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In this section, we explore how to price and value three types o f equity swaps: ( I ) a swap to pay a fixed rate and receive the return on the equity, (2) a swap to pay a floating rate and receive the return on the equity, and ( 3 )a swap to pay the return on one equity and receive the return on another.
To price or value an equity swap, we must determine a combination of stock and bonds that replicates the cash flows on the swap. As we saw with interest rate and currency swaps, such a replication is not difficult to create. W e issue a bond and sell a bond, with one being a fixed-rate bond and the other being a floating-rate bond. I f we are dealing with a currency swap, we require that one o f the bonds be denominated in one currency and the other be denominated in the other currency. With an equity swap, it would appear that a replicating strategy would involve issuing a bond and buying the stock or vice versa, but this is not exactly how to replicate an equity swap. Remember that in an equity swap, we receive cash payments representing the return on the stock, and that is somewhat different from payments based on the price.
Pricing a Swap to Pay a Fixed Rate and Receive the Return on the Equity: By example, we will demonstrate how to price an n-payment m-day rate swap to pay a fixed rate and receive the return on equity. Suppose the notional principal is $1, the swap involves annual settlements and lasts for two years (n = 2),and the returns on the stock for each o f the two years are 10 percent for the first year and 15 percent for the second year. The equity payment on the swap would be $0.10 the first year and $0.15 the second. I f ,    however, we purchased the stock instead o f doing the equity swap, we would have to sell the stock at the end o f the first year or we would not generate any cash. Suppose at the end o f the first year, the stock is at $1.10. W e sell the stock, withdraw $0.10, and reinvest $1.OO in the stock. At the end o f the second year the stock would be at $1.15. W e then \ell the stock, taking cash of $0.15. But we have $1.OO left over. To get rid of,or offset,this cash flow, suppose that when we purchased the stock we borrowed the present value of $1.00 for two years. Then two years later, we would pay back $1.00 on that loan. This procedure would offset the $1.00 in cash we have from the stock. The fixed payments on the swap can be easily replicated. I f the fixed payment is denoted as FS(O,n,m),we simply borrow the present value o f FS(O,n,m) for one year and also borrow the present value of FS(O,n,m)for two years. When we pay those loans back, we will have replicated the fixed payments on the swap.Equity

We have already alluded to the similarity between swaps and assets. For example, a currency swap is identical to issuing a fixed- or floating-rate bond in one currency, converting the proceeds to the other currency, and using the proceeds to purchase a fixed- or floating- rate bond denominated in the other currency. An interest rate swap is identical to issuing a fixed- or floating-rate bond and using the proceeds to purchase a floating- or fixed-rate bond. The notional principal is equivalent to the face value on these hypothetical bonds.
Equity swaps appear to be equivalent to issuing one type of security and using the proceeds to purchase another, where at least one of the types of securities is a stock or stock index. 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. As it turns out, however, these two transactions are not exactly the same, although they are close. The stock position in the transaction is not the same as a buy-and-hold position; some adjustments are required on the settlement dates to replicate the cash flows of a swap.
The equivalence of a swap to transactions we are already familiar with, such as owning assets, is important because it allows us to price and value the swap using simple instruments, such as the underlying currency, interest rate, or stock. We do not require other derivatives to replicate the cash flows of a swap. Nonetheless, other derivatives can be used to replicate the cash flows of a swap, and it is worth seeing why this is true.