Category: Level II Derivatives

Remember that the price of a swap is the fixed rate on the swap.  A currency swap can take one of three forms: Each side pays a fixed rate: one in one currency, the other in a different currency.  In this case, there are two prices for the currency swap: the two fixed rates (which…

Somewhat surprisingly, a plain vanilla interest rate swap is one of the easiest derivatives to value; once again, as with all derivatives, the formula for the value is: \[Value\ =\ PV(what\ you\ will\ receive)\ –\ PV(what\ you\ will\ pay)\] Because the swap is equivalent to two bonds (one long, one short, one fixed, one floating),…

The formula for computing the value to the long position of a currency forward is: \[V_t\ =\ \frac{S_t}{\left(1\ +\ r_{BC}\right)^{(T\ -\ t)}}\ -\ \frac{F_T}{\left(1\ +\ r_{PC}\right)^{(T\ -\ t)}}\] where: \(V_t\): value of the currency forward (to the PC payer / BC receiver) at time \(t\) (in \(\dfrac{PC}{BC}\)) \(T\): expiration of the forward contract \(S_t\): spot…

A currency forward contract is an agreement to exchange a given amount of one currency for a given amount of another currency at a future date.  The price of a currency forward is the exchange rate for the currencies at the expiration of the contract, and is related to the spot exchange rate by covered…

Recall that an FRA is essentially an agreement to enter into two loans (one long, one short) in the future: a fixed-rate loan and a floating-rate loan.  (The difference between an FRA and an actual agreement to enter into these two loans is that the FRA will be settled at the beginning of the loan…

The formulae for valuing all derivatives are essentially the same: \[Value\ =\ PV(what\ you\ will\ receive)\ –\ PV(what\ you\ will\ pay)\] First, the notation: \(V_t\): value of the forward (to the long) at time \(t\) \(T\): expiration of the forward contract \(S_t\): spot price at time \(t\) \(F_T\): forward price at time \(T\) \(r_f\): effective…

Remember that the price of a forward/future contract is the agreed price of the underlying at the expiration of the contract, which has to be: \[F_T\ =\ S_0\left(1\ +\ r_f\right)^T\] where: \(T\): expiration of the forward/futures contract \(F_T\): forward/futures price of the underlying (at time \(T\)) \(S_0\): spot price of the underlying today \(r_f\): effective…

Remember that the price of a plain vanilla interest rate swap is the fixed rate on the swap. The key to pricing swaps is the realization that a swap is essentially an exchange of bonds.  A plain vanilla (fixed-for-floating) interest rate swap can be replicated by the fixed payer issuing a fixed-rate bond to the…

The formulae for valuing all derivatives are essentially the same: \[Value\ =\ PV\left(what\ you\ will\ receive\right)\ –\ PV\left(what\ you\ will\ pay\right)\] The one valuing formula that needs some explanation is the formula for valuing a currency forward; it is slightly different from the other formulae, but the difference is never explained. Here goes: Given: \(V_t\):…