By Lauryn Silverhardt
Come and play on the seashore with Dora and Boots!
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Additional info for A Day at the Beach (Dora the Explorer)
5 Suppose the strike prices X1 and X2 satisfy X2 > X1 , show that for European calls on a nondividend paying asset, the difference in the call values satisfies −B(τ )(X2 − X1 ) ≤ c(S, τ ; X2 ) − c(S, τ ; X1 ) ≤ 0, where B(τ ) is the value of a pure discount bond with par value of unity and time to maturity τ . Furthermore, deduce that −B(τ ) ≤ ∂c (S, τ ; X) ≤ 0. ∂X In other words, suppose the call price can be expressed as a differentiable function of the strike price, then the derivative must be nonpositive and not greater in absolute value than the price of a pure discount bond of the same maturity.
The fixed rate payer will receive floating rate interest payments semi-annually according to the six-month LIBOR. This cash stream of interest payments will be identical to those generated by a floating rate bond having the same maturity, par value and reference interest rate as those of the swap. Unlike the holder of the floating rate bond, the fixed rate payer will not receive the notional principal on the maturity date of the swap. On the other hand, he or she will pay out, fixed rate interest rate payment semi-annually, like the issuer of a fixed rate bond with the same fixed interest rate, maturity and par value as those of the swap.
1 Interest Rate Swaps The most common form of an interest rate swap is a fixed-for-floating swap, where a series of payments, calculated by applying a fixed rate of interest to a notional principal amount, are exchanged for a stream of payments calculated using a floating rate of interest. The exchange of cash flows in net amount occurs on designated swap dates during the life of the swap contract. In the simplest form, all payments are made in the same currency. The principal amount is said to be notional since no exchange of principal will occur and the principal is used only to compute the actual cash amounts to be exchanged periodically on the swap dates.
A Day at the Beach (Dora the Explorer) by Lauryn Silverhardt