# Level I Derivatives

## Roll Yield (Roll Return)

The idea of roll yield – or roll return, same thing – is relatively straightforward: it’s part of the increase or decrease in the value of your portfolio that arises specifically when you roll over an expiring futures or forward contract into a new contract.  The other parts of that increase or decrease are the […]

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## Equivalence of Derivatives (Swaps, FRAs, and Interest Rate Options)

Various interest rate derivatives are, in fact, equivalent to each other; i.e., they can be structured to generate equivalent (though not necessarily identical) cash flows.  This article will explain how these derivatives can be structured to be equivalent to each other. First note that you will not be asked on an exam to create equivalent […]

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## Swap Diagrams

This article’s going to turn out to be fairly short, but, I hope, quite useful.  It has pictures. Floating-Rate Inflow: Rates are Expected to Decrease Here’s the situation: you own a portfolio of investments (floating-rate bonds) paying 6-month USD LIBOR + 100bp; payments are every 6 months for the next three years.  You’re concerned that interest […]

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## Binomial Pricing Trees (for Options)

Binomial trees are used in a variety of contexts in finance: Calculating probabilities for Bayes’ Formula type problems Calculating the value of options on stocks, commodities, and so on (you are here) Calculating the option-adjusted spread (OAS) for bonds Calculating the value of bonds with embedded options Calculating the value of floating-rate bonds Calculating the […]

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## FRAs

A forward rate agreement (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 […]

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## Put-Call Parity

Put-call parity is nothing more than an equation that shows how the price of a (European) put option (on, say, a stock) relates to the price of a (European) call option (on the same stock).  The equation arises from a simple finance fact: If, given any set of circumstances, portfolio A and portfolio B have […]