage that it often leads to a closed form solution for derivatives prices, but empirical studies strongly contradict the normality assumption of re-turns. Generally, empirical log returns of equities, currencies and commodities have higher peaks and fatter tails, which is indicative of a distribution with differing variances, see Gatheral (2011), Cassese and Guidolin (2006) and Chiarella et al (2015). Options, in terms of implied volatilities which are anything but flat, provide further evidence that underlyings are not lognormal.…”