610 CHAPTER 16. INTERNATIONAL FIXED-INCOME MARKETS
be 4 percentp.a.or 2 percent effective. Interpret the 3.5% floor as an option on a
PN: who holds and who writes the option, what type of option is it, what exactly
are the terms and conditions of the underlyingPN?
Both the example and the DoItYourself are summarized in Table 16.2.
In short, the floor on the interest rate is a call option on a promissory note, and
the option is held by the lender and written by the borrower. The cap on the interest
rate is a put option on a promissory note, and the option is held by the borrower
and written by the lender. The reason why it is useful to re-state caps and floors
as puts and calls onPN’s is that aPN, unlike an interest rate, is an asset. So one
can express a Put-Call parity in terms of option prices, underlyingPNprice, and
discounted strike price. There is no similar direct link between option values and
interest rates, except when prices are expressed as functions of interest rates:
DoItYourself problem 16.2
Buying a European-style call and selling a European-style put still means a forward
purchase, and the forward purchase at strikeX still has the same value as the
underlying. So Put-Call parity still takes the form
(
Call pre-
mium)
−
(
Put pre-
mium)
=
(
market value for-
ward purchase)
= PV asset−X
1 +rt,T. (16.1)
Write the PV of the asset as a function of the limit rate (e.g. the 3% from the
example) and the current market rate. Show that the right-hand side of the equation
can be written as thediscounteddifference between the limit and market effective
rates of return.
Hasty traders occasionally ignore the discounting, and express option prices as
p.a.percentages so as to get a link with the p.a. interest rates in the formula.
Costs of a loan
There are various costs associated with a euroloan. These include:
- An up-frontmanagement fee andparticipation fee, sometimes 0.25 percent
and sometimes a few percentages, see below. The up-front feature means that
this amount is deducted from the principal. That is, the borrower receives
only 99 percent to 99.5 percent of the nominal value of the loan. - Apaying agent’s feeof a few basis points to cover the administrative expenses.
- Therisk spreadabove the risk-free rate (that is, aboveLIBORin the case of a
floating-rate loan, or above the long-term fixed rate paid by a government of
excellent credit standing). This spread depends on the quality of the borrower,
the transfer risk of his or her country, the maturity and grace period, and the
up-front fee. Also, the market situation affects the spread: there are strong