Month: February 2014

  • Triangular Arbitrage

    Triangular arbitrage is nothing more than determining whether an arbitrage opportunity exists amongst three currencies with three exchange rates; the complicating factor is that the exchange rates each have a bid rate and an ask rate.  (Note: the arbitrage could, in fact, involve more than three currencies.  As the principles are the same, only three…

  • Valuing Derivatives

    Valuing derivatives – forwards, futures, FRAs, and swaps – is much the same as pricing them.  The value of a derivative is the amount that one party would have to pay the other if the derivative were to expire today; it depends on the price of the underlying today compared to the price at the…

  • Valuing Plain Vanilla Interest Rate Swaps

    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),…

  • Valuing Currency Forwards

    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…

  • Pricing Currency Forwards

    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…

  • Valuing FRAs

    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…

  • Valuing Forwards and Futures

    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…