DAILY CALL OPTION
Common in the natural gas markets, this option allows the buyer to take additional volumes of gas with a single day’s notice.
DEBT service fund
Debt service funds are usually required to be deposited with a trustee or in another segregated manner on a monthly basis to meet semi-annual debt service interest payments (1/6 per month) and annual principal payments (1/12 per month). Traditional investment techniques result in these monies being invested short-term and earning short-term rates of interest.
As an alternative, a debt service fund forward purchase agreement offers an issuer a higher rate of return on invested monies, along with the option of receiving an up-front payment equaling the present value of that future stream of income.
These agreements can be structured on either a delivery versus payment (DVP) or swap basis. On a DVP basis, the counterparty will deliver to the issuer or issuer’s trustee a U.S. Treasury security maturing prior to the semi-annual debt service payment date with a face value equaling the debt service amount deposited with the counterparty. On a swap basis, the issuer transmits the actual semi-annual earnings on U.S. Treasury Bill investments (variable) in exchange for the guaranteed rate (fixed). On this basis, the counterparty can deliver an upfront payment of a fixed yield over time.
Collateral on the agreements can range from treasury securities to agency securities to commercial paper to uncollateralized. The collateral requirement corresponds directly with the yield.
In the event the issue is refunded, a breakage fee may be incurred requiring a payment to the counterparty, thereby reducing the earlier received cash payment. For instance, if an issuer were to enter into an agreement and receive an up-front payment of the cash flow for thirty years, the issuer is contracting to deliver a 20-year stream of monthly cash payments. If the issuer later chooses to call the bonds after seven years, the issuer will be subject to a breakage fee because the issuer will be unable to deliver this stream of cash. To avoid this the issuer can limit the agreement to the first call date rather than out to the final maturity of the issue.
DEBT service reserve fund
The Debt Service Reserve Fund (“DSRF”) has traditionally been invested in a long term treasury security combined with a simultaneous purchase of a par put option to insure liquidity and par value of the treasury. The problem with purchasing the treasury put is that it can be expensive (up to 100 bps), reducing the overall yield of the DSRF. Furthermore, once purchased, a treasury put is relatively illiquid with little resale value. Sometimes, the long term treasury is bought “naked,” that is, without the put option, which eminently sets up the issuer for a probable underfunded DSRF sometime in the future.
The DSRF Forward Purchase Agreement (“FPA”) provides essentially the same long term rate as long term treasuries, while eliminating the need for a treasury put option. The DSRF FPA works as follows: A FPA provider would initially deliver a 90 day T-Bill to the trustee. When that T-bill matured the FPA provider would deliver a new 90 day T-Bill in exchange for the cash resulting from the previous maturing T-Bill. This cycle would continue for the term of the agreement. The yield for this type of instrument is fixed for the term of the agreement. The agreement is extremely safe, as the issuer always has either cash or a T-Bill in the trustee possession, and will be approved by most bond counsel.
If allowed by the indenture, the interest to be earned for the term of the FPA can be taken over time or taken up front as a lump sum payment. An issuer can partially fund the DSRF by taking earnings up-front which reduces the overall bond issuance amount. The up-front payment can represent 25-50% of the total DSRF requirement. Similarly, if an issuer had bought a long term treasury in a lower interest rate environment to fund a DSRF which is now underfunded, a partial up-front payment from an FPA can bring the DSRF back to par, eliminating the need to look to other sources of monies to fill the requirement. The remaining interest can then be taken over time or be taken up-front to release locked DSRF funds for other uses.
DEBT WARRANT
A warrant that allows the holder to buy a given bond at a fixed price for a given period.
DEBT-EQUITY SWAP
This is not a swap in the usual sense. It is a one-off transaction of physical instruments without any exchange of future cashflows. It involves substituting equity for debt, either bonds or loans, usually when the debt becomes unserviceable. They are used by heavily indebted companies and countries.
DEFAULT PUT
See
credit default swap
DEFAULT RISK
See
credit risk
DEFAULT SWAP
See
credit default swap
DEFERRED PAY-OUT OPTION
A deferred pay-out option is a variation on American-style options similar to a shout option. The holder of the option may exercise it at any time, for the value taken by the underlying at that time, but the pay-out is delayed until the expiry date. This term is also applied to certain digital options whose pay-out is not paid when triggered, but deferred until the final maturity.
See also
option styles
DEFERRED PREMIUM OPTION
See
pay-later option
DEFERRED START OPTION
See
forward start option
DEFERRED SWAP
A swap in which the payments are deferred for a specified period, usually for tax or accounting reasons. Unlike a forward swap, where the entire swap is delayed, in a deferred swap only the payments are deferred. For example, a company wanting to enter a swap, but not wanting cashflows until a future period, might want to defer payment.
DELAYED RESET SWAP
Also known as an in-arrears swap. A swap in which floating payment is based on the future, rather than present, value of the reference rate. For six-month delayed Libor reset swaps, for example, instead of fixing Libor six months and two days before the payment date, the floating-rate borrower delays fixing until two days before payment. Such swaps are popular in a steep yield curve environment, when a fixed-rate receiver may think rates will not rise as fast as the yield curve predicts.
DELEVERAGED FLOATING-RATE NOTE
An instrument developed in the US on the back of a positive yield curve to increase the yield of floating-rate assets by indexing them to higher-yielding long-term fixed-rate bonds. The underlyings are normally constant maturity Treasuries. The rates are called deleveraged FRNs because the investor receives a portion (usually 50%) of the reference rate of those securities plus a fixed spread (which increases the longer the FRNs maturity).
DELTA
The delta of an option describes its premium’s sensitivity to changes in the price of the underlying. In other words, an option’s delta will be the amount of the underlying necessary to hedge changes in the option price for small movements in the underlying. The delta of an option changes with changes in the price of the underlying. An at-the-money option will have a delta of close to 50%. It falls for out-of-the-money options and increases for in-the-money options, but the change is non-linear: it changes much faster when the option is close-to-the-money. The rate of change of delta is an option’s gamma.
DELTA-HEDGING
An option is said to be delta-hedged if a position has been taken in the underlying in proportion to its delta. For example, if one is short a call option on an underlying with a face value of $1 million and a delta of 25%, a long position of $250,000 in the underlying will leave one delta-neutral with no exposure to small changes in the price of the underlying. Such a hedge is only effective instantaneously, however. Since the delta of an option is itself altered by changes in the price of the underlying, interest rates, the option’s volatility and its time to expiry, changes in any of these factors will shift the net position away from delta-neutrality. In practice, therefore, a delta-hedge must be rebalanced continuously if it is to be effective.
DERIVATIVE
A derivative instrument or product is one whose value changes with changes in one or more underlying market variables, such as equity or commodity prices, interest rates or foreign exchange rates. Basic derivatives include, forwards, futures, swaps, options, warrants and convertible bonds. In mathematical models of financial markets, derivatives are known as contingent claims.
DETERMINISTIC VOLATILITY
The family of options pricing models (including those of Dupire, Derman, Kani and Zou) that seek to incorporate the volatility skew and assume that the local volatility of the underlying stock is a deterministic function of time and the stock price itself.
DIFFERENCE OPTION
See
spread option
DIFFERENTIAL SWAP
A quanto product, typically involving the combination of a simple interest rate swap in the denominating currency, and a quantized swap denominated in the same currency but referenced to a different currency. For example, a counterparty receives euro six-month Libor, denominated in euros, and pays US dollar six-month Libor, denominated in euros plus a spread approximately equal to the difference between the fixed rates of the simple swap and the quantized swap as quoted on the same basis, e.g., semi-annual 360.
DIFFUSION PROCESS
A continuous-time model of the behavior of a random variable. An example of such a model is Generalized Brownian Motion (GBM) which is often used to model the behavior of spot rates.
DIGITAL OPTIONS
See
binary option
DIGITAL SWAP
A swap in which the fixed leg is only paid on each swap settlement date if the underlying has met certain trigger conditions over the period since the previous payment date. Nothing is paid if this is not the case. The premium for such a swap is amortized over the maturity of the swap and an installment paid at each payment date.
See also
binary option
DISCOUNT SWAP
An off-market swap in which the fixed payments are below the market rate. At the end of the swap the shortfall is made up by one payment. Construct-ion and project finance companies use this type of structure to reduce interest rate payments before start-up and during completion of a project. The more interest rate payments are discounted, the more credit risk is taken by the counterparty.
DISCRETE BARRIER OPTION
Barrier options where the trigger level is only active for part of the option’s lifetime. This includes barrier options where the trigger is only valid on certain fixing dates, as well as cases where the trigger is valid for sub-intervals of the option’s lifetime.
See also
barrier option
DISTRIBUTION
The probability distribution of a variable describes the probability of the variable attaining a certain value. Assumptions about the distribution of the underlying are crucial to option models because the distribution determines how likely it is that the option will be exercised. Many models assume the logarithm of the relative return has a normal distribution, which can be described by two parameters.
The first is the distribution’s mean; the second its standard deviation (equivalent, if annualized, to volatility). In practice, most empirically observed asset distributions depart from normality. This departure can be described in terms of the skew (how much it tilts to one side or the other) and kurtosis, which describes how fat or thin are the tails at either side. Most markets tend to have fat tails (to be leptokurtic) rather than thin tails (platykurtic). This pushes up the price of out-of-the-money options.
DOUBLE TOPS/ DOUBLE BOTTOMS
A double top formation is a chart pattern of commodity or financial asset price movements that reflects a rising market which hits resistance at a certain level. The market rises, retreats, rises again, but still cannot breach the previous resistance point, and falls back again. These price patterns are used by technical analysts to recognize the reversal of a price trend. The inverse of this would be a double bottom, which reflects a support level that has been established and serves as support under a falling market.
DOUBLE TRIGGER FORWARD
See
trigger forward
DOwngrade termination
Provision in some swap agreements allowing one party to terminate the swap at its market value if the other party’s long-term, unsecured debt rating falls below a given level.
DROP-LOCK SWAP
A swap in which, if the rate on the index initially used to set the fixed-rate payments differs from that prevailing at the outset of the swap by a specified amount and for a specified amount of time, the fixed rate is reset.
Dsf
See
debt service fund
Dsrf
See
debt service reserve fund
DUAL CURRENCY SWAP
Dual currency swaps are currency swaps that incorporate the foreign exchange options necessary to hedge the interest payments back into the principal currency for dual currency bonds.
DUAL-STRIKE OPTION
See
multiple-strike option
DURATION
Duration is the average life of the present values of all future cashflows from a bond. For a given maturity, the higher the coupon, the more it (rather than the redemption payment) contributes to yield. So the higher the coupon, the shorter the duration. Although the duration of a bond increases monotonically as the maturity increases, it is non-linear (except for zero-coupon bonds), because the coupon payments are increasingly important to the yield. Duration usually refers to what technically should be described as modified duration. This measures the effect on a bond’s price of a unit change in yield. So if a bond has a duration of two, a yield change of 1% will produce a price change of 2% in the other direction. The higher the modified duration, the more sensitive the bond is to interest rate changes.
See also
convexity
DYNAMIC CREDIT SWAP
A credit swap with a dynamic notional that for a fixed fee provides the protection buyer with a contingent payment that matches the mark-to-market on any given day of a specified derivative (or other market-sensitive instrument). Also known as a credit intermediation swap. Also known as a credit intermediation swap.
DYNAMIC HEDGING
See
delta-hedging
DYNAMIC REPLICATION
To replicate the pay-out of an option by buying or selling the underlying (or for some markets, because of cheaper transaction costs, futures) in proportion to an option’s delta. If replicating a short call position, the replicator would, as the underlying went up, buy increasing amounts in proportion to the theoretical option’s delta, and likewise decrease the hedge amount as the market falls. Dynamic replicators are at risk from increases in volatility, as this makes it more difficult for the necessary hedge amounts to be transacted at the desired rate.
See also
static replication