Volatility refers to the degree of variation of a trading price series over time. It is a statistical measure of the dispersion of returns for a given security or market index. High volatility indicates a greater potential for significant price swings, both upward and downward, while low volatility suggests a …

Employee stock options (ESOs) are a compensation tool offered by companies to their employees, granting them the right to purchase shares of the company’s stock at a predetermined price. ESOs serve as incentives for employees, aligning their interests with the company’s success and long-term growth. Typically, these options have a …

A startup is a fledgling company or entrepreneurial venture in its early stages of development, typically characterized by innovation, a focus on disruptive technology or business models, and the pursuit of rapid growth. Startups often face high levels of uncertainty and risk, seeking to fill a gap in the market …

Dividends are a fundamental component of many investment strategies and a crucial aspect of equity ownership. They represent a portion of a company’s profits that is distributed to its shareholders, typically on a regular basis, such as quarterly or annually. Dividends are an input in the pricing model for equity …

An Asian option is a type of financial derivative contract commonly used in the world of finance. What sets it apart from traditional options, such as European or American options, is its unique method of calculating the payoff. Rather than being determined solely by the underlying asset’s price at the …

In the realm of finance, the risk-neutral measure takes precedence in pricing financial derivatives. However, the real-world measure remains significantly valuable and indispensable across various domains. It plays a pivotal role in risk management and asset/liability applications, facilitating comprehensive evaluation and mitigation of risks. Real-world measures are useful for simulation-based …

The volatility smile is a phenomenon observed in the options market where implied volatility tends to be higher for out-of-the-money (OTM) options compared to at-the-money (ATM) options. It refers to the graphical shape of the volatility curve, resembling a smile when plotted against the strike prices of options. The volatility …

The Black-Scholes option pricing model is a widely used mathematical formula for calculating the theoretical value of European-style options. Developed by economists Fischer Black, Myron Scholes, and Robert Merton in 1973, the model takes into account various factors such as the current stock price, strike price, time to expiration, risk-free …

In option pricing theory, the risk-neutral measure is a measure that allows for the valuation of financial instruments such as options. The risk-neutral measure is obtained by assuming that investors are indifferent to the risk and that the expected rate of return on all assets is equal to the risk-free …

Implied volatility is an estimation of the future volatility of a security’s price. It is calculated using an option-pricing model, such as the Black-Scholes model, as it takes into account various factors including the current price of the underlying asset and its strike price. Implied volatility helps investors to gauge …