# Extinguishable or Knock Out Options

An extinguishable or knockout option is operational from the start but disappears as soon the spot rate of the underlying asset reaches a certain predetermined level or barrier. This event can happen at anytime throughout the life of the option.

There are two main knock-out options:

1. The up and out put
2. The down and out call

#### The up and out put

This is a simple European put option which extinguishes or gets knocked out at any time during the life of the option, the underlying asset price or the out point. That is, until the option maturity date, the option resembles a standard European pt as long as the underlying asset remains lower than the barrier.

For example during the 1980’s many Japanese investors were bullish on their stock market but desired cheap protection for their fully invested portfolios. Investors could have purchased a one-year, at the money European put with Nikkei trading at around 30,000. Alternatively, they could buy up and out put with the same structure but with a barrier of 31,500. The cost savings would be approximately 35%.

The investor holding this position would own an option with a pay-off equivalent to an European put if at no time during the life of the option did the index rise over 31,500. If the index rose above 31,500 at any time, then the option would extinguish.

The investor is prone to market whipsaws that cause a hedge to be knocked out. However, since the investor is fundamentally bullish, he has achieved a lower cost protection than European puts and enhanced the return on his portfolio. The second major type of knock out option is the down and out call.

#### The down and out call

In the same way that the up and out gets extinguished once the barrier is reached, a down and out call is simple European call option which extinguishable if the underlying asset falls below the barrier out level. That is, until the option maturity date, the option resembles a standard European call as long as the underlying asset remains higher than the barrier. Once breached, it is extinguished.

An example of a down and out call is an interest rate cap. While caps are a series of put options on Eurodollar future prices, they can also be viewed as a series of call options on Libor interest rates. Many Treasurers desire to purchase caps but avoid them due to the high up-front premium associated with these European options. The cost of a standard 2-year, 5.00% cap with Libor at 3.5% typically exceeds a Treasurer’s hedging budget.

As an alternative, he could purchase the same cap but with a barrier of 3.00%. This structure will cheaply hedge the Treasurer against higher interest rates as the up-front premium is 15% less. If 6 month Libor falls below 3.00%, then the barrier is hit and the call is extinguished.

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