OIS Forward Rates with QuantLib

 

M 917 536 3378 maksim_kozyarchuk@yahoo.com

When analyzing historical Overnight Indexed Swap (OIS) rates, the data looks like a step function. Most days, these rates fluctuate by less than a basis point, reverting gently around a certain baseline level. Occasionally, however, they exhibit sharp, substantial jumps, typically 25 basis points or more. These notable changes are directly tied to central bank meeting dates, where benchmark interest rate decisions are announced.

Selecting the Appropriate Curve Interpolation     Given this characteristic step-function pattern in historical OIS rates, it's logical to use an interpolation method that mirrors this structure when projecting forward OIS rates from the constructed discounting curve. Rather than opting for smooth interpolation methods, in QuantLib one can use PiecewiseFlatForward or PiecewiseLogLinearDiscount to model this behavior. From practical experimentation, both these interpolation methods produce nearly identical forward-rate behaviors. However, the PiecewiseLogLinearDiscount method offers a smoother profile for derived zero-coupon and par rates, making it slightly preferable for practical modeling and reporting purposes. Aligning Curve Pillars with Central Bank Meeting Dates     Another important consideration is aligning the curve's pillar dates with scheduled central bank meetings, especially on the short end of the curve. Since these dates are known well in advance (the U.S. Federal Reserve, for example, publishes its meeting schedule for at least the current and following year), this alignment significantly improves the curve's realism and predictive accuracy. To achieve this alignment, two primary approaches can be used: Explicitly setting pillar dates on the OISRateHelpers: This allows you to dictate exactly when forward rates should exhibit step movements without introducing new points into the curve. Interpolation with insertion of phantom points: Alternatively, you might first construct your curve without explicitly setting these meeting dates, and afterward interpolate and insert "phantom" points aligned precisely with central bank meetings. However, this method adds more points into the curve and creates some ambiguity at which point the step would occur. Given these options, explicitly defining pillars through the OISRateHelpers is preferable, one additional consideration is on distance between swap tenor and pilar date. The pilar date must be on/or before the maturity of the swap, and the closer the better. For the Kupala-Nich platform, I chose 60 days as the cutoff. Please see below for implementation of building OISSwapHelpers with meeting dates.  def _get_pilar_date(self, period, min_diff = 60):     tenor_date = self.calendar.advance(self.settlement_date, ql.Period(period))     closest_meeting_date = None     for meeting_date in self.MEETING_DATES:         if meeting_date < self.settlement_date:             continue         diff = tenor_date.serialNumber() - meeting_date.serialNumber()         if 0 <= diff <= min_diff:             min_diff = diff             closest_meeting_date = meeting_date     if closest_meeting_date in self._seen_meet_dates:         closest_meeting_date = None     if closest_meeting_date:         self._seen_meet_dates.add(closest_meeting_date)     return closest_meeting_date # Build helper pillar_date = _get_pilar_date(p['tenor']) if pillar_date:     ql.OISRateHelper(self.settlement_day, ql.Period(p['tenor']),          ql.QuoteHandle(p['quote']), self.index,         paymentFrequency=frequency, forwardStart=forward_start,            pillar=ql.Pillar.CustomDate,  customPillarDate=pillar_date) ) else:     ql.OISRateHelper(self.settlement_day, ql.Period(p['tenor']),        ql.QuoteHandle(p['quote']), self.index,        paymentFrequency=frequency, forwardStart=forward_start) ) Managing Realistic Jump Sizes in Rates     One practical modeling consideration is reflecting the realistic magnitude of central bank rate changes. Typically, central banks adjust rates in increments of at least 25 basis points. QuantLib's current implementation does not directly provide a straightforward way to explicitly constrain forward rate jumps to increments such as 25 basis points. Therefore, while the interpolation method and pillar alignment ensure the jumps occur at the right times, they do not inherently restrict the size of these jumps. If anyone has thought through this problem before, would appreciate your input.