# Forward Rate Agreements and Swaps

Energy derivative Freight derivative Inflation derivative Property derivative Weather derivative. Reputation risks also exist.

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Each ZCB gives us a rate at which we can put money on deposit now for expiry at a specific time, and we can construct a discount curve from the collection of all ZCBs that we have available to us. In the case of a ZCB, we deposit the money now and receive it back at expiry. A Forward Rate Agreement extends the idea of putting money on deposit now for a fixed period of time to putting it on deposit at a future date for a specific period of time.

An FRA, just like a deposit, involves two cash flows. We pay the counterparty a notional at time , and receive our notional plus interest of at time ; where the first term is the Year Fraction, the second is the Forward Rate, and the final is the Notional.

Since f will be fixed when we sign the contract, we can hedge these two cash flows exactly at using ZCBs. The value of the FRA is the value of receiving the second sum minus the cost of making the first payment:. Note that the price of all FRAs is uniquely determined from the discount curve [although in reality our discount curve will be limited in both temporal resolution and maximum date by the ZCBs or other products available on the market which we can use to build it].

A Swap is an agreement to exchange two cash flows coming from assets, but not the assets themselves. By far the most common is the Interest Rate Swap, in which two parties agree to swap a stream of fixed rate interest rate payments on a notional M of cash for a stream of floating rate payments on the same notional.

Although the notional might be quite large, usually only the differences between the payments at each time are exchanged, so the actual payments will be very much smaller. The mechanics are probably best demonstrated by example:. The gain one party receives through the swap will be equal to the loss of the other party. Interest rate swaps are traded over the counter, and if your company decides to exchange interest rates, you and the other party will need to agree on two main issues:.

Generally, only the net payment will be made. In short, the swap lets banks, investment funds, and companies capitalize on a wide range of loan types without breaking rules and requirements about their assets and liabilities. Swaps can help make financing more efficient and allow companies to employ more creative investing strategies, but they are not without their risks. There are two risk types associated with swaps:.

Swaps are a great way for businesses to manage their debt more effectively. The value behind them is based on the fact that debt can be based around either fixed or floating rates. When a business is receiving payments in one form but prefers or requires another, it can engage in a swap with another company that has opposite goals. But they still have important risks to consider before company leaders sign a contract. Has your company or investment firm ever used an interest rate swap?

Did you come out ahead, or were you on the losing side? Extra Income Amazon vs. If you're looking for ways to pick up a little extra cash, it's probably crossed your mind to try going through your closets looking The first homeowner in my collegiate social circle bought a barely habitable two-story Craftsman on the wrong side of the tracks.

But sorting through the best offers can be tricky. At Money Crashers, we Advertiser Disclosure X Advertiser Disclosure: Become a Money Crasher! How Interest Rate Swaps Work Generally, the two parties in an interest rate swap are trading a fixed-rate and variable-interest rate. Interest rate swaps are traded over the counter, and if your company decides to exchange interest rates, you and the other party will need to agree on two main issues: Varying levels of creditworthiness means that there is often a positive quality spread differential that allows both parties to benefit from an interest rate swap.

The interest rate swap market in USD is closely linked to the Eurodollar futures market which trades among others at the Chicago Mercantile Exchange. Typically these will have none of the above customisations, and instead exhibit constant notional throughout, implied payment and accrual dates and benchmark calculation conventions by currency.

The net present value PV of a vanilla IRS can be computed by determining the PV of each fixed leg and floating leg separately and summing. For pricing a mid-market IRS the underlying principle is that the two legs must have the same value initially; see further under Rational pricing. Calculating the fixed leg requires discounting all of the known cashflows by an appropriate discount factor:. Calculating the floating leg is a similar process replacing the fixed rate with forecast index rates:.

This has been called 'self-discounted'. Some early literature described some incoherence introduced by that approach and multiple banks were using different techniques to reduce them.

It became more apparent with the — global financial crisis that the approach was not appropriate, and alignment towards discount factors associated with physical collateral of the IRSs was needed. Post crisis, to accommodate credit risk, the now-standard pricing framework is the multi-curves framework where forecast -IBOR rates and discount factors exhibit disparity. Note that the economic pricing principle is unchanged: As regards the rates forecast, since the basis spread between LIBOR rates of different maturities widened during the crisis, forecast curves are generally constructed for each LIBOR tenor used in floating rate derivative legs.

Regarding the curve build, under the old framework a single self discounted curve was "bootstrapped" , exactly returning the prices of selected instruments. Under the new framework, the various curves are best fitted — as a "set" — to observed market data prices, one for discounting, one for each forecast curve as below. Here, since the OIS average-rate is swapped for the -IBOR rate the most liquid in that market , and the -IBOR swaps are in turn discounted on the OIS curve, the problem entails a nonlinear system , and specialized iterative methods are usually employed — very often a modification of Newton's method.

See [4] [5] [1]. The complexities of modern curvesets mean that there may not be discount factors available for a specific -IBOR index curve. These curves are known as 'forecast only' curves and only contain the information of a forecast -IBOR index rate for any future date.

Some designs constructed with a discount based methodology mean forecast -IBOR index rates are implied by the discount factors inherent to that curve:. During the life of the swap the same valuation technique is used, but since, over time, both the discounting factors and the forward rates change, the PV of the swap will deviate from its initial value.

Therefore, the swap will be an asset to one party and a liability to the other. Swaps are marked to market by debt security traders to visualize their inventory at a certain time. Interest rate swaps expose users to many different types of financial risk. Predominantly they expose the user to market risks. The value of an interest rate swap will change as market interest rates rise and fall. In market terminology this is often referred to as delta risk.

Other specific types of market risk that interest rate swaps have exposure to are basis risks where various IBOR tenor indexes can deviate from one another and reset risks where the publication of specific tenor IBOR indexes are subject to daily fluctuation.

Interest rate swaps also exhibit gamma risk whereby their delta risk increases or decreases as market interest rates fluctuate.

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