The Black–Scholes–Merton (BSM) model is the most frequently used option pricing framework in finance. However, it relies on simplifying assumptions, some of which are not realistic. Ongoing efforts aim to extend and generalize the BSM model, and Reference represents a recent contribution in this direction. The paper proposes an …

The Black–Scholes–Merton (BSM) model is a cornerstone of derivative pricing; however, it is not without limitations, and researchers continue to extend it. Reference proposes an extension by incorporating intraday momentum into the BSM framework. This is achieved by introducing a drift term that represents intraday momentum, measured using a …

VIX futures and Exchange-Traded Products (ETP) are widely used instruments for both volatility speculation and hedging, making a clear understanding of their behavior essential for these purposes. Several studies have examined the relationship between spot VIX, VIX futures, and volatility-linked ETPs. Reference contributes to this literature by analyzing the …

It is well known that put options are often overpriced, especially in equities. The literature is filled with papers explaining this phenomenon. However, most research still relies on the Black-Scholes-Merton framework, where the underlying asset follows a Geometric Brownian Motion (GBM). Reference also addresses this question, but it departs …

The implied volatility surface is a fundamental building block in modern financial markets, as it underpins the pricing of both vanilla and exotic instruments and supports key risk-management functions such as hedging and scenario analysis. It has been modeled extensively in traditional finance; in crypto, however, few studies exist. Given …

Options are powerful tools. They serve not only as an effective instrument for risk management and speculation, but they also provide valuable information about the underlying asset. That is, we can use option‐implied signals to predict the underlying. For example, when the correlation between the S&P 500 and its implied …

Volatility is an important measure of market uncertainty and risk. For decades, realized volatility has been computed from the squared returns. Recent research, however, has highlighted several deficiencies in traditional volatility measures. Reference continues this line of inquiry, identifying three key inefficiencies in conventional volatility estimation, Volatility is path-independent …

A growing body of research has recently investigated anomalies in option returns, such as option return momentum, and these anomalies are often attributed to market inefficiencies. Reference , however, proposed and tested a different hypothesis: these anomalies originate from option returns around expiration days. Specifically, the author isolated the return …

Modeling and forecasting volatility is essential in trading and risk management. Extensive research has been conducted on volatility modeling in traditional financial markets, and recently, attention has increasingly been directed toward cryptocurrency volatility. The standard approach often relies on econometric models. Reference applied the GARCH-MIDAS model to study Bitcoin …

Geometric Brownian Motion (GBM) is the fundamental stochastic process used to model asset prices in continuous time. It serves as the foundation for pricing models such as the Black–Scholes–Merton framework. However, some critics argue that the assumptions of GBM are unrealistic, and researchers continue to explore ways to modify and …