Covered Interest Parity When the Fixing Date Precedes Spot
Summary
The document explains how to apply covered interest parity when a forward’s fixing date falls before its spot date, a situation that can arise when holidays delay spot settlement. It uses an example involving the Vietnamese dong, where a Lunar New Year holiday pushes the spot date past the fixing date, and asks whether the usual forward-rate equation must change.
The answer says the equation itself remains the same when discount factors are consistently defined as values at each date measured from today. A discount factor between two dates is the ratio of their date-specific discount factors. Reversing the order of the dates reverses the ratio, and the corresponding quote direction also changes, leaving the forward-rate relationship intact. The explanation is conceptual and does not work through the numerical VND example; careful date and currency-quote conventions remain necessary when applying it.
Key ideas
- Define discount factors at each date relative to today, then express an interval discount factor as a ratio.
- The covered interest parity relationship does not require a different formula when fixing precedes spot.
- Reversing the date order changes the discount-factor ratio, and the quote direction must be handled consistently.
- Holiday calendars can produce a fixing date that falls before the spot date.
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Full text
# Forward rate from Covered Interest Parity when spot date is after expiry date
# Forward rate from Covered Interest Parity when spot date is after expiry date
I am using Covered Interest Parity to impute a forward rate. The Webpage https://osf.io/ez6an describes how to calculate the forward rate from discount factors and spot rate. Normally, the spot date precedes the expiry date of the forward. However, the expiry date may precede the spot date when there are holidays. Why is the equation for calculating the forward rate different when the expiry date precedes the spot date?
I am trying to impute forward rates for the currency VND (VIETNAMESE DONG). The relevant data is as follows:
- Tenor - 1W
- Trade date - 2011-01-28
- Spot date - 2011-02-09
- Expiry date (Fixing date) - 2011-02-08
- Delivery date - 2011-02-10.
The spot date is greatly delayed because of Lunar New Year holidays which are from 2011-01-31 to 2011-02-07.
The discount factor for the non-deliverable currency VND would normally run from the spot date to the fixing date. But here the fixing date 2011-02-08 precedes the spot date 2011-02-09.
## Answer by Attack68 (score 1, accepted)
https://quant.stackexchange.com/a/79895
The formula described is:
$$ f_t = f_s \frac{D_b(s,t)}{D_q(s,t)}$$
Where $D_b(s,t)$ and $D_q(s,t)$ are unhelpfully labelled as the discount factors from one date to the next. If you instead label these as discount factors at a particular date as measured from today, where today's discount factor is precisiely 1.0 then:
$$D_b(s,t) = \frac{D_b(t)}{D_b(s)}, \quad D_q(s,t) = \frac{D_q(t)}{D_q(s)} $$
The formula for a forward date that precedes spot does not change.
You only have to observe that the author flips the direction; $D_b(T_s, T) \; -> D_b(T, T_s)$ and then he also flips the quotient, resulting in the same formula.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.