Interest Rate Swap Valuation

Published on January 2017 | Categories: Documents | Downloads: 51 | Comments: 0 | Views: 224
of 7
Download PDF   Embed   Report

Comments

Content

Interest Rate Swap – Work Paper

Introduction An interest rate swap is a contract between two counterparties to exchange periodically fixed “interest” payments for floating “interest” payments. The payments are in the same currency and are calculated on a notional principal amount. These swaps are normally described as “Plain Vanilla” interest rate swaps. The swap is usually “fixed to floating” As per the contract, on each payment date (also referred to as reset date) during the swap period, the cash payments based on difference in fixed & floating rates are exchanged by the parties from one another. The party incurring a negative interest rate differential for that leg pays the other counterparty. Example Consider a hypothetical swap is initiated on 5 March 2003 between Party A (“A”) and ABC Bank (“the Bank”). Party A may agree for a period of 4 years to pay ABC Bank interest at 7% per annum (with semi-annual compounding) on Rs. 50 million in return for receiving interest on Rs. 50 million at 6 month KIBOR (Karachi Inter-Bank Offer Rate), payments to be made semiannually. The first payment would be exchanged on 5 September 2003 (i.e. 6 months after 5 March 2003). A would pay the Bank Rs. 1.75 million, this is the interest on the Rs. 50 million principal for 6 months at 7% per annum, and the Bank would pay A interest on Rs. 50 million principal at the 6 month KIBOR rate prevailing six months prior to 5 September 2003 i.e. on 5 March 2003. Suppose that 6 month KIBOR on 5 March 2003 is 6.2%, the Bank would pay Rs. 1.55 million (Rs. 50 x 6.2% x ½). In total there are 8 exchanges of payment on the swap. The fixed payments to be made by A are always Rs. 1.75 million. The floating rate payments on a payment date are computed using the 6 month KIBOR rate prevailing six months before the payment date. In practice the payments will be made net from one party to the other. If KIBOR > 7% ABC Bank will pay the difference to A. If KIBOR is less than 7% party A will pay the difference to ABC Bank. As mentioned in the above paragraph A will pay Rs. 0.2 million (difference of Rs. 1.75 and Rs. 1.55 million) on 5 September 2003. Features IRS has the following features: IRS is customized product negotiated over the counter directly between banks and their clients. The ‘notional principal’ and the reset dates are determined when the contract is signed. − No restriction has been imposed by SBP on the minimum or maximum size of `notional principal’ amounts of IRS. − No restriction has been imposed by SBP on the minimum tenor, however the maximum tenor of the IRS has initially being restricted to 5 years. Any transaction, which exceeds this tenor, requires separate approval from State Bank of Pakistan. − IRS involves multiple payment obligations based on two interest rates in contrast to Forward Rate Agreements which involve only one payment obligation occurring on the settlement date.


Interest Rate Swap – Work Paper

Exposure of UBL As at 30 September 2008 UBL has 32 IRS deals with the notional principal amounting to Rs. 18 billion outstanding in respect of such deals. Unrealized loss in respect of such contracts is Rs. 162 million. . Valuation of IRS Below is a summary of the principles which are generally adopted in the mark to market valuation of interest rate swaps. The principles are based on the international theories and practices which may not be applicable completely to the Pakistani environment where the derivative markets are at the infancy stage. The principles mentioned below are then aligned to the Pakistan and UBL specific valuation model. The mark to market revaluation of an interest rate swap involves calculating the net present value of the future cash flows under the swap discounted at appropriate market rates of interest. Interest rate swaps involve a stream of interest rate cash flow receipts and a separate stream of interest rate cash flow payments. These two streams are generally revalued separately and the results combined to determine the overall mark to market valuation of the swap. Bond pricing method with the derivation of zero curves is used internationally to revalue the IRS portfolios. This can be a complex process and there are a variety of practices used. From an audit perspective the key matters to consider are:
n n n n n

the methodology used; determination of the discount rates; allowing for credit risk; allowance for market liquidity; and providing for future administration costs.

Of these matters, determining the appropriate discount rates is the most critical and should receive particular attention when we are auditing the valuation of a swap portfolio. Bond Pricing Method Under the bond pricing method two legs of the IRS (i.e. fixed and floating legs) are considered as the fixed and floating leg bond issued / purchased according to the positions held in the swap transaction. The party having long position in the fixed leg and short position in the floating leg (i.e. receiving fixed rate from the counter party) will be assumed to have purchased a fixed rate bond and issued floating rate bond. The party which is long in fixed leg and short in fixed leg (i.e. receiving floating rate from the counter party) will be assumed to have purchased a floating rate bond and issued fixed rate bond. In case of above example Party A is considered to have purchased a floating rate bond from the Bank and issued a fixed rate bond to the Bank. Vice versa is the position of the Bank. Net present value of the IRS is computed as follow:

Interest Rate Swap – Work Paper
n

The value of the fixed leg is computed by discounting the fixed leg cash flows, in the above example Rs. 1.75 million every six months and Rs. 50 million notional at the maturity, using the appropriate discount rate which is commonly the rate on zero curve of the relevant maturity. There is no need to value the floating leg on the premise and common logic that floating rate bonds (floater) are always traded at the par value because there is no difference in the market interest rate and coupon rate on the floater. Floaters are traded at above or below par value only in following cases: - Between two reset dates where the coupon rate is determined and market interest rates are changed between the reset dates; and - There is a change in the market sentiments regarding the credit spread of the issuer.

n

The difference between the value of fixed and floating leg is the value of the swap. It should also be noted that the notional principle amounts included in the fixed and floating leg revaluation offset each other as the notional principal is deducted in one leg and added on the other. Zero Coupon Rate Zero coupon bonds are the type of bond that is issued below par value (i.e. at discount) and redeemed at the par value on maturity. There is no intermediate coupon payments on the zero coupon bonds. The zero coupon rate is the rate of interest earned on an investment that starts today and lasts for n number of years. All the interest and principal is realized at the end of n years and there are no intermediate payments. Many of the interest rates we observe directly in the market are not pure zero rates. Consider a 5 year PIB that provides an 8 % coupon. The price (yield) on this PIB does not exactly determine the 5 year zero rate because some of the return on the bond is realized in the form of coupons prior to the end of year five. The question arises as to the fact as why to use the zero coupon rate and why not use the market yields on the bonds having various maturities? In other words why there is a need to plot a zero coupon curve and why we cannot use the yield curve? There is a conceptual difference between the yield of 5 year PIB making intermediate coupon payments and the zero coupon bond of the same maturity. The yield on the five year PIB represents the IRR (weighted average yield) of the instrument and assumes that all the cash flows of the bonds during its tenor have the same level of risk including reinvestment risk. This is the reason why all the cash flows are discounted at the same yield to arrive at the market price. On the other hand zero coupon rates takes into account the differing level of risk associated with the cash flows in the different maturity band i.e. it recognizes that a cash flow in year 1 is not worth the same as an equal flow in year 2 solely because of the time value of money but also because of the relative risk associated with each flow. It is also to be noted that the zero coupon method also automatically accounts for the reinvestment risk by using different discount rates for different maturity bands. Internationally zero coupon rates for different maturities are determined using following variables / quoted interest rates:
n n

Treasury spot rates (quoted yields on securities issued by the government) Interest rate futures

Interest Rate Swap – Work Paper
n

Swap rates (internationally quoted by the investment banks to make the swap markets)

In the context of Pakistan only treasury rates are available i.e. the rates on the treasury bills and PIBs issued by the Government of Pakistan, the yields on the same represents the market sentiments on the interest rates in the economy. So any model for the valuation of derivatives must derive the discount rates using yields on treasury securities. Complexity arises as to how the zero rates should be computed? Zero rates can be computed from the prices of the trading instrument in market i.e. T-bills and PIBs. One approach is known as Bootstrap Method. Bootstrapping is a method for constructing a zero-coupon fixed income yield curve from the prices of a set of coupon bearing products by forward substitution. Following is the general methodology of bootstrapping: Define set of yielding products; these will generally be coupon bearing bonds like PIBs. Derive discount factors for all terms; these are the IRR of the above bonds. The IRR / yield are quoted on the Reuters / Bloomberg. n Bootstrap the zero coupon curve step-by-step.
n n

The following example sets out the calculations of the “zero-coupon” discount factors. Bond Principal 100 100 `100 100 100 Time to Maturity (in years) 0.25 0.5 1 1.5 2 Annual Coupon+ 0 0 0 8 12 Bond Price 97.5 94.9 90 96 101.6 Yield ^ 2.56% 5.37% 11.11% 10.96% 11.09% Annual Yield with Annual Compounding * 10.66% 11.04% 11.11% 11.26% 11.39% Zero Coupon Rate (Continuous Compounding) ** 10.129% 10.471% 10.538% 10.676% 10.791%

+ Coupon rates are paid semi annually. ^ Yield is equivalent to IRR. * Computed by using the effective interest rate formula ((1+2.56%)^4)-1. ** Continuous compounding is computed using the same effective interest rate formula ((1+10.66%)^(1/365)-1)*365. Continuous compounding is achieved where the compounding frequency tends to infinity (usually equal to 365 days). Example of IRS Revaluation The following example sets out the calculations of the estimated market value of a “plain vanilla” interest rate swap under the “bond pricing method” using “zero coupon” discount factors. Swap details Party A (“A”) agreed on 1 January 2007 to transact the following interest rate swap agreement with Party B (“B”): Type “Plain Vanilla” Interest Rate Swap

Interest Rate Swap – Work Paper
Currency Notional Trade date Value date Maturity date A Pays Pay rate Pay frequency A Receives Receive rate Receive frequency PKR Rs. 50 million 1 January 2007 1 January 2007 31 December 2010 Fixed 7% per annum Semi-annual Floating 6 month KIBOR Semi-annual

The valuation below is from the perspective of Party B in which case B is assumed - to receive the fixed rate on the bond issued by the Party A; and - to pay floating rate to Party A on floating rate bond issued.
Date Period to Next Cash flows (Years) [B] = A - 30 June 2007 0.5 1 1.5 2 2.5 3 3.5 3.5 Fixed rate Cash f lows Zero Coupon Rate (%) Discount Factor Present Value

[A] 31-Dec-07 30-Jun-08 31-Dec-08 30-Jun-09 31-Dec-09 30-Jun-10 31-Dec-10 31-Dec-10

[C] = (50,000,000*7%*1/2) 1,750,000 1,750,000 1,750,000 1,750,000 1,750,000 1,750,000 1,750,000 50,000,000

[D]** 10.66 11.04 11.11 11.26 11.39 10.98 10.69 10.04

[E] = 1/(1+H14/100)^B 0.951 0.901 0.854 0.808 0.764 0.732 0.701 0.715 Value of Fixed Leg Value of Floating Leg Value of Swap

[F] = C * E 1,663,576 1,576,009 1,494,199 1,413,709 1,336,357 1,280,277 1,226,475 35,771,979 45,762,580 50,000,000 (4,237,420)

** Zero-coupon rate is derived in the valuation of IRS section heading. The swap has positive fair value of Rs. 4,237,420 to Party A and negative fair value of the same amount to the Party B. Valuation as envisaged in IAS 39 Para AG 82 of IAS 39 envisaged that following variables should be incorporated into the valuation technique:

a) Time value of money: this is best represented by interest at the basic or risk free rate, which
usually is derived from government bond prices (treasury yields). But consideration then needs to be given to the credit risk included in this rate versus the credit risk of the instrument / counterparty being valued.

Interest Rate Swap – Work Paper b) Credit risk: this can be derived from the prices of traded instruments with differing credit
qualities or from interest rates actually charged by lenders for loans of various credit ratings. A swap portfolio exposes a bank to credit risk arising from default by the counterparty over the period of the deal. Practices for providing for this credit risk vary widely. When assessing specific provisions, the credit risk on swaps, as with all off balance sheet transactions, should be included to establish whether any provision is required. In addition to this, some banks raise a “general provision” against possible future losses based upon some measure of credit risk. In certain circumstances a dealer may alter the pricing of an interest rate swap so as to reflect a premium for credit risk. Whilst the adjustment is likely to be much smaller, the concept of the credit risk premiums is analogous to that used when setting interest rates for lending purposes. From the above discussion it is concluded that the revaluation of swaps should be adjusted for credit risk either through adjusting the discount rate (zero rate) or incorporating a general provision in the books against possible future losses.

c) Allowing for market liquidity: the concept of mark to market is predicated on the concept
that the dealer could sell his swap portfolio in the market at current market prices and therefore the most appropriate measure of its value is given by current market rates. While this does not imply a valuation based upon a forced disposal, it is necessary that the market has reasonable liquidity so that positions could be meaningfully closed out. Where markets are not liquid, the appropriateness of using market rates to revalue the swap portfolio should be questioned. Practical solutions are difficult but one alternative where markets are relatively illiquid is to broaden the spreads used. Valuation Model of UBL Interest rates derivatives are valued using IT system known as Principia. Market interest curves are entered into the system which then uses these rates to calculate curves. There are two relevant curves Treasury curve and Swap curve. Treasury curve The treasury curve represents the yields on marketable GOP issued securities (T-bills and PIBs). The PKRV rates published in Reuter’s page are used for valuation. IRS and FRAs uses T-bills or PIBs as a pricing benchmark, the prevailing PKRV rates curves are used to value these transactions. The curve points used will be for all tenors up to 12 months and then for 3 years, 5 years and 10 years points. Once entered into the principia the system will automatically interpolate the interim points. Swap curve The swap curve is used for valuing IRS and FRA transactions where KIBOR is used as a pricing benchmark. KIBOR represents the clean lending rate used for banks in the Pakistan Rupee money market, and this benchmark is now widely used for pricing corporate / commercial market loans.

Interest Rate Swap – Work Paper

KIBOR is a clean lending rate for institutions having a good credit rating, where as PKRV is the market rate on government securities. The securities under PKRV rates are far more liquid then KIBOR based instruments. Furthermore GOP PKR denominated securities is assumed to be risk free and hence the credit characteristics are different. For these two reasons the former is always higher than the latter. For tenor upto 12 months KIBOR rates published in Reuter’s page are used. For tenor more than 12 months PKRV rates of relevant tenors are used and the spread between the PKRV and KIBOR based on the historical data is added. KIBOR Tenor 3 years 5 years 7 years 10 years PKRV Tenor 3 years 5 years 7 years 10 years 1.25 1.25 1.30 1.40 Multiplier^ Historical Spread** 87 87 87 87 bps bps bps bps

3 Year KIBOR (Swap curve) = 3 Year PKRV + (1.25 * 87 bps) ^ The multiplier in the calculation takes into account under-estimation of previous model’s 3 year point calculation relative to average market quotations. ** Historical spread is the spread between KIBOR and PKRV for the last 1 year.

The swap curve for 30 June 2008 using the PKRV rates is derived as follow:
Average Spread of 6-m KIBOR and 6-m PKRV (last one year data) Tenor 3 months (actual) 6 months (actual) 1 year (actual) 3 years 5 years 7 years 10 years Actual PKRV / KIBOR (%) A 13.88 14.19 14.47 12.53 13.00 13.13 13.29 Historical Spread B N/A N/A N/A 0.84 0.84 0.84 0.84 Multiplier C N/A N/A N/A 1 1.1 1.1 1.25 0.84% Swap Rates (%) D = (B * C) + A 13.88 14.19 14.47 13.37 13.92 14.05 14.34

See the attached sheet for the valuation of IRS on excel based valuation model.
D:\Docum ents and Settings\htola\My Docum ents\Irs working.xls

Sponsor Documents

Or use your account on DocShare.tips

Hide

Forgot your password?

Or register your new account on DocShare.tips

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close