Category: DERIVATIVES

A Utility-based Option Pricing Model

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 …

An Option Pricing Model Based on Market Factors

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 …

Diffusive Volatility and Jump Risks

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 …

Pricing Options In The Real-World Measure

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 …

Do Path-Independent Volatilities Exist?

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 …

Collateral Choice Option

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 …