The arbitrage principle is one of the cornerstones of modern finance, and it’s being used widely, from derivative pricing to hedging, trading, and risk management. Theoretically, there is only one arbitrage principle. Practically, however, there are other types of arbitrage, some of which are relaxed forms of the strictest one. …

Volatility estimators are a useful tool in volatility trading and risk management. We have discussed several types of volatility estimators, ranging from the simple Close-to-Close Historical Volatility to more complex ones like the Garman-Klass-Yang-Zhang volatility. As discussed in Reference , volatility estimators can also be used directly in delta-one trading …

Accounting numbers are prevalent in financial reporting, business valuation, and investment management. They’re so frequently used that the practitioners rarely asked pragmatic questions such as: are they useful, do they account for some meaningful risks, can they be used to price assets. A recent article attempts to bring some …

Options market efficiency is a topic of interest not only to academics but also to practitioners. There is a body of research focusing on market inefficiency. For example, we recently highlighted a research paper dealing with sector ETFs’ implied volatilities and correlations. The research result implies that the options market …

We previously demonstrated that stock indices exhibit mean-reverting property in the short term and trending property in the long term. Reference further explored the trending/mean-reverting properties in a longer timeframe and pointed out that in the very long term, the markets mean-revert, We provide further evidence that markets trend …

The volatility risk premium is a common phenomenon that exists in the volatility space. It is often defined as a stock’s or index’s implied volatility (IV) minus its realized volatility (RV). For equity indices, over the long term IV is generally greater than RV, thus giving rise to the popularity …

Volatility term structure is believed to be a common phenomenon across asset classes. In equity indices, it’s well-known that implied volatility (IV) is generally greater than realized volatility (RV) (i.e. there exists a so-called volatility risk premium), and out-of-the-money (OTM) IV is greater than at-the-money (ATM) IV (i.e. there exists …

Most of the studies on time-series momentum have been performed in the daily, weekly, and monthly timeframes. Relatively less research has been conducted in the intraday timeframe. So naturally, we would ask the question: Does the momentum exist intraday? Reference answers this question. It examined the time-series momentum of …

Trend following is a popular trading strategy used by Commodity Trading Advisors (CTA) and Hedge Funds around the world. The traded assets are often futures on commodities, FX, fixed-income, and equity indices. We previously demonstrated that stock indices exhibit trending property in the long term, i.e. their returns are positively …

Testing and validating a trading strategy is an important step in trading system development. It’s a commonly-known fact that a well-optimized trading strategy’s performance often deteriorates after it goes live. Thus, developing a robust strategy that performs well out-of-sample is quite a challenge. To this effect, we previously discussed a …