Derivatives Articles

A Barrier option becomes active or inactive when a pre-set price barrier is breached. For example an “up-and-in” call option would only be active if at some point during the option’s life the price of the underlying exceeded the barrier, if it failed to do so it could not be exercised regardless of whether it finished in-the-money or not. Similary a “down-and-out” put option would be automatically cancelled if, during the option’s, life the underlying asset’s price fell below the barrier.

Double barrier options have two barriers, one above the spot price (ie the market price of the asset at the start of the option’s term) and one below the spot.
Barrier options are always less expensive than equivalent European/American options as there is always a probability that the options will be knocked out or not be knocked in. The only input in addition to the black scholes inputs is barrier level and the barrier type (ie knock in or knock out).

Barrier options cannot be valued using a Black Scholes model and are typically valued using a monte-carlo or binomial option pricing model

Derivatives ONE features a free valuation tool for pricing a single and double Barrier Options on Stocks, Currencies, Commodities and Futures.

European Options are options which are only exercisable on the expiry date of the option and are normally valued using the Black Scholes option pricing forumla. There are only five inputs to the classic Black Scholes model : spot price, strike price, time until expiry, interest rate, and volatility. As such European options are typically the simplest options to value The dividend or yield on the underlying asset can also be an input on some extentions of the model. In contrast American Options can be exercised at any time up until and including the expiry date of the option.

The term European is confined to describing the exercise feature of the option (ie exercisable only on the expiry date) and is does not describe the geographic region of the underlying asset. For example, a European Option can be issued on a stock of a company listed on an Asian exchange.

Derivatives ONE features a free valuation tool for European and American options

An American Option is an option which can be exercised at any time up to and including the expiry date of the option. This added flexibility over European options results in American options having a value of at least equal to that of an identical European option, although in many cases the values are very similar as the optimal exercise date is often the expiry date.

The early exercise feature of American options complicates the valuation process as the standard Black-Scholes continuous time model cannot be used. The most common model for valuating American Options is the binomial model. The binomial model begins by evolving an seet price over a lattice with the asset price moving either up or down at each node of the the lattice. Once a lattice of asset prices has been determined the model iterates back through the lattice of prices to determine at each node if early exercise is optimal or not. The binomial model is simple to implement but is slower and less accurate than ‘closed-form’ models such as Black Scholes.

DerivativeOne features a binomial model for valuing american options on Stocks, Currencies, Commodities and Futures