# Option pricing using high-frequency futures prices

## Stavros Degiannakis, Christos Floros, Thomas Poufinas, George Filis and Konstantinos Gkillas

#### Need to know

• We examine two potential routes to improve the outcome of option pricing
• We extract the variance from futures prices instead of the underlying asset price
• We calculate the variance in different frequencies with intraday data instead of daily closing prices
• We perform the valuation of call and put options for six volatility measures
• We realize that the implied volatility exhibits the lowest deviation from the market price

#### Abstract

Option pricing depends heavily on the volatility measure used. We examine two potential routes to improve the outcome of option pricing: extracting the variance from futures prices instead of the underlying asset prices, and calculating the variance in different frequencies with intraday data instead of daily closing prices. We perform a valuation of call and put options for six volatility measures, namely unconditional volatility, historical volatility, conditional volatility, realized volatility and implied volatility, to examine which one gives the optimal result versus the (market) price. We show that the implied volatility exhibits the lowest deviation from the market price, as judged by the mean and the standard deviation of the relative difference of the option value from the market price (as calculated using each of the volatility measures). Also, using econometric models, we find the determinants of the deviation of the calculated option value from the actual market price. We show that the time to expiration, the spread and the moneyness, as well as their squares, are all statistically significant at all levels for all volatility measures. Moreover, the time-to-expiration coefficient implies that all volatility measures yield option values closer to the observed market price for shorter times to expiration.