Okay. So we've covered options pretty well. We know how to plot their payoff and profit structures. And we understand the six different factors that drive their value. Now, let's look at how options might be combined with a position in the underlying asset, or combine together with other options so as to provide a desired payoff structure. Let's head back to Judy's position after she purchased a corn call option with an exercise price of $9 a bushel. When we combine the payoff from the call option with the unhedged price that Judy faced, we see that the call option has provided her with a price cap on corn. Now what about Frank's position? Recall that he purchased a corn put option with an exercise price of $5. When we combine the payoff and the put option with the price that he would have received, had the hedge not been in place, we end up with another kinked line that illustrates that his purchase of the put option enabled him to set a floor price he would receive for corn. Caps and floors are very popular in lots of other markets, such as interest rate and currency markets. For example, take a borrower who has borrowings of pay interest at a variable rate. The risk that the borrower faces is that the interest rates might increase. To protect against this, the borrower might buy an interest rate cap at, say, 4%. So if interest rates increase beyond 4%, the payoff from the interest rate cap will compensate them for the higher interest rate that they need to pay their lenders. From the borrower's perspective, it might be very expensive to buy an interest rate cap especially when interest rate volatility is high. To help offset the cost of the cap, the borrower may simultaneously sell an interest rate floor, which is equivalent to selling a put option. The impact of the floor is that the borrower is effectively saying, I will pay the floor rate even when interest rates are lower than that. Now, let's assume our borrower sells a floor at 2% to help offset the cost of the cap they have in place at 4%. Now, as you can see, the interest rate that the borrower now faces is one of three values. Firstly, it is equal to the floor rate whenever interest rates are below that rate. When interest rates are above the cap rate, they are effectively paying the cap rate. And when interest rates are between the floor and the cap rate, the borrower is effectively borrowing at the market rate. Combining a cap and a floor together with the position in the underlying asset, yields what we call a collar. In this instance, as the underlying asset was an interest rate, we have here an interest rate collar. An interest rate collar might also be attractive to an investor facing the opposite risk to the borrower. The investor would buy a floor, guaranteeing a minimum rate of return, and sell a cap, thereby limiting their maximum return from an investment in debt securities. Now, there are a lot of other settings where hedges buy and sell caps, floors and collars, particularly in foreign exchange markets where the extremely high levels of volatility make straight out option positions extremely expensive. In this session, we've demonstrated how to combine an exposure in the underlying asset with option so as to generate caps, floors, and collars. More generally, we spend a lot of time thinking about how to use forwards, futures, and options. But the really important question, we've not quite answered yet, is why should a company hedge at all? That will be the topic for our next session.
