YieldX: The Market Works

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Yield-X The Market Works The workings of the
Yield-X yield curves, products and Calm
margining system.
Rogan Etheredge 07 February 2005
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Programme

• Introduction to Yield-X
• Yield curves
• Products
• Margining

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Yield-X Products

• jBonds liquid RSA bonds (in Govi)
• jCarries 1 and 13 weeks on jBonds
• jFutures futures on jBonds
• jTRIs and jGOVI futures on Total Return Indices
• jSwaps bond lookalike swaps
• jRods swaps against overnight interest rate
• jNotes futures on notional swaps
• jFRAs futures on FRAs / Jibar
• jOptions options on all futures

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Yield-X Products
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Explicit mark-to-market
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Implicit mark-to-market
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Trading on Yield-X

• Screen-based central order book
• Yield to three decimal places (1/10th basis
  point)
• Central counterparty
• settlement guaranteed
• margining
• Report-only trades
• derivatives fall within risk positions and are
  guaranteed
• jBonds only if both Clearing members agree

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Mark-to-market
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Margining
All positions All instruments full
offset. Estimate maximum loss which position can
suffer next 24 hours, 99.95 confidence. Loss
is potential exposure of the Exchange take the
amount in margin now! Margin earns interest at
wholesale rates re-estimated daily returned
when position is closed.
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Daily cashflows

• Explicit mark-to-markets
• Change in margin
• Settlements of spot bonds
• Net interest payments on jSwaps and jRods
• Conversion payments
• Interest on margin
• Booking fees

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Yield curve methodology

• BEASSA
• Perfect fit
• Available on website daily to 30 years

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Four curves

• Yield-X Curve
• RODI, 3 mth Jibar, jFRAs, jNotes
• jBonds curve
• RODI, 1 and 13 week jCarries, jBonds
• jSwaps curve
• RODI, 3 mth Jibar, jSwaps
• jRods curve
• RODI, jRods

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Spreads

• Market price paramount
• Instruments in generating set have zero spreads
• Others have spreads calculated so that the Curve
  Spread prices them back to the market
• Instruments without market prices priced off
  their curve, using their latest recorded spread

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Use of curves

• Market information
• Pricing illiquid instruments
• Resets
• Close-out prices of jFRAs and jNotes
• Margining

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jBonds

• R194, R153, R201, R157, R203, R186
• Quoted on yield to maturity
• Bond pricing formula ("BPF")
• Spot t3
• Forward settlement date by agreement
• On-screen through central order book
• included in Risk Positions
• settlement guaranteed
• Report only
• both Clearing Members must explicitly agree
• Guaranteed forwards subject to yield resets
• Settlement margins

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jCarries

• On all jBonds
• 1st leg settled on t3
• priced at current market price, using BPF
• 2nd leg settled 1week or 13 weeks after t3
• Quoted on carry rate as a simple yield between
  settlement dates
• quoted rate converted to ccr to find price of 2nd
  leg
• jCarries are on-screen through the central order
  book
• included in risk positions
• settlement of both legs guaranteed
• 2nd leg subject to yield resets
• Settlement margins

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jFutures

• On all jBonds
• Expire 1st business Thursday of Feb, May, Aug and
  Nov
• Physically settled on t3 of expiry date
• Quoted on yield to maturity
• Priced using BPF for settlement date
• Settlement guaranteed
• Settlement margins
• Safex positions will be carried over
• to Yield-X

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jSwaps

• Bond lookalike swaps on all jBonds
• j194, j153, j201, j157, j203, j186
• Expire on parent bonds' (mid) redemption dates
• Semi-annual interest payments on same days as
  parent bonds'
• Floating rate is 3-mth Jibar, compounded at mid
  interest period
• Quoted on fixed rate yield for the period
• Standard fixed rate, reset on interest payment
  dates (or when market has moved) to market rate,
  rounded to 25 bps
• Dealt positions are converted to the standard
  rate
• Conversion payments PV off jSwaps Curve (
  spread) of difference in fixed interest payments
• Interest payments net through the Exchange
• Guaranteed by the Exchange

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jSwap Interest Calculations
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jSwap Equation
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jRods

• Swaps of floating RODI against fixed 3-mth rate
• Expire monthly on last business day of each month
• Quarterly interest payments on last business day
  of month
• Floating rate is jRODI (RODI converted from nacm
  to nacd), compounded daily
• Quoted on fixed rate yield for the period
• Standard fixed rate, reset on interest payment
  dates (or when market has moved) to market rate,
  rounded to 25 bps
• Dealt positions are converted to the standard
  rate
• Conversion payments PV off jRods Curve (
  spread) of difference in fixed interest payments
• Interest payments net through the Exchange
• Guaranteed by the Exchange

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jRod Interest Calculations
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The jRod Equation
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jNotes

• Futures on notional swaps
• Expire 1st business Thursday of Feb, May, Aug and
  Nov
• Swaps are for 2, 5 and 10 years from expiry date
• Quarterly interest payments on 1bThu 2, 5, 8, 11
  cycle
• Floating rate is 3-mth Jibar
• Quoted on fixed rate yield for the period
• Marked-to-market at closing fixed rate
• Cash settled on expiry off the Yield-X Curve

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jNote Interest Calculations
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jFRAs

• Futures on FRAs / Jibar
• Expire 1st business Thursday of Feb, May, Aug and
  Nov
• FRA interest payment date is 3 months from expiry
  on 1bThu 2, 5, 8, 11 cycle
• Floating rate is 3-mth Jibar
• Quoted on fixed rate yield for the period
• Marked-to-market at closing fixed rate
• Cash settled on expiry off the Yield-X
• Curve / 3 mth Jibar

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jFRA Interest Calculations
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jOptions

• On all futures contracts
• American calls and puts
• Expire on underlying future's expiry date
• Strike prices in same units as future's quote
• Each option on one futures contract
• Fully margined premium not paid up-front, but
  realised over the life of the option through the
  mark-to-market process
• Naked options traded on price
• Options with delta traded on volatility
• Early exercise allowed but never optimal
• Automatic exercise of options more than 2.5 in
• the money on expiry
• Long options may be abandoned
• Pricing via Modified Black Option Formula

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Volatilities and Skews

• Time structure each expiry has its own atm vol
• Skew Moneyedness grid defines additive skew for
  various degrees of moneyedness
• Vol Atm Vol SMoneyedness
• Grid and atm vol found by weighted linear
  regressions of traded volatilities
• weight by vega number of options
• atm vol also weighted by time since trade
• historical trades also brought forward,
• with decay factor
• Manual override possible

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Yield-X Margining

• Comprehensive
• All-embracing
• Logical
• Margining
• Calm

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Two prerequisites

• Logical all interest rate instruments may be
  valued by reference to a single construct
• The yield curve
• Technical the existence of reliable yield curves

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The two stages of margining
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Data

• Zero coupon yield curves from 08 May 2002 685
  days
• Data cleaned
• Extend backwards
• Yield-X Curve when available
• 1d, 1w, 1m, 3m-12m, 18m-60m, 6y-30y

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Historical yields
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Yield changes

• Compare todays yields with yesterdays forwards
  one day
• Log of ratio
• Basic unit Trading day

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Yield changes 1d rates
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Yield changes 60m rates
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Yield changes 30y rates
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30 day exponential weighting
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750 day exponential weighting
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Double exponential weighting
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Vols 1d
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Vols 60m
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Vols 30y
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Correlations 1d vs 30y
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Principal Components Analysis

• The curse of dimensionality
• PCA reduces it
• Find variance / covariance matrix for latest day
• Find its eigenvectors the components
• First n eigenvectors the principal components
• Eigenvalues are variances of components
• First n account for most of the variance

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Vols Curves and Components
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First component
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Second component
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Third component
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Fourth component
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Fifth component
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Construct historical components
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Vols - PC1
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PC3 Yield Changes
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Vols PC3
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Correlations PC1 vs PC3
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PC1 distribution
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PC1 Smoothed distribution
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ReproBars

• Choose 5 percentile ranges
• 5, 25, 40, 25, 5
• Find expected value in each range from smoothed
  distribution
• Get a discrete distribution with just 5 points

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PC5 Reprobars
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Construction of scenario curves

• All 55555 3125 combinations of 5
  abscissae/ordinates from 5 PC distributions
• Each combination is a set of 5 independent
  component changes, and has its own probability
• Apply the changes to the base curve to get 3125
  scenario curves, each with its own probability.

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Valuation of positions

• Value position 3125 times, to get 3125 values,
  each with its own probability
• Smooth the resulting distribution
• Find EWCV at .05 over 1 trading day

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Expected worst case value
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Margin

• "On the one day in 2,000 when things are really
  bad, just how bad are they likely to be?"

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Calm Results

• Assumptions
• Positions as at 28 Jan 2005
• Yield curve and bond yields as at same date
• Settlement day is 02 Feb 2005
• Margining valuations for 31 Jan 2005
• Margins calculated as the one-trading-day
  Value-at-Risk (VAR) of the position at 99.95
  confidence level

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Physical Bonds

• (NB settlement margins are ignored. Once a deal
  has been irrevocably committed to, it falls out
  of the risk position.)

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Forward Bonds
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Carries
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Compound Spot Position
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Positions with Futures
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Positions with jSwaps
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jNotes
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Distribution of Scenario Values
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Scenario Values jN05
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Scenario Values jN10
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jFRAs
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jRods
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jGovi
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Questions