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.