Now let's talk about options once again, it will be the last time in this course. So what we know about that that's options in, put that like Project valuation again. Well, here in these projects we have basically two major classes of projects. One is what we called real projects that deal with some industrial development, manufacturing, it may be advanced technology, or something but not financial instruments. And the other area is when you talk about valuation of securities. Now, the major challenges in both areas are sort of different. Now, for real projects, the idea is to identify or if you will recognize, and then sort of quotedly adapt for valuation. So here in these projects, remember where we talked about abandonment options, about the option to make postponed investments, future investments. We said that the key story is first of all to recognize that the option exists there, that some ability to do something in the future may be looked at as an option. And the next thing is sort of find some proxies for option valued drivers, that's what I called here adapt valuation. So, this is the key story because then if you did that maybe approximately, then you can use any kind of option valuation approach, you can use black and scholes you can sometimes use binomial. So the key story is to realize where it is and then because in any cases, it's not going to be a very accurate valuation, but it will be sort of importantly seen as a qualitative contributor. Now, when we talk about securities, here the story is different. So especially, well, it deals both with equity, fixed income, and derivatives. Here, we deal with advanced models. If you try to evaluate a very special collateralized mortgage obligation, then unfortunately, we have to deal with all these prepayment rates for all the underlying then to follow through all the process how the holders of the ultimate tranches of the CMO receive cash flows and so on and so forth, without some really mathematical loaden and cumbersome models, you unfortunately cannot proceed. The good news is that these technologies are widely developed and used at most investment houses and the asset management companies. People really study that all the time, they find some better ways. So these people are more or less mathematicians if you will, but their results are widely used in valuation of advanced securities and securities with various embedded options. We said that for fixed income, it's almost always like that, and for derivatives, it's sort of in the major part of cases, this is really a challenging thing. But now, so here, like I said, it's easy to realize where the option is. For example, for callable bond, you don't have to embark on a really hard intellectual road to recognize that. Now the question is how to value that. And again here you are forced to use advanced mathematical models. But now, I would also like to draw your attention to the following thing. This is a tradeoff in option valuation. This is like benefit versus cost. Well, the story is that for fixed income securities, there is no question. You cannot ignore that even if the cost is high. But without the correct valuation of these options, you cannot proceed. You cannot manage these securities. Your potential losses if you ignore that would be huge. However, if you talk about some real projects in which options are not all that difficult to recognize but progressive and difficult to properly evaluate and even if the range of this valuation is wide, then you say, what benefit do I get from that? Maybe we're better off if we sort of ignored that to a first approximation. So you always have to keep this in mind because well in some areas, it more in finance when you deal with international finance and especially in hedging in some advanced instruments, this question also exists. For example, if the cost of the program that is used to sort of reduce some other risk is so high that it is really unlikely to be sure that you gain something, then you might stick to a famous do nothing case. Well, I'm not trying to push that because that creates a temptation. People here will say, "Well, we've not have good enough input. So basically, we are better off if we just stopped here and ignored them." Well, not quite. But what I am saying is that in your analysis of real projects, you have to keep this in mind. If to get a minor refinement of value, you have to spend a lot of time and effort, you have to spend really highly paid personnel and a lot of calculation power, then the question is, is it worth it? And this is an open question. So I always reiterated that, that this idea of cost and benefit is also one of the key ideas in finance. So you may spend a lot of time and effort for the very modest result. In this case, sometimes it's better to do nothing.
