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##### Subject 7. Pricing and Valuing Swap Contracts
Swap pricing means determining the fixed rate and any relevant terms, such as the foreign notional principal on a currency swap, at the start of the swap.

All swaps have a market value. Swap valuation means determining the market value of the swap, which is the present value of one stream of payments less the present value of the other stream of payments.

• The fixed terms, such as the fixed rate, are established at the start to give the swap an initial market value of zero. At this point neither party pays anything to the other. It is neither an asset nor a liability to either party.

• The market value of a swap will become positive for one party (an asset to that party) and negative for the other (a liability to that party) during the life of the swap, as market conditions change and time passes.

To determine the market value of a swap, we replicate the swap using other instruments that produce the same cash flows. Knowing the values of these instruments, we are able to value the swap. This value can be thought of as what the swap is worth if we were to sell it to someone else. In addition, we can think of the value as what we might assign the swap on our balance sheet. The swap can have a positive value, making it an asset, or a negative value, making it a liability.

The equivalence of a swap to transactions (such as assets) we are already familiar with is important because it allows us to price and value the swap using simple instruments, such as the underlying currency, interest rate, or stock.

Swaps and Assets

Currency swaps are like issuing a bond denominated in one currency and using the proceeds to buy a bond denominated in another currency.

Interest rate swaps are like issuing a fixed-rate bond and using the proceeds to buy a floating-rate bond or vice versa. The notional principal is equivalent to the face value on these hypothetical bonds.

Equity swaps are like issuing a bond and using the proceeds to buy stock or vice versa. For example, a pay-fixed, receive-equity swap looks like issuing a fixed-rate bond and using the proceeds to buy a stock or index portfolio. Equity swaps with both sides paying an equity return are like selling short one stock and using the proceeds to buy another stock. The stock position is not, however, a buy-and-hold position and requires some rebalancing.

Swaps and Forward Contracts

A swap can be viewed as combining a series of forward contracts into a single transaction. However, there are some small differences.

An interest rate swap is like a series of off-market FRAs, meaning that the rate on each FRA is set at the swap rate, not at the rate it would be set if priced as an FRA with zero market value at the start. In addition, the first payment on a swap is just an exchange of known amounts of cash.

Currency swaps and equity swaps are similar to forward contracts, but the connection is not as straightforward as with interest rate swaps.

Swaps and Options

Interest rate swaps are like being long (short) interest calls and short (long) interest rate puts. Buying a call and selling a put would:

• force the transacting party to make a net payment if the underlying is below the exercise rate at expiration, or
• result in receipt of a payment if the underlying is above the exercise rate at expiration.

The payment will be equivalent to a swap payment if the exercise rate is set at the fixed rate on the swap. Therefore, a swap is equivalent to a combination of options with expirations at the swap payment dates.

Currency swaps and equity swaps are also similar to combinations of options, but the connection is not as straightforward. 