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Part 2 – Exotic swap products
• Asset swaps• Total return swaps• Forward swaps • Cancellable swaps and swaptions• Spread-lock interest rate swaps• Constant maturity swaps• Credit default swaps• Equity-linked swaps
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Asset swaps• Combination of a defaultable bond with an interest rate swap.
B pays the notional amount upfront to acquire the asset swap package.1. A fixed coupon bond issued by C with coupon c payable on
coupon dates.2. A fixed-for-floating swap.
A BLIBOR + sA
c
defaultable bond C
The asset swap spread sA is adjusted to ensure that the asset swap package has an initial value equal to the notional.
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• Asset swaps are more liquid than the underlying defaultable bond.
• The Asset Swap may be transacted at the time of the security purchase or added to a bond already
owned by the investor.
• An asset swaption gives B the right to enter an asset swap package at some future date T at a predetermined asset swap spread sA.
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Example 1. An investor believes CAD rates will rise over the medium term. They
would like to purchase CAD 50million 5yr Floating Rate Notes.
2. There are no 5yr FRNs available in the market in sufficient size. The investor is aware of XYZ Ltd 5yr 6.0% annual fixed coupon Bonds currently trading at a yield of 5.0%. The bonds are currently priced at 104.38.
3. The investor can purchase CAD 50million Fixed Rate Bonds in the market for a total consideration of CAD 51,955,000 plus any accrued interest. They can then enter a 5 year Interest Rate Swap (paying fixed) with the Bank as follows:
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Notional: CAD 50,000,000
Investor Pays:
6.0% annual Fixed (the coupons on the bond)
Investor Receives:
LIBOR plus say 50bp
Up front Payment:
The Bank Pays CAD 1,955,000 plus accrued bond interest to investor
The upfront payment compensates the investor for any premium paid for the bonds. Likewise, if the bonds were purchased at a discount, the investor would pay the discount amount to the Bank. This up front payment ensures that the net position created by the Asset Swap is the same as a FRN issued at par so that the initial outlay by the investor is CAD 50million.
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Pricing1. From the investors viewpoint, the net cash flows from the Bond
plus the Asset Swap are the same as the cash flows from a Floating Rate Note.
2. The yield on the Asset Swap (in the example LIBOR plus 50bp), will depend upon the relationship between the Bond yield and the Swap Yield for that currency. When converting a fixed rate bond to floating rate, LOWER swap rates relative to bond yields will result in HIGHER Asset Swap yields. When converting FRNs to fixed rate, HIGHER swap rates relative to bond yields will result in HIGHER Asset Swap yields.
Remark It is a common mistake to assume that the yield over LIBOR on the Asset Swap (50bp in the example above) is merely the difference between the Bond Yield (5%) and the 5yr Swap yield. It is necessary to price the Asset
Swap using a complete Interest Rate Swap pricing model.
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Target Market
Any investor purchasing or holding interest bearing securities. The Asset Swap can either be used to create synthetic securities unavailable in the market, or as an overlay interest rate management technique for existing portfolios. Many investors use Asset Swaps to "arbitrage" the credit markets, as in many instances synthetic FRNs or Bonds produce premium yields compared to traditional securities issued by the same company.
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• Exchange the total economic performance of a specific asset foranother cash flow.
A commercial bank can hedge all credit risk on a loan it has originated.The counterparty can gain access to the loan on an off-balance sheetbasis, without bearing the cost of originating, buying and administeringthe loan.
Total return swap
Total return payer
Total return receiver
LIBOR + Y bp
total return of asset
Total return comprises the sum of interests, fees and anychange-in-value payments with respect to the reference asset.
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The payments received by the total return receiver are:
1. The coupon of the bond (if there were one since the last payment date Ti 1)
2. The price appreciation of the underlying bond
C since the last payment (if there were only).
3. The recovery value of the bond (if there were default).
c
)()( 1ii TCTC
The payments made by the total return receiver are:
1. A regular fee of LIBOR + sTRS
2. The price depreciation of bond C since the last
payment (if there were only).
3. The par value of the bond C if there were a default in the meantime).
)()( 1 ii TCTC
The coupon payments are netted and swap’s termination date is earlier than bond’s maturity.
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Some essential features
1. The receiver is synthetically long the reference asset without having to fund the investment up front. He has almost the same payoff stream as if he had invested in risky bond directly and funded this investment at LIBOR + sTRS.
2. The TRS is marked to market at regular intervals, similar to a futures contract on the risky bond. The reference asset should be liquidly traded to ensure objective market prices for making to market (determined using a dealer poll mechanism).
3. The TRS allows the receiver to leverage his position much higher than he would otherwise be able to (may require collateral). The TRS spread should not be driven by the default risk of the underlying asset but also by the credit quality of the receiver.
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Used as a financing tool
• The receiver wants financing to invest $100 million in the reference bond. It approaches the payer (a financial institution) and agrees to the swap.
• The payer invests $100 million in the bond. The payer retains ownership of the bond for the life of the swap and has much less exposure to the risk of the receiver defaulting.
• The receiver is in the same position as it would have been if it had borrowed money at LIBOR + sTRS to buy the bond. He bears the market risk and default risk of the underlying bond.
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1. Investors can create new assets with a specific maturity not currently available in the market.
2. Investors gain efficient off-balance sheet exposure to a desired asset class to which they otherwise would not have access.
3. Investors may achieve a higher leverage on capital – ideal for hedge funds. Otherwise, direct asset ownership is on on-balance sheet funded investment.
4. Investors can reduce administrative costs via an off-balance sheet purchase.
5. Investors can access entire asset classes by receiving the total return on an index.
Motivation of the receiver
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The payer creates a hedge for both the price risk and default risk of the reference asset.
* A long-term investor, who feels that a reference asset in the portfolio may widen in spread in the short term but will recover later, may enter into a total return swap that is shorter than the maturity of the asset. This structure is flexible and does not require a sale of the asset (thus accommodates a temporary short-term negative view on an asset).
Motivation of the payer
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Forward swaps
Forward swaps are executed now but begin at a preset future date.
They allow asset and liability managers to implement their view of the yield curve. Two examples:
• Corporations may wish to lock into forward rates in the belief that they will be lower than the spot rate at a future date but at the same time may wish to leave their liabilities floating at an attractive lower rate for a period.
• Municipalities have used them to lock in rates for future debt refinancing.
Suppose a corporation wants to enter into a swap beginning one year’s time for a period of 4 years (one-year-by-four-year swap), the swap house will have to enter into two offsetting swaps immediately to hedge its position.
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Swaptions
Product nature
• The buyer of a swaption has the right to enter into an interest rate swap by some specified date. The swaption also specifies the maturity date of the swap.
• The buyer can be the fixed-rate receiver (put swaption) or the fixed-rate payer (call swaption).
• The writer becomes the counterparty to the swap if the buyer exercises.
• The strike rate indicates the fixed rate that will be swapped versus the floating rate.
• The buyer of the swaption either pays the premium upfront or can be structured into the swap rate.
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TARGET MARKET
• Investors with floating rate assets may wish to buy Receiver Swaptions which will convert their assets from floating to fixed when rates fall below the strike.
• This strategy is similar to a Floor. While under a Floor the investor remains floating but with a guaranteed minimum level, here the asset is converted to a fixed rate.
• The option can also be used as a speculative instrument for investors who believe fixed rates will fall.
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Hedge against cash flow uncertainties
Used to hedge a portfolio strategy that uses an interest rate swap but where the cash flow of the underlying asset or liability is uncertain.
Uncertainties come from (i) callability, eg, a callable bond or mortgage loan, (ii) exposure to default risk.
Example
Consider a S & L Association entering into a 4-year swap in which it agrees to pay 9% fixed and receive LIBOR.
• The fixed rate payments come from a portfolio of mortgage pass-through securities with a coupon rate of 9%. One year later, mortgage rates decline, resulting in large prepayments.
• The purchase of a put swaption with a strike rate of 9% would be useful to offset the original swap position.
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Management of callable debtThree years ago, XYZ issued 15-year fixed rate callable debt with a coupon rate of 12%.
Strategy
The issuer sells a two-year receiver option on a 10-year swap, that gives the holder the right, but not the obligation, to receive the fixed rate of 12%.
3 0 2 12originalbond issue
today bondcalldate
bondmaturity
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Call monetizationBy selling the swaption today, the company has committed itself to paying a 12% coupon for the remaining life of the original bond.• The swaption was sold in exchange for an upfront swaption premium received at date 0.
Company XYZ Swap Counterparty
Bondholders
SwaptionPremium
Pay 12%Coupon
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Call-Monetization Cash Flow: Swaption Expiration DateInterest Rates 12%
Company XYZ Swap Counterparty
Bondholders
Pay 12%Coupon
Interest Rates< 12%
Company XYZ Swap Counterparty
New Bondholders
Pay FRNCoupon at LIBOR
12%
LIBOR
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• The fixed rate on a 10-year swap was below 12% in two years but its debt refunding rate in the capital market was above 12% (due to credit deterioration)
• The company would be forced either to enter into a swap that it does not want or liquidate the position at a disadvantage and not be ableto refinance its borrowing profitably.
Disasters for the issuer
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Cancellable Swap
• One of the counterparties has the right to terminate the transaction on a predetermined date at no cost.
• If the client is the payer of the fixed rate and he (counterparty) has the right to cancel the swap, the rate paid will be higher (lower) than that paid under a plain vanilla Swap.
• Usually, it is Bermudan (cancellable on more than one date).
• A pre-agreed fixed cancellation fee can be paid to the client upon termination.
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Use of cancellable swaps
Assume that the following bond is available in the secondary market:Terms of the callable bondIssue Date 1 July 2001
Maturity 1 July 2011 (10 years)
Coupon 7.00% pa annual
Call provisions Callable at the option of the issuer commencing 1 July 2006 (5 years) and annually thereafter on each coupon date.
Initially callable at a price of 101 decreasing by 0.50 each year and thereby callable at par on 1 July 2008 and each coupon date thereafter.
Bond price Issued at par
An investor purchases the bond and enters into the following swap to convert the fixed rate returns from the bond into floating rate payments priced off LIBOR.
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Terms of the cancellable swap
Final Maturity 1 July 2011
Fixed coupon Investor pays 7.00% pa annually (matching the bond coupon).
Floating coupon Investor receives 6 months LIBOR + 48 bps pa
Swap Termination Investor has the right to terminate the swap commencing 1 July 2005 and each anniversary of the swap. On each termination date, the investor pays the following fee to the swap counterparty:
Date Fee (%)
1 July 2006 1.00
1 July 2007 0.50
1 July 2008 to 1 July 2010 0.00
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• The swap combines a conventional interest rate swap (investor pays fixed rate and receives LIBOR) with a receiver swaption purchased by the investor to receive fixed rates (at 7.00% pa) and pay floating (at LIBOR plus 48 bps).
• The swaption is a Bermudan style exercise. The investor can exercise the option on any annual coupon date commencing 1 July 2006 (triggering a 5 year interest rate swap) and 1 July 2010 (triggering a 1 year interest rate swap).
• There are no initial cash flows under this swap. The only initial cash flow is the investment by the investor in the underlying
bonds.
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The investor’s cash flow on each interest payment date will be as follows:
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If the bond is called, then the investor is paid 101% of the face value of the bond by the issuer (assuming call on 1 July 2006). The investor passes 1% to the dealer for the right to trigger the swaption and cancel the original 10 year interest rate swap. This effectively gives the investor back 100% of its initial investment.
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The pricing of the overall transaction incorporate
• Interest rate swap rate.
• Pricing of the swaption purchased by the investor.
The value of the swaption may be embedded in the fixed rate.
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Rationale for doing these transactions
• There is a limited universe of non-callable fixed rate bonds.
• When interest rates decrease below the coupon, the bond is called. The investor is left with an out-of-the-money interest rate swap position (the swap fixed rate is above market rates).
• The swap is expensive to reverse, creating losses for investors. Puttable swaps are structured as a means of mitigating the
potential loss resulting from early redemption of the asset swap.
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Callable debt management• In August 1992 (two years ago), a corporation issued 7-year
bonds with a fixed coupon rate of 10% payable semiannually on Feb 15 and Aug 15 of each year.
• The debt was structured to be callable (at par) offer a 4-year deferment period and was issued at par value of $100
million.
• In August 1994, the bonds are trading in the market at a price of 106, reflecting the general decline in market
interest rates and the corporation’s recent upgrade in its credit quality.
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Question
The corporate treasurer believes that the current interest rate cycle has bottomed. If the bonds were callable today, the firm would realize a considerable savings in annual interest expense. Considerations• The bonds are still in their call protection period.• The treasurer’s fear is that the market rate might rise
considerably prior to the call date in August 1996.
NotationT = 3-year Treasury yield that prevails in August, 1996T + BS = refunding rate of corporation, where BS is the company specific bond credit spreadT + SS = prevailing 3-year swap fixed rate, where SS stands for the swap spread
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Strategy I. Sell a receiver swaption at a strike rate of 9.5% expiring in two years.
Initial cash flow: Receive $2.50 million (in-the-money swaption)
August 1996 decisions:• Gain on refunding (per settlement period):
[10 percent – (T + BS)] if T + BS < 10 percent, 0 if T + BS 10 percent.
• Loss on unwinding the swap (per settlement period):[9.50 percent – (T + SS)] if T + SS < 9.50 percent, 0 if T + SS 9.50 percent .
With BS = 1.00 percent SS = 0.50 percent, these gains and losses in 1996 are:
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Gains
Losses
9%
Loss on selling receiver swaption
T
If SS goes down
If BS goes up
Gain on Refunding
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Gains
Losses
If SS goes downor BS goes up
9%
Net Gain
T
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Comment on the strategy
By selling the receiver swaption, the company has been able to simulate the sale of the embedded call feature of the bond, thus fully monetizing that option. The only remaining uncertainty is the basis risk associated with unanticipated changes in swap and bond spreads.
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Strategy II. Enter an off-market forward swap as the fixed rate payer
Agreeing to pay 9.5% (rather than the at-market rate of 8.55%) for a three-year swap, two years forward.
Initial cash flow: Receive $2.25 million since the the fixed rate is above the at-market rate.
Assume that the corporation’s refunding spread remains at its current 100 bps level and the 3-year swap spread over Treasuries remains at 50 bps, then the annual reduction in interest rate expense after refunding 10% - (T + 1.0) if the firm is able to refund 0 if it is not.The gain (or loss) on unwinding the swap is the fixed rate at that time = [T + 0.5% - 9.5%].The two effects offset each other, given the assumed spreads. The corporation has effectively sold the embedded call option for $2.25m.
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Gains and losses
August 1996 decisions:• Gain on refunding (per settlement period):
[10 percent – (T + BS)] if T + BS < 10 percent, 0 if T + BS 10 percent.
• Gain (or loss) on unwinding the swap (per settlement period): [9.50 percent – (T + SS)] if T + SS < 9.50 percent,[(T + SS) – 9.50 percent] if T + SS 9.50 percent.
Assuming that BS = 1.00 percent, SS = 0.50 percent, these gains and losses in 1996 are:
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Callable Debt Management with a Forward Swap
Gains
Losses
Gain onRefunding
Gain onUnwinding Swap
If BS goes up
If SS goes down
T9%
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Gains
Losses
If SS goes downor BS goes up
9%
Net Gain
T
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Comment on the strategy
Since the company stands to gain in August 1996 if rates rise, it has not fully monetized the embedded call options. This is because a symmetric payoff instrument (a forward swap) is used to hedge an asymmetric payoff (option) problem.
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Spread-lock interest rate swaps
Enables an investor to lock in a swap spread and apply it to
an interest rate swap executed at some point in the future.
• The investor makes an agreement with the bank on
(i) swap spread, (ii) a Treasury rate.
• The sum of the rate and swap spread equals the fixed rate paid by the investor for the life of the swap, which begins at the end of the three month (say) spread-lock.
• The bank pays the investor a floating rate. Say, 3-month LIBOR.
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Example
The current 5yr swap rate is 8% while the 5yr benchmark government bond rate is 7.70%, so the current spread is 30bp an historically low level.
A company is looking to pay fixed using an Interest Rate Swap at some point in the year. The company believes however, that the bond rate will continue to fall over the next 6 months. They have therefore decided not to do anything in the short term and look to pay fixed later.
It is now six months later and as they predicted, rates did fall. The current 5 yr bond rate is now 7.40% so the company asks for a 5 yr swap rate and is surprised to learn that the swap rate is 7.90%. While the bond rate fell 30bp, the swap rate only fell 10bp. Why?
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Explanations• The swap spread is largely determined by demand to pay or
receive fixed rate.
• As more parties wish to pay fixed rate, the "price" increases, and therefore the spread over bond rates increases.
• It would appear that as the bond rate fell, more and more companies elected to pay fixed, driving the swap spread from 30bp to 50bp.
• While the company has saved 10bp, it could have used a Spread-lock to do better.
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• When the swap rate was 8% and the bond yield 7.70%, the company could have asked for a six month Spread-lock on the 5yr Swap spread.
• While the spot spread was 30bp, the 6mth forward Spread was say 35bp.
• The company could "buy" the Spread-lock for six months at 35bp. At the end of the six months, they can then enter a swap at the
then 5yr bond yield plus 35bp, in this example a total of 7.75%. The Spread-lock therefore increases the saving from 10bp to 25bp.
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A Spread-lock allows the Interest Rate Swap user to lock in the forward differential between the Interest Rate Swap rate and the underlying Government Bond Yield (usually of the same or similar tenor).
The Spread-lock is not an option, so the buyer is obliged to enter the swap at the maturity of the Spread-lock.
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CONSTANT MATURITY SWAP
• An Interest Rate Swap where the interest rate on one leg is reset periodically but with reference to a market swap rate rather than LIBOR.
• The other leg of the swap is generally LIBOR but may be a fixed rate or potentially another Constant Maturity Rate.
• Constant Maturity Swaps can either be single currency or Cross Currency Swaps. The prime factor therefore for a Constant Maturity Swap is the shape of the forward implied yield curves.
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EXAMPLE – Investor’s perspective
• The GBP yield curve is currently positively sloped with the current 6mth LIBOR at 5.00% and the 3yr Swap rate at 6.50%, the 5yr swap at 8.00% and the 7yr swap at 8.50%.
• The current differential between the 3yr swap and 6mth LIBOR is therefore +150bp.
• The investor is unsure as to when the expected flattening will occur, but believes that the differential between 3yr swap and LIBOR (now 150bp) will average 50bp over the next 2 years.
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In order to take advantage of this view, the investor can use the Constant Maturity Swap. They can enter the following transaction for 2 years:
Investor Receives: 6 month GBP LIBORInvestor Pays: GBP 3 yr Swap mid rate less 105bp (semi annually)
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• Each six months, if the 3yr Swap rate is less than 105bp, the investor will receive a net positive cashflow, and if the differential is greater than 105bp, pay a net cashflow.
• As the current spread is 150bp, the investor will be required to pay 45bp for the first 6 months. It is clear that if the investor is correct and the differential does average 50bp over the two years, this will result in a net flow of 55bp to the investor.
• The advantage is that the timing of the narrowing within the 2 years is immaterial, as long as the differential averages less than 105bp, the investor "wins".
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Example – Corporate perspective
• A Swedish company has recently embraced the concept of duration and is keen to manage the duration of its debt portfolio.
• In the past, the company has used the Interest Rate Swap market to convert LIBOR based funding into fixed rate and as swap transactions mature has sought to replace them with new 3, 5 and 7yr swaps.
• The debt duration of the company is therefore quite volatile as it continues to shorten until new transactions are booked when it jumps higher.
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Corporate Receives: 6 month SEK LIBORCorporate Pays: SEK 5 yr Swap mid rate less 35bp (semi annually)
The Constant Maturity Swap can be used to alleviate this problem. If the company is seeking to maintain duration at the same level as say a 5 year swap, instead of entering into a 5 yr swap, they can enter the following Constant Maturity swap:
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• The tenor of the swap is not as relevant, and in this case could be for say 5 years. The "duration" of the transaction is almost always at the same level as a 5yr swap and as time goes by, the duration remains the same unlike the traditional swap.
• So here, the duration will remain around 5yrs for the life of the Constant Maturity Swap, regardless of the tenor of the transaction.
• The tenor however, may have a dramatic effect on the pricing of the swap, which is reflected in the premium or discount paid (in this example a discount of 35bp).
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Credit default swapsThe protection seller receives fixed periodic payments from the protection buyer in return for making a single contingent paymentcovering losses on a reference asset following a default.
protectionseller
protectionbuyer
140 bp per annum
Credit event payment(100% recovery rate)
only if credit event occurs
holding arisky bond
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Protection seller• earns investment income with no funding cost• gains customized, synthetic access to the risky bond
Protection buyer• hedges the default risk on the reference asset
1. Very often, the bond tenor is longer than the swap tenor. In thisway, the protection seller does not have exposure to the fullmarket risk of the bond.
2. Basket default swap gain additional yield by selling defaultprotection on several assets.
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A bank lends 10mm to a corporate client at L + 65bps. The bank alsobuys 10mm default protection on the corporate loan for 50bps.
Objective achieved• maintain relationship• reduce credit risk on a new loan
CorporateBorrower Bank Financial
House
Risk Transfer
Interest andPrincipal
Default SwapPremium
If Credit Event:obligation (loan)
Default Swap Settlement following Credit Event of Corporate Borrower
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50bpsannual
premium
Funding cost arbitrage – Credit default swap
A-rated institutionas Protection Seller
AAA-rated institutionas Protection Buyer
Lender to the AAA-rated Institution
LIBOR-15bpsas funding
cost
BBB riskyreference asset
Lender to the A-rated Institution
coupon= LIBOR + 90bps
funding cost ofLIBOR + 50bps
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The combined risk faced by the Protection Buyer:
• default of the BBB-rated bond
• default of the Protection Seller on the contingent payment
The AAA-rated Protection Buyer creates a synthetic AA-asset with a coupon rate of LIBOR + 90bps 50bps = LIBOR + 40bps. This is better than LIBOR + 30bps, which is the coupon rate of a
AA-asset (net gains of 10bps).
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For the A-rated Protection Seller, it gains synthetic access to a BBB-ratedasset with earning of net spread of
50bps [(LIBOR + 90bps) (LIBOR + 50bps)] = 10bps
the A-rated Protection Seller earns 40bps if it owns the BBB asset directly
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In order that the credit arbitrage works, the funding cost of the default protection seller must be higher than that of the default protection buyer.
Example
Suppose the A-rated institution is the Protection buyer, andassume that it has to pay 60bps for the credit default swappremium (higher premium since the AAA-rated institutionhas lower counterparty risk).
The net loss of spread = (60 40) = 20bps.
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Supply and demand drive the priceCredit Default Protection Referencing a 5-year
Brazilian Eurobond (May 1997)
Chase Manhattan Bank 240bpsBroker Market 285bpsJP Morgan 325bps
* It is very difficult to estimate the recovery rate upon default.
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Credit default exchange swaps
Two institutions that lend to different regions or industries candiversify their loan portfolios in a single non-funded transaction hedging the concentration risk on the loan portfolios.
commercialbank A
commercialbank B
loan A loan B
* contingent payments are made only if credit event occurs on areference asset
* periodic payments may be made that reflect the different risksbetween the two reference loans
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Counterparty risk
Before the Fall 1997 crisis, several Korean banks were willing to offercredit default protection on other Korean firms.
US commercialbank
Hyundai(not rated)
Korea exchangebank
LIBOR + 70bp
40 bp
* Political risk, restructuring risk and the risk of possible future warlead to potential high correlation of defaults.
Advice: Go for a European bank to buy the protection.
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Risks inherent in credit derivatives
• counterparty risk – counterparty could renege or default
• legal risk arises from ambiguity regarding the definition of default
• liquidity risk – thin markets (declines when markets become moreactive)
• model risk – probabilities of default are hard to estimate
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Market efficiencies provided by credit derivatives
1.
2.
3.
Absence of the reference asset in the negotiation process - flexibilityin setting terms that meet the needs of both counterparties.
Short sales of credit instruments can be executed with reasonableliquidity - hedging existing exposure or simply profiting from anegative credit view. Short sales would open up a wealth of arbitrage opportunities.
Offer considerable flexibilities in terms of leverage. For example,a hedge fund can both synthetically finance the position of a portfolio of bank loans but avoid the administrative costs of directownership of the asset.
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Contract Date: June 13, 2003
Effective Date: June 18, 2003
Termination Date: The earlier of (1) June 19, 2006 and (2) the Settlement Date relating to the Observation Date on which the Trigger Event takes place (maturity uncertainty).
Auto-Cancellable Equity Linked Swap
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Trigger Event: The Trigger Event is deemed to be occurred when the closing price of the Underlying Stock is at or above the Trigger Price on an Observation Date.
Observation Dates: 1. Jun 16, 2004, 2. Jun 16, 2005, 3. Jun 15, 2006
Settlement Dates: With respect to an Observation Date, the 2nd business day after such Observation Date.
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Underlying Stock: HSBC (0005.HK)Notional: HKD 83,000,000.00Trigger Price: HK$95.25
Party A pays: For Calculation Period 1 – 4: 3-month HIBOR + 0.13%,For Calculation Period 5 – 12: 3-month HIBOR - 0.17%
Party B pays: On Termination Date, 8% if the Trigger Event occurred on Jun 16, 2004;16% if the Trigger Event occurred on Jun 16, 2005;24% if the Trigger Event occurred on Jun 15, 2006; or24% if the Trigger Event occurred on Jun 15, 2006; or0% if the Trigger Event never occurs.
Final Exchange: Applicable only if the Trigger Event has never occurredParty A pays: Notional AmountParty B delivers: 1,080,528 shares of the Underlying Stock
Interest Period Reset Date: 18th of Mar, Jun, Sep, Dec of each year
Party B pays Party A an upfront fee of HKD1,369,500.00 (i.e. 1.65% on Notional) on Jun 18, 2003.
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Model Formulation
• This swap may be visualized as an auto knock-out equity forward with terminal payoff
1,080,528 x terminal stock price - Notional.
• Modeling of the equity risk: The stock price follows the trinomial random walk. The “clock” of the stock price trinomial tree is based on trading days. When we compute the drift rate of stock and “equity” discount factor, “one year” is taken as the number of trading days in a year.
• The net interest payment upon early termination is considered as knock-out rebate. The contribution of the potential rebate to the swap value is
given by the Net Interest Payment times the probability of knock-out.
• The Expected Net Interest Payment is calculated based on today’s yield curve. Linear interpolation on today’s yield curve is used to find the HIBOR at any specific date. The dynamics of interest rate movement has been neglected for simplicity since only Expected Net Interest Payment (without cap or floor feature) appears as rebate payment.
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Quanto version
Underlying Stock: HSBC (0005.HK)Notional: USD 10,000,000.00Trigger Price: HK$95.25
Party A pays: For Calculation Period 1 – 4: 3-month LIBORFor Calculation Period 5 – 12: 3-month LIBOR - 0.23%,
Party B pays: On Termination Date, 7% if the Trigger Event occurred on Jun 16, 2004;14% if the Trigger Event occurred on Jun 16, 2005;21% if the Trigger Event occurred on Jun 15, 2006; or0% if the Trigger Event never occurs.
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Final Exchange: Applicable only if the Trigger Event has never occurredParty A pays: Notional AmountParty B delivers: Number of Shares of the Underlying Stock
Number of Shares: Notional x USD-HKD Spot Exchange Rate on Valuation Date / Trigger Price
Interest Period Reset Date: 18th of Mar, Jun, Sep, Dec of each year
Party B pays Party A an upfront fee of USD150,000.00 (i.e. 1.5% on Notional) on Jun 18, 2003.
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Model Formulation
• By the standard quanto prewashing technique, the drift rate of the HSBC stock in US currency = rHK qS S F ,
where rHK = riskfree interest rate of HKD
qS = dividend yield of stock = correlation coefficient between stock price and exchange rate
S = annualized volatility of stock price
F = annualized volatility of exchange rate • Terminal payoff (in US dollars)
= Notional / Trigger Price (HKD) x terminal stock price (HKD) - Notional.
• The exchange rate F does not enter into the model since the payoff in US dollars does not contain the exchange rate. The volatility of F appears only in the quanto-prewashing formula.
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Worst of two stocks
Contract Date: June 13, 2003Effective Date: June 18, 2003
Underlying Stock: The Potential Share with the lowest Price Ratio with respect to each of the Observation Dates.
Price Ratio: In respect of a Potential Share, the Final Share Price divided by its Initial Share Price.
Final Share Price: Closing Price of the Potential Share on the Observation Date
Party A pays: For Calculation Period 1 – 4: 3-month HIBOR + 0.13%, For Calculation Period 5 – 12: 3-month HIBOR - 0.17%,
Initial Trigger Number
Potenital Share Share Price Price of SharesHSBC (0005.HK) 95.25 95.25 1,080,528HK Electric (0006.HK) 29.00 29.00 3,549,193
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Party B pays: On Termination Date, 10% if the Trigger Event occurred on Jun 16, 2004;20% if the Trigger Event occurred on Jun 16, 2005;30% if the Trigger Event occurred on Jun 15, 2006; or0% if the Trigger Event never occurs.
Final Exchange: Applicable only if the Trigger Event has never occurredParty A pays: Notional AmountParty B delivers: Number of Shares of the Underlying Stock as shown above
Interest Period Reset Date: 18th of Mar, Jun, Sep, Dec of each year
Party B pays Party A an upfront fee of HKD1,369,500.00 (i.e. 1.65% on Notional) on Jun 18, 2003.
