# Product Description

A note is a legal wrapper issued by a financial institution.

If B(T0, T) is one unit of the capital guaranteed at maturity, then 1 - B(T0, T) is called the available.

A fixed maturity can then be constructed with any type of payoff as long as the price of the derivative product matches the available.

When buying a note, the goal of the investor is to have a return that is higher than the riskless IR one.

However, the problem the client faces with fixed maturity notes is that his capital is blocked up until maturity.

Autocallable notes solve that issue. The autocallable structure doesn’t have a fixed maturity.

What we call maturity is in fact the maximum duration this product can stay alive.

The terms of a typical equity-linked autocallable note are:

- At T0, the client invests 100

- The product maturity is T and we consider Ti, 1 ≤ i ≤ N the autocallable dates with T0 < T1 < ... < TN = T.

- If S is the underlying, Ki a set of strikes, Ci a set of coupon, the payoff is as follows:

• at Ti, if the note has not yet been recalled and if STi ≥ Ki, then the note is terminated and the client receives 100 + Ci.
• at T,  if the note has not yet been recalled  and if STN ≥ KN, then the client receives 100 + C; otherwise, he receives 100.

Usually, we observe the following features:

- the autocallable dates have a fixed frequency.

- the strikes are equal.

- the coupons have a linear progression:  Ci = iC   with C higher than riskless IR on the interval ∆T = Ti+1 - Ti

In a bullish market:

- the investor can have a higher return on his capital than the IR one.

- his capital is available as soon as his target is reached.

This explains why autocallable notes are very popular in the equity markets and have been massively traded in the past years.

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