Session 7 - Derivatives - FRAs & Eurodollar Futures

During this class we learned what a zero-coupon rate is and how to calculate discount factors (have a look at the Excel file).

We also reviewed how to calculate forward discount factors and forward rates avoiding potential arbitrage opportunities. A forward rate is a rate to be applied to a forward starting loan/deposit. The idea behind this concept is that if I do a 1) 12m deposit or 2) a 6m deposit and I reinvest the proceeds in a new forward starting 6m deposit, the outcome should be the same.

Additionally, we had a look at how FRAs (Forward Rate Agreements) and Eurodollar Futures work.

The presentation can be found here.

Session 5 - Derivatives - 2014

We started this session reviewing how simple interest rates and compounded interest rates work. Remember that for this course we will use continous compounding (discount factor = e ^ (-r*T); future value = e ^ (r*T)). It is interesting to remember also how to work with Natural Logs. Remember that Ln e ^(r*T) = r*T.

When we value Futures, we consider an Eonia curve (Eonia is a riskless interest rate and Futures are riskless due to the margining process). When we value forwards, we consider a Euribor curve. Additionally, we would have to charge an additional spread that depends on the creditworthiness of the counterparty (CVA).

We valued Forward for an asset producing no income assuming a no-arbitrage hypothesis. If the forward is too expensive, we can sell (short) the forward and ask for a loan to buy the underlying asset. At maturity, we give the asset to the person who bought the forward from us and we make a riskless profit. So, if the forward is expensive, many arbitrageurs will enter into this strategy, taking the price of the forward down.

If the forward is too cheap, we buy the forwards and short the underlying asset. We will make a deposit with the amount that we obtain by shorting the asset. At maturity, we buy the asset from the person who sold us the forward and we give it back through the short contract. We would make a riskless profit. So, if the forward is cheap, many arbitrageurs will enter into this strategy, taking the price of the forward up.

The only possible value to avoid any potential arbitrage opportunity would be F = S*e ^ (r*T). Please review the Excel file. Khan Academy explains this potential arbitrage opportunity here and here.

We applied the same logic to assets producing a discrete income and to assets producing a yield. You can find the presentation here.

Clase 7 curso 2013-2014 - FRAs y Futuros de Eurodollar

Durante esta clase vimos como determinar tipos de interés forward por medio de una demostración que asume que no puede haber arbitraje. Fijar un tipo de interés forward nos puede servir para cubrir el coste financiero de una póliza de crédito que aún no está dispuesta, pero que sé que dispondré de ella en el futuro. El tipo de interés forward se puede cubrir por medio de un FRA (instrumento OTC) o por medio de futuros.

Podéis encontrar la presentación aquí.