atility hedging and recognize that part of the Vega is hedged by theDelta, which we shall term as Vega P&L due to Delta and quantify lateron (which is good in reducing the Vega hedging cost).CEV (Constant Elasticity of Variance) and shifted lognormal modelscan model this volatility skew dynamics by making the volatilities asdeterministic functions of the underlying variables. However, this requires hedging calibration, an additional calibration for adjusting or calibrating certain model parameters (such as the CEV power) so that themodel can produce market consistent hedging ratios or hedge dynamics,which, in turn, can be inferred from, e.g., historical data. This is in contrast with the PV or price calibration of the primary and secondary modelcalibrations (that calibrate other model parameters).Sometimes, the hedging calibration produces direct adjustments tothe hedge ratios, rather than adjustment to the model parameters due tothe parsimonious nature of the hedging model (needed for producingnumerically stable hedges).In general, CEV and shifted lognormal models cannot handle thevolatility smile dynamics, which requires a stochastic volatility model,which indeed can produce market consistent volatility smile that the localvolatility model cannot produce. It is interesting to mention in passingthat while the stochastic volatility diffusion models can handle the volatility smile in general, they tend to have difficulties in handling the volatility smiles in short time horizon (or short option expiry). The typicaldifficulties include: the volatility of volatility being too high and the fitting of the volatility smiles being not accurate enough or being not stable.Intuitively speaking, this is due to that the market implies the existence of jumps in the short time horizon, but a diffusion stochastic volatility process does not have enough time to diffuse far from its initialvalue without extraordinarily high volatility (or high volatility of volatility in this case), A jump process does not have this limitation and canproduce high equivalent volatility of volatility or fatter tail distributions.So, we can combine a diffusion and a jump process together to form ajump-diffusion process to model the volatility smile dynamics at bothshort and longer time horizons.It is also interesting to mention that the limitation of a diffusionprocess in short time horizon also occurs in other areas, such as in the
Sec. 2.2
Subtleties in Arbitrage Pricing in Real Market
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modeling of a default process with Merton’s firm value model (Merton,1974) where the firm value follows a diffusion process and the defaultoccurs when the firm’s asset is less than its liability (the knock-out ordefault barrier). A practical issue is that the short term credit spread produced by this model with a constant default barrier is much smaller thanwhat is observed in the market. This is due to the same reason that, in ashort time horizon, a diffusion process does not have enough time to diffuse far from its initial value. In other words, the short term distance todefault is too large. A promising way to overcome this issue is to introduce a random default barrier in Merton’s firm value model to allowjump to default (see, e.g., Finkelstein, Lardy, et al, 2002).Similar to the case of CEV and shifted lognormal models, in a stochastic volatility model, some of the model parameters are used for PVor price calibrations and some for the hedging calibration. A stochasticvolatility model can also be used to produce hedge ratio adjustments toother models.Another significant driving factor for the pricing model and thehedging model being different is the existence of un-hedgeable variables.While it is necessary to use the secondary model calibration in the pricing model, the secondary model calibration should not be used in thehedging model in general. The role of the secondary model calibration isoften to produce a conservative price in order for a dealer to buy a derivatives instrument at a low price or sell it at high price. If the dealerbuys a derivatives instrument at a low price, he or she normally shouldnot hedge with the pricing model that produces this low price, as this isthe same as locking in this low price. Rather, the dealer should hedgewith a hedging model that produces a higher price, which is equivalent asselling the hedge or replication portfolio at a higher price. In otherwords, in order to capture appropriate bidask spread, a dealer needs tobwy/price low, but hedge high, or sell/price high, but hedge low.In order to achieve the global consistency for portfolio-based hedging for a well diversified portfolio, a dealer can chose a hedging modelthat produces the mid market prices.As we mentioned earlier, the counterparty credit risk can have significant effects on both pricing and hedging, as well as early exerciseboundaries and decisions.In general, if a pricing model cannot produce market consistenthedging dynamics, it does not necessarily mean that the model is wrong.Rather, it means that one needs to use hedging corrections or a different
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model for hedging. There are various examples for this situation. Anextreme example is the Black-Scholes model and the Black model,which are the mostly widely used pricing models, but cannot be used forhedging in general due to the volatility skews and smiles. For this reason, the Black-Scholes model and the Black model are often consideredprice quoting tools.If the pricing model and the hedging model indeed produce differentprices, then this inconsistency may be a potential source of leakingmoney. So, the P&L produced by these models should not be consideredas filly realized immediately, rather part of the P&L needs to be put intoa model reserve to be releases gradually over time. Nonetheless, in general, it is still better than using the wrong hedge ratios.
2.2.7
Incomplete Market and Completing the Market
The major reason for the market being incomplete for complex derivatives instruments is the existence of un-hedgeable variables, which a derivatives instrument depends on, but no other liquid traded instruments orassets depend on or cannot be fully determined by the prices of liquidtraded instruments, as we discussed previously.In general, non-traded variables can potentially be un-hedgeable andthus can potentially make the market incomplete.It is important to point out that non-traded variables are not automatically un-hedgeable. For instance, while the interest rate is not atraded asset per se, there are large amount of other liquid assets, such asfutures, swaps, and bonds that can be used to determine the interest rateand thus to hedge and replicate other interest rate derivatives.It is important to point out that traded assets do not necessarily helpthe market become complete. For instance, while electricity is a tradedasset, it cannot be stored with low cost. Thus, some SFTS that requiresbuying and holding the underlying asset (also termed as the cash andcarry strategy) cannot be practically applied in this case.In general, non-traded variables can be made tradable by using htures. For instance, weather variables, such as temperature, are not naturally tradable. But futures in temperature, such as heating degree days(HDD) or cooling degree days (CDD) at various locations, have been
Sec. 2.3
Arbitrage Models and Non-arbitrage Models
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trading at CME (Chicago Mercantile E~change).~‘Other non-traded variables include some of the emerging market currencies which can be indirectly traded with NDF (non-deliverable forward) and NDO (non-deliverable option) whereby the contracts are cashsettled in traded currencies.In general, establishing liquid futures markets or exchange tradedfunds (ETF) on, e.g., the non-traded variables or assets that cannot beeasily replicated or stored, is a possibility to complete any market. This,of course, depends on, among other factors, whether or not there arestrong demands for such fhtures markets in the general capital marketand among various market participants, such as hedgers (e.g., bond issuers, such as government agencies, corporations, and local governments,as well as some funds), speculators (e.g., various funds and proprietarytrading desks in investment banks), arbitrageurs (e.g., some funds andmarket making desks in investment banks), and other investors. It is alsoimportant for such demands to be two-way with balanced supply anddemand, or, roughly speaking, when the situation that “one man’s trash isanother man’s treasure” applies.Another interesting way of completing the market is through a paramutuel process, which, under certain conditions, can have a unique equilibrium price based on the supply and demand. Due to the existence oflimit orders, this is an interesting and challenging combinatorial problem.This has been applied to the trading of various economic indicators andmortgage prepayment rates (that are otherwise non-tradable). For moreinformation, the reader can refer to Lange and Economides (2001) andhttp://www.longitude.com. An example of dealers for these trades canbe found at: http://www2.goldmansachs.com/econderivs/index.html.
2.3
Arbitrage Models and Non-arbitrage Models
2.3.1
Arbitrage Models and Non-arbitrage Models
Aside from the arbitrage pricing models that we have discussed and shalldiscuss further, there are also non-arbitrage models that are not based onarbitrage arguments. For our purposes, these are mainly forecastingmodels based on econometrics or technical financial analysis (includingPlease refer to http://www.cme.com/edu/comwea/tradingwea/index.htmlfor more details. Please also refer to http://www.wrma.org of the Weather Risk Management Association (or WRMA).
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statistical analysis of historical data) and fundamental financial analysis,and equilibrium models (e.g., based on the equilibrium of the supply anddemand).These different categories of models serve different objectives orutility functions of different financial market participants.The objective of the forecasting models is to forecast what will happen in the market in the future under the real world probability measure(or the statistical measure), or, more realistically, to forecast the distributional or statistical properties (such as mean and variance) of certainmarket variables.For instance, there are models for forecasting stock prices, interestrates, foreign exchange (FX) rates, mortgage prepayment rates, variousvolatilities, and various economic indicators. There are also models thatcan identify rich and cheap assets or market sectors.These models help the investors (such as various funds) identify investment opportunities, including speculation and relative value opportunities. In an investment bank, these models are developed by researchgroups that are different from the derivatives modeling groups who develop the arbitrage models.The (explicit or implicit) equilibrium models for our purpose aremodels mainly for determining the current spot prices, based on the equilibrium of supply and demand or the market consensus. These (explicitor implicit) equilibrium models are used by the Futures Exchanges andbrokers in determining the prices and order matching.The most liquid underlying instruments, such as the most liquid futures, swaps, Treasury bonds, stocks, spot FX trades, that, by definition,cannot be replicated by more liquid instruments are normally priced bythe equilibrium models (explicitly or implicitly).The paramutuel process that we discussed earlier is also an exampleof such equilibrium models, which has been applied to the trading ofvarious economic indicators and mortgage prepayment rates (that areotherwise non-tradable). For more information, the reader can refer toLange and Economides (200 1) and http://www.longitude.com.The goal of the arbitrage models is, as we discussed before, to price(and hedge) derivatives instruments through (static or dynamic) replication using their more liquid underlying instruments or to price derivativesinstruments relative to the underlying instruments. Thus, arbitrage pricing is also referred to as relative pricing. These models do not focus onpredicting what will happen in the future under the real world probability
Sec. 2.3
Arbitrage Models and Non-arbitrage Models
63
measure (or the statistical measure); rather they focus on the arbitragerelationship (through hedging and replication) between derivatives instruments and their underlying instruments. To a certain extent, the arbitrage models predict what will happen under the arbitrage-free probability measures.The arbitrage models are mainly used by dealers or dealers for themarket making process in derivatives instruments, but can also be usedby investors to identify relative value opportunities.It is important to point out that while derivatives pricing mainly relies on the arbitrage models, the forecasting models often come into thepicture.For instance, for the un-hedgeable variables, the arbitrage modelsindeed predict or imply their future values under the real world probability measure (or the statistical measure). Thus, for the un-hedgeable variables, the arbitrage models behave similarly to the forecasting modelsand the equilibrium models.In addition, the forecasting models are also needed in hedging costpricing, hedging scenario analysis, and risk analysis, such as VAR(Value at Risk) and credit PE (Potential Exposures). More specifically,the future market scenarios are generated by the forecasting models (orunder the real world probability measure) and the scenario pricing (orderivatives pricing at each market scenario) is performed by the arbitragemodels (or under the arbitrage probability measure). This is particularlyimportant for analyzing and reducing the hedging cost associated withGamma, cross Gamma, Delta due to Vega, etc.There is also a related category of models - the statistical arbitrage(stat arb) models whereby one identifies violations of equilibriums basedon statistics and bet on the mean reversion to the equilibrium. Thesemodels are typically used in program trading.In the first part of the book, we shall focus on the arbitrage pricingmodels and, in the second part of the book, we shall discuss more on thestat arb models.
2.3.2
Financial Market Participants and Financial Activities
The financial industry or “Wall Street” is divided into two sides, the buyside and the sell side.The buy side includes various asset management firms managingvarious funds, such as mutual fund, pension fund, hedge fund, endowment fund, and asset management divisions in insurance companies and
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banks, as well as other investors. The sell side includes dealers or dealers in investment banks and brokerage firms. The buy side is the supplier of capital and typically buys various financial instruments from thesell side for the purpose of achieving capital appreciation. Its financialactivities are often speculative in nature. The sell side, on the other hand,tries to be market neutral (through arbitraging or hedging and replication)and earn the bidask spread, except for the un-hedgeable variables.The main driving factors of the financial activities include capitaldemand and supply, and risk mitigation.In a financial market, some market participants, such as central governments, government agencies, corporations, local governments, andfinancial institutions, need capital to fund their business or projects.Some market participants, such as the buy side, have capital and hope toinvest the capital to achieve capital appreciation.Those who need the capital can get loans or issue (with the help ofthe sell side) various securities, such as debt instruments (e.g., simplebonds, commercial papers, and structured notes), stocks, and convertiblebondsS5*Those who have the capital can invest in various securities andnon-securitized financial instruments (such as OTC derivatives).The OTC derivatives have an advantage of allowing unfunded transactions whereby an investor needs to pay very little (as compared to par)at the beginning of the transaction. This allows significant leveragingthat is a critical measure of boosting the percentage return of the investment.Bridging the capital demand and supply is a major source of businessfor the investment banking division of an investment bank through public
’*
A convertible bond is a bond with an embedded equity call option (and a bond calloption) to convert the bond to a pre-specified number of shares of the underlying stock,which is a hybrid instrument involving equity, credit, and IR. The motivation of the issuer of a convertible bond is to lower the funding cost by selling the equity option (orvolatility). The motivation of the buyer of a convertible bond is typically to buy (andstrip off) cheap equity volatility (e.g., by shorting the underlying stock), which is alsotermed as convertible arbitrage. A convertible bond is typically callable so that the issuer can force a conversion. The recent significant decline of equity volatilities has reduced the issuance amount of convertible bonds. The accounting treatment of EPS (eamings per share) with regard to convertible bonds assuming the bonds are fully convertedalso negatively impacts the issuance amount. A convertible bond has a lower seniority inthe capital structure than a corresponding senior unsecured bond and, thus, will havelower recovery upon default. A stock will have (almost) zero recovery upon default. AnIR swap on a senior unsecured bond, on the other hand, has the same seniority as thebond itself.
Sec. 2.3
Arbitrage Models and Non-arbitrage Models
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offerings of securities (after lengthy underwriting and marketing processes).Private equity/debt investment/placement without going throughpublic offering is another approach to bridge the capital demand andsupply. This includes various funds (including venture capitalists) investing in private companies. This can help the funds acquire assets at adiscount price and, thus, enhance the return. Sometimes, this can entailsignificant risks, especially in the case of venture capital investing. Theinvestment banks can also be the principal investors in this case.Another major source of business for the investment banking division of an investment bank is advising merger and acquisition (M&A).The risk mitigation is the essence of asset management and liabilitymanagement, which includes enhancing the return on asset, hedgingagainst the (uncertain) depreciation of asset, and hedging against the (uncertain) appreciation of liability. This is a major source of business forthe derivatives trading division of an investment bank. Some marketparticipants (hedgers) would like to pay to hedge away (or sell) the risks.Some market participants (speculators), such as the buy side and otherinvestors, would like to take (or buy) the risks and get paid.These can be achieved through unfunded derivatives transactions by,e.g., using a futures or swap contract. The unfunded derivatives transactions can be very risky in that it can create over-leveraging for the investor. Since some of the investors are not allowed to enter OTC derivativestransactions, often times, the derivatives transactions are structured asfunded transactions or embedded in structured notes.The popular yield enhancement measures, which we shall discussmore in the next section, are essentially to allow investors to get paidmore by taking more risks (with the investors hoping that the potentialrisks will not be realized). Asset management divisions of an investmentbank are also market participants in this area.Hedgers can be a variety of financial and non-financial entities. Forexample, debt issuers need to hedge their debt outstanding. Some entities, such as insurance companies, commercial banks, and pension funds,which typically have huge assets (or receivables) and huge liabilities (orpayables), need to also hedge against the (uncertain) asset and liabilitymismatch. Importers (or exporters) typically have long positions in domestic (or foreign) currency and long positions in foreign (or domestic)currency, and, thus, need to hedge against the depreciation (or appreciation) of the domestic currency.
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Yet some other market participants, i.e., the arbitrageurs, would liketo take no (or little) risk, but still make a profit. To a certain extent, brokers and dealers are arbitrageurs. However, in general, dealers do take orhouse significant risks, especially, on the un-hedgeable variables.Typically, a market participant is a combination of a speculator, ahedger, and, possibly, an arbitrageur.In an interest rate market, important activities include the debt issuance of the central government, government agencies, local governments, financial firms, and corporations, as well as mortgage related activities.
2.4
Trading Opportunities and Strategies
Derivatives trading opportunities are largely driven by the risk mitigation(including, e.g., hedging, yieldcoupon enhancement, funding cheapening, and leveraging) in asset management and liability management, andare often motivated by the differences in the views in arbitrage modelsand forecasting models. Conceptually, these opportunities essentially aretrading activities between the arbitrage-free probability measure and thereal world probability measure. Some are driven by various arbitrageand quasi-arbitrage strategies, including stat arb and funding cost arbitrage.Here we provide some simple examples of various trading opportunities and strategies.The arbitrage and forecasting models can imply very different views,or, equivalently, the real world probability measure (or the statisticalprobability measure) and the no-arbitrage probability measure are verydifferent.For instance, roughly speaking, for pricing linear or volatilityinsensitive instruments, the arbitrage pricing models imply that a spotquantity (such as a spot LIBOR rate or a spot FX rate, or a spot stockprice) will follow the corresponding forward curve or quantities (such asthe forward LIBOR rate, the forward FX rate, or the forward stockprice). This is the result of arbitrage replication. In other words, theforward curves are assumed to be realized and become the spot quantitiesin the future (under the no-arbitrage measure). The forecasting modelsand historical analysis often show the contrary, i.e., the forward curvesare normally not realized (under the real world measure) and the spotquantities tend to have random distributions around their current levels.
Sec. 2.4
Trading Opportunities and Strategies
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More specifically, in an upward sloping yield curve environment, inan arbitrage model, the spot rate “climbs” up along the forward yieldcurve. On the other hand, a forecasting model typically predicts that theyield curve is close to stationary or “slides” in parallel to today’s yieldcurve. In other words, the future spot rate will be close to today’s spotrate and the 5 year forward rate 1 year from today will be close to today’s 4 year forward rate. An exception to this forecasting is that a yieldcurve can indeed become inverted (or downward sloping) with a smallprobability.One important consequence of the different views of these two categories of models is that the value of the same financial instrument can bevery different according to these models. This reveals a significantamount of trading or speculation opportunities and turns out to be an important motivation or driving factor for derivatives transactions, especially exotic derivatives transactions that are often embedded in structured notes.Another important and related motivation or driving factor for trading is the investors’ demands for higher coupons or higher potential yieldor returns. A typical strategy for coupon or yield enhancement is for theinvestors to take some risks or to give up some of the upside potentials inthe trades. Part of the economic value for the coupon enhancementcomes from the fact that the investors think that the risk that they take orthe upside potential that they give up will occur at low probabilities (inthe real world or under the real world probability measure), but the dealers think the same events will occur at higher probabilities (under thearbitrage-free probability measure). Thus, the dealers can price and sellthe trades lower (with arbitrage models) than what the investors think(with forecasting models). In other words, if the investors’ forecastingmodels or views are correct, the investors will receive more values in thecoupon enhancement than the risk that they take or the values of the upside potential that they give up.In other words, in an upward sloping yield curve environment, theinvestors tend to long the market (or assume a bullish view) and/or longyield curve steepeners for yield enhancement purposes. Some maychoose a bearish view on the longer term market if they think that thecurrent longer term interest rate is too low.Similar curve strategies can be applied to the FX market (and othermarkets), which we shall discuss more. But, the reader may want to startthinking about how to derive such strategies.
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Unless otherwise indicated, going forward, we shall assume that theyield curves are upward sloping.To achieve further yield enhancement, the investors typically sell (orshort) (implied) volatilities. For instance, the investor can sell the canceloption in a cancelable swap and the cap in a capped floater.The investor can also sell the implied equity volatility in an equityvariance swap (partially hedged by buying the realized volatility). Othervolatility based instruments include forward starting options (cliquet)whose strike is set ATM on a forward date. There are also bonds withcoupons linked to volatilities (that are termed as Vol bonds). These volatility instruments offer investors close to market neutral trading strategies.In summary, one of the most important motivations of derivatives,especially exotic derivatives, is to create undervalued assets for the investor either directly or through structured products (or notes). Whilethese assets are undervalued according to the investor’s forecasting modes, it does not mean that the dealer will incur any loss. Though it is azero sum for this particular trade, the dealer, being market neutral, canmake a significant amount of profit from his or her hedges for this tradeto offset the loss in this trade (and still lock in the initial profit). It lookslike that it is a win-win situation for both the investor and the dealer.So, an interesting question is where does the economic value comefrom or who provides the economic value? We shall give some examples later on.2.4.1
Simple Bonds and IR Swaps
Let’s first start with a simple plain vanilla interest rate (IR) swap that, aswe discussed previously, is a contract for exchanging a set of fixed coupons or payments (or the fixed leg) with a set of floating coupons orpayments (or the floating leg), typically with the floating coupon rateequal to the corresponding LIBOR of the same accrual dates (plus asmall funding spreads3).The swap is typically structured with zero PV at the time of tradingor the total PV of the floating payments (or the floating leg) being equalto the total PV of the fixed payments (or the fixed leg) assuming that the53 The funding spread can also be negative which can be achieved through fundingcheapening strategies. If one of the swap counterparties is of low credit rating, then thefunding spread can be significant. As usual, we start with the case where the counterparty credit risk is not significant.
Sec. 2.4
Trading Opportunities and Strategies
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forward curve is realized or under the no-arbitrage measure. The tradingor speculation opportunities come from the prediction of the forecastingmodels (assuming that the spot rate slides along) that the total PV of thefloat payments (or the floating leg) is (most likely) less than the total PVof the fixed payments (or the fixed leg) under the real world probabilitymeasure in a upward sloping yield curve environment.Consequently, to benefit from the valuation difference from differentmodels, an investor can enter into a receiver swap (or a receiving-fixedpaying-floating swap) with a dealer. In this case, the investor is long inthe interest rate market. The risk that the investor is taking is mainly onthe overall level of the yield curve (or the first or the most dominantprincipal component of the yield curve movement). More specifically, ifthe overall level of the yield curve rises (or the market sells off), thevalue of the swap to the investor will decline.In this swap trade, the dealer is long the opposite swap, i.e., a payerswap (or a paying-fixed-receiving-floating swap). One interesting question is that, given the above information, why would a dealer like to enterinto such a swap. As we pointed out, essentially, the dealer can actuallyrealize the forward curve by arbitraging (or replication or hedging) usingan arbitrage pricing model with interest rate Euro futures and other moreliquid swaps.54 This allows the dealer to be market neutral (or close tomarket neutral) and yet earn a bidask spread,55 which is typically aspread (or funding spread) applied to the floating leg (which is also referred to as the funding leg).As we pointed out before, the investor can make a significant amountof profit from this trade, if his or her forecasting models or views are correct. But, this does not mean that the dealer will incur any loss. It lookslike that it is a win-win situation for both the investor and the dealer. So,the question is where does the economic value come from or who provides the economic value?It turns out that typically those who provide the economic value areThere is hedging cost associated with this arbitraging coming from the bidask spreadof the hedge instruments and the number of round-trip hedge transactions.55The market making activities tend to be leveraged in the sense that a market maker ordealer tends to buy and sell financial instruments with PVs significantly greater than thedealer’s own equity. As such, the dealers have very strict risk management to ensure thattheir positions or portfolios are close to market neutral quantified by the VAR (Value AtRisk) limit, which, in turn, limits their Delta, Vega, and Gamma exposures. An interesting aspect of this is that the dealers can and need to conduct proprietary trading withinthese limits, but this is a separate subject.54
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those who need long term funding or capital (such as bond issuers if thebonds are not swapped to floating bonds) or who need to hedge againstthe rising of the long term interest rates (such as future bond issuers) andthus need to pay the high long term (fixed) interest rates. This is a partof the debt liability management. If you have a 30 year fixed rate mortgage loan, then you have provided part of the economic value too.The reader may want to think about and analyze the situationwhereby the yield curve is inverted.It is important to point out that the probability for the investor tomake a profit is less than one, as the investors would incur a loss if themarket significantly sells off (or the rate increases significantly). This isa potential economic cost to the investor that also drives the economicvalue in that the investor demands to receive high enough fixed-couponin the swap. This is also a driving factor to the supply and demand that,in turn, is a determining factor of the levels of interest rates.Other determining factors of the levels of interest rates include theintervention of the FOMC (Federal Open Market Committee) in settingthe Fed fund target rate (an over night interest rate)56,as well as the inflation rate.57Among the major users of swaps are the bond and structured noteissuers, asset swaps buyers, and unfunded investors.For instance, when a bond issuer needs to issue a simple bond tofund or finance its business activities, in the simplest case, it needs toissue a fixed-coupon bond (as opposed to floating-coupon bonds to makethe bond attractive to investors). Then, the bond issuer will typicallyenter into a receiver swap (or a receiving-fixed-paying-floating swap)with a dealer with the fixed rate matching the bond coupon and the floating rate based on LIBOR plus a (fixed funding) spread. This essentiallyconverts (or swaps) the fixed-coupon bond into a floating-coupon bond(with a fixed funding spread). The funding spread can be negative (forsub-LIBOR funding) or (significantly) positive depending on the creditrisk involved in the bond and the supply and demand.56 This largely (though not completely) determines the short-term interest rates. In recentyears, FOMC has increased the Fed fund rate many times and the FOMC meetings, decisions, and outlooks have been among the most important market events that impact thetrading activities.57 As we pointed out before, unless otherwise indicated, the interest rate that we workwith is the nominal interest rate (which, unless under special situations, should not benegative), and it is consisted of an aggregation of the real interest rate (which can benegative) and the inflation rate (which can also be negative).
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Trading Opportunities and Strategies
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One motivation for the bond issuer to enter into this swap is to benefit from the valuation difference between the arbitrage models and forecasting models. More specifically, the bond issuer can save a significantamount of the funding cost in the bond (if the bond issuer’s forecastingmodels or views are correct). This is historically true in USD and othercurrencies.Another motivation for the bond issuer to enter into this swap is forhedging the (realized) volatility of the PV of the bond