# Pricing and Valuing Equity Swaps

• Three common types of equity swaps are:

• Pay Fixed Interest Rate, Receive Return on Equity

• Pay Floating Interest Rate, Receive Return on Equity

• Pay Return on One Equity, Receive Return on a Different Equity

• Pricing Equity Swaps

• The same formula used to find the fixed interest rate when pricing a plain vanilla interest rate swap or a currency swap to obtain an initial swap value of zero is applied.

• The market value of a pay floating-receive return on equity swap is automatically zero at swap initiation since the floating rate portion of the swap equals 1.0 (making the numerator of the rate pricing equation zero, because it is 1 minus 1).

• Pricing an equity for equity swap can be done by going long on one stock and short on the other. Like other swaps, this swap is valued at zero on initiation.

• Valuing Equity Swaps

The market value of an equity swap at any day "t"

\= (St/S0) - Bt(hn) - (FS(0,n,m)*ΣBt(hj))

• St = stock (or index) price at time t
• S0 = stock (or index) price at time 0
• Bt(hn) = present value of \$1 to be repaid at swap's expiry time "n"
• FS(0,n,m) = fixed rate on the swap
• Bt(hj) = present value factor for each interest rate payment, based on the current structure of interest rates; these are calculated at time t and summed.