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 …

Option pricing is usually carried out in the risk-neutral world where the market participants are assumed to be indifferent between taking a certain payoff or investing in an asset with that same expected return. Mathematically, an option’s price is the expected value of its payoff in the risk-neutral measure discounted …

Implied volatility is a theoretical value that measures the expected volatility of a financial instrument over a specific period of time. It is derived from the price of a financial instrument and can be used to gauge market expectations. Implied volatility is often used by traders to make decisions about …

Volatility of an asset is a measure of how much the price of that asset varies over time. In other words, it is a measure of how “risky” an investment in that asset is. The higher the volatility, the greater the risk. There are two main types of volatility: historical …

The Black-Sholes-Merton model is a mathematical model for pricing financial options. The model is used to calculate the theoretical value of an option, which is the amount that the option holder would be paid if they exercised the option. The model takes into account factors such as the underlying asset’s …

Commodity derivatives are financial instruments whose value is based on an underlying commodity. These derivatives can be used for hedging purposes or for speculation. The most common types of commodity derivatives are futures, options, and swaps. Due to their seasonal nature, valuing commodity derivatives requires pricing models that are different …

Derivative transactions may include collateral offered by the parties involved. These transactions require both parties to document the security provided by either one. Therefore, they may use a credit support annex (CSA). This document may give rise to a collateral choice option. Before discussing this option, it is crucial to …

A convertible bond is a bond that can be converted into a certain amount of the company’s stock at specified prices and dates. Convertible bonds are usually issued by young, growing companies that want to raise capital without giving up too much control of their company. For example, a company …

An option’s implied volatility is a measure of the option’s expected price fluctuation. It is a forward-looking, market-based estimate of volatility and is determined by the market price of the option. Implied volatility is a key ingredient in options pricing models such as the Black-Scholes model. It can be used …