A rather fancy, but real-life example of a structured bond is the following: - Bond maturity is

Question:

A rather fancy, but real-life example of a structured bond is the following:

- Bond maturity is four years.

- At maturity, the payment of the face value is guaranteed, plus a single coupon; the coupon, too, will be paid at maturity, and no periodic coupon will be paid.

- The coupon is linked to the monthly average value of a basket of ten stock shares in the telecommunication industry; since maturity is 4 years, 48 monthly observations of ten stock prices are involved in the average.

- The average return of the portfolio might well be negative, but in this case the coupon will just be zero, and no loss will be sustained.

- It will be possible to ask for the anticipated payment of the coupon every six months, starting from the end of year 2.

- It is also possible to ask for the anticipated repayment of the face value, but this implies a reduction with respect to the face value.

This looks like a very complicated security, but it may be assembled by bundling a zero-coupon bond and an exotic option. The zero ensures the payment of the face value, which is reduced if early repayment is requested. The option is a complicated version of a call. Let \(S_{j}\left(t_{i}\right)\) be the price of each underlying stock share, indexed by \(j=1 \quad 10\), at time \(t_{i}=i 12\), where \(i=\begin{array}{llll}0 & 12\end{array}\) 48. Note that we are considering one year as the time unit, as customary in finance, and for the sake of simplicity we are assuming that one year consists of 12 identical months, which is not really the case. Finally, let us consider the following payoff:
\[\max \quad 0 \frac{1}{48}{ }_{i=1 j=1}^{48} S_{j}\left(t_{i}\right) \quad K\]
where \(K\), the strike, is just the initial value of the portfolio, \[K={ }_{j=1}^{10} S_{j}\left(t_{0}\right)\]
This option has three features:
- It is a rainbow option, as it is written on multiple underlying assets.
- It is an Asian option, since its payoff is related to the average price, rather than to a single price at maturity (or early exercise).
- It is a Bermudan-style option, since it features early exercise opportunities, but only at a limited set of epochs, corresponding to \(t=225335\) years; thus, it is halfway between American- and European-style options.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Question Posted: