Hi In Assgt X3.5ii) one has to employ Black's formula to value a floorlet. For the formula, I need the forward volatility of the 3 mth LIBOR but the question has only provided me with a value for the spot rate volatility. Is it logical to assume that they are the same or is there a formula to convert it? I would be really surprised if they are the same, particularly since they do not have a linear relationship. Any assistance is much appreciated!
The volatility used in valuing each caplet using the Black model is called the “spot volatility”, and is the volatility of the forward rate. If all the caplets are assumed to have the same volatility, then the volatility is referred to as the “flat volatility”. Similar to the bootstrapping method for interest rate, you can bootstrap volatilities using the value of interest rate caps. In other words, given flat volatilities, you can bootstrap out the spot volatility for each caplet. The volatilities quoted in the market are usually flat volatilities. However, many traders like to work with spot volatilities because this allows them to identify underpriced and overpriced caplets. Generally speaking I would think that it is safe to assume that you don't have to bootstrap volatilities unless the question specifically asks for it. In this case I think that the 'logical thing to do' - depending on your definition of logic of course, is to use what you've been given as a spot rate - for a forward rate.
Hi Olly Thanks for your explanation. I just realised that it has also been detailed in the notes as well but your explanation was pretty good. Missing that section on terminology had got me slightly confused but anyway thank you so much for your help!
