Yield-X: The Market Works The workings of the Yield-X yield curves, products and Calm margining system. Rogan Etheredge 07 February 2005. Programme. Introduction to Yield-X Yield curves Products Margining. Yield-X Products. jBonds: liquid RSA bonds (in Govi)

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Yield-X: The Market Works The workings of the Yield-X yield curves,

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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

Programme • Introduction to Yield-X • Yield curves • Products • Margining 06 Feb 2005

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 06 Feb 2005

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 06 Feb 2005

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. 06 Feb 2005

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 06 Feb 2005

Yield curve methodology • BEASSA • Perfect fit • Available on website daily to 30 years 06 Feb 2005

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 06 Feb 2005

Use of curves • Market information • Pricing illiquid instruments • Resets • Close-out prices of jFRAs and jNotes • Margining 06 Feb 2005

jBonds • R194, R153, R201, R157, R203, R186 • Quoted on yield to maturity • Bond pricing formula ("BPF") • Spot: t+3 • 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 06 Feb 2005

jCarries • On all jBonds • 1st leg settled on t+3 • priced at current market price, using BPF • 2nd leg settled 1week or 13 weeks after t+3 • 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 06 Feb 2005

jFutures • On all jBonds • Expire 1st business Thursday of Feb, May, Aug and Nov • Physically settled on t+3 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 06 Feb 2005

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 06 Feb 2005

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 06 Feb 2005

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 06 Feb 2005

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 06 Feb 2005

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 06 Feb 2005

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 + S[Moneyedness] • 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 06 Feb 2005

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 06 Feb 2005

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 06 Feb 2005

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 06 Feb 2005