**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Implied volatility

Summary

In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of said option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security. To understand where implied volatility stands in terms of the underlying, implied volatility rank is used to understand its implied volatility from a one-year high and low IV.
An option pricing model, such as Black–Scholes, uses a variety of inputs to derive a theoretical value for an option. Inputs to pricing models vary depending on the type of option being priced and the pricing model used. However, in general, the value of an option depends on an estimate of the future realized price volatility, σ, of the underlying. Or, mathematically:
where C is the theoretical value of an option, and f is a pricing model that depends on σ, along with other inputs.
The function f is monotonically increasing in σ, meaning that a higher value for volatility results in a higher theoretical value of the option. Conversely, by the inverse function theorem, there can be at most one value for σ that, when applied as an input to , will result in a particular value for C.
Put in other terms, assume that there is some inverse function g = f−1, such that
where is the market price for an option. The value is the volatility implied by the market price , or the implied volatility.
In general, it is not possible to give a closed form formula for implied volatility in terms of call price (for a review see ). However, in some cases (large strike, low strike, short expiry, large expiry) it is possible to give an asymptotic expansion of implied volatility in terms of call price.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (98)

Related concepts (14)

Related courses (24)

Related units (10)

Related people (19)

Related MOOCs (1)

Related lectures (61)

Option (finance)

In finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction.

Volatility smile

Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.

Mathematical finance

Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.

MGT-482: Principles of finance

The course provides a market-oriented framework for analyzing the major financial decisions made by firms. It provides an introduction to valuation techniques, investment decisions, asset valuation, f

FIN-503: Advanced derivatives

The course covers a wide range of advanced topics in derivatives pricing

FIN-401: Introduction to finance

The course provides a market-oriented framework for analyzing the major financial decisions made by firms. It provides an introduction to valuation techniques, investment decisions, asset valuation, f

Interest Rate Models

This course gives you an easy introduction to interest rates and related contracts. These include the LIBOR, bonds, forward rate agreements, swaps, interest rate futures, caps, floors, and swaptions.

Portfolio Optimization: Risk and ReturnMGT-482: Principles of finance

Explores the tradeoff between risk and return in portfolios, the benefits of diversification, and the impact of correlation on portfolio risk.

Efficient Portfolio: CAPM ApplicationFIN-401: Introduction to finance

Explores efficient portfolios and the CAPM model in finance, analyzing risk, returns, and market relationships.

Introduction to Finance: Risk and Return in PortfoliosFIN-401: Introduction to finance

Covers risk and return tradeoffs in portfolios, diversification benefits, and the efficient frontier with multiple assets.

Pierre Collin Dufresne, Jan Benjamin Junge

We study the extent to which credit index (CDX) options are priced consistent with S&P 500 (SPX) equity index options. We derive analytical expressions for CDX and SPX options within a structural credit-risk model with stochastic volatility and jumps using ...

Throughout history, the pace of knowledge and information sharing has evolved into an unthinkable speed and media. At the end of the XVII century, in Europe, the ideas that would shape the "Age of Enlightenment" were slowly being developed in coffeehouses, ...

Volkan Cevher, Efstratios Panteleimon Skoulakis, Luca Viano, Ali Kavis

Motivated by alternating game-play in two-player games, we study an altenating variant of the Online Linear Optimization (OLO). In alternating OLO, a learner at each round t ∈[n] selects a vector xt and then an adversary selects a cost-vector ct ∈[−1,1]n. ...

2023