字幕表 動画を再生する 英語字幕をプリント The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. JAKE XIA: This is the second time we are having this class. We had it last year in a smaller version. That was for six units of a credit, and we had it once a week. And mostly practitioners from the industry, from Morgan Stanley, talking about examples how math is applied in modern finance. And so we got some good response last year. So, with the support of the math department, we decided to expand this class to be 12 units of credit and have twice a week. So, we have every Tuesday and Thursday afternoon from 2:30 to 4:00, as you know, in this classroom. So last year, Dr. Vasily Strela and I-- by the way, I'm Jake Xia and that's Dr. Vasily, and we were the main instructors last year. Now we doubled it up to four main instructors. That's Dr. Peter Kempthorne and Dr. Choongbum Lee. The reason we doubled up the main instructors is we have newly added math lectures, mostly focusing from linear algebra, probability to statistics, and some stochastic calculus to give you the foundation to understand the math will be used in those examples in the lecture taught by the practitioners from the industry. And the purpose of this course is really to give you a sampling menu to see how mathematics is applied in modern finance and help you to decide if this is a field that you would be-- RECORDED VOICE: Thank you, for using WebEx. Please visit our website at www.webex.com. JAKE XIA: OK, you heard that. And so hopefully, this will give you enough information to decide this is a field you would like to pursue in your future career. In fact, last year when we finished the class, we had a few students coming to work in the industry. Some work at Morgan Stanley, some work at elsewhere. So that's really the goal. And at the same time, obviously, you will further solidify your math knowledge and learn new content. And we put the prerequisite about the math part a bit later. So I will use today's first lecture's time to give you an introduction, really, to prepare you some basic background knowledge about the financial markets. Some terminologies will be used, which you may not have heard before. So before I get into the introduction, I always like to know who are actually in the classroom, so let me ask you a few questions. You just need to raise your hands so I know roughly what kind of background and where you are. So how many undergraduate students are here? So I would say 80% percent. How many graduate students are here, just to verify? Yep, that's about right, 20%. And how many students are in finance and business major? Just one. And how many of you are a math major? Most of you. How many of you are engineering majors? A few. How many of you actually are from other universities? Great, because last year we had quite a few, so I want to specifically tell you that you're very welcome to attend the classes here. So it's open door. And last year I remember we had a couple of students from Harvard. That's where I actually work right now. I forgot to mention that, but I'm affiliated with both the math department and the Sloan school here. So anyway, thanks for that. We will be doing a bit more polling along the way, mainly to get feedback of how you feel about the class. Last year we had it online, so if you feel the class is going too fast, or the math part is going too slow, or the finance part is a bit confusing, the easiest way is really just to send us emails, which you will find from the class website. So anyway, today-- VASILY STRELA: And all of us got MIT emails. JAKE XIA: Yes. We all have MIT emails, which are listed on the website. VASILY STRELA: [INAUDIBLE]. JAKE XIA: And obviously, we have offices here. You can easily stop by Peter and Choongbum's offices. And Vasily and I probably will be less often on campus, but we'll be here quite often and definitely love to be more. So anyway, I will start today's lecture with a story, and a quiz at the end. Don't worry, it's not a real quiz. Just going to ask you some questions you can raise your hand and give your answer. But let me start with my story. This is actually my personal story. I want to tell you why I tell the story later. But the story actually was in the mid '90s. I just left Salomon Brothers -- that was my first financial industry job -- to go to Morgan Stanley in New York to join the options trading desk. So the first day, I sat down, I opened the trading book, I found something was missing. So, I turned around, I asked my desk quant. I said, where is the vega report? So, let me show you. So that's the story. So I'm obviously not going to tell you the story of Pi or "Life of Pi." That's not a financial story. The rest of the story, alpha, beta, delta, gamma, theta, which you will learn from Peter and Choongbum and Vasily's classes. So I'm going to talk about vega. So by the way, before I tell you the story, what's unique about vega on this list? AUDIENCE: It's not a Greek letter. JAKE XIA: It's not a Greek letter. That's right. So I turned around and asked my desk quant, I said, where's the vega report? But how many of you actually know what a vega is? OK, lot of people know. So anyway, I'm not going to-- just for the people who haven't heard about it before, it's a measurement about a book or portfolio or position's sensitivity to volatility. So, what is volatility? Which again, you will learn more in rigorous terms how it's defined in mathematics. But the meaning of it is really a measurement or indication of how volatile, or what's the standard deviation of a price can change over time. That's all you need to know right now. I'm not going to ask you questions later. So my desk quant look at me, said-- this is supposed to be options trading desk, so he look at me puzzled. So instead of answering my question, he handed over me a training manual for new employees and new analysts. So I opened the training manual and looked it through. I actually found my answer. So actually, at Morgan Stanley this is not called vega, it's called kappa. So now, I remember to call it kappa. Kappa is actually a Greek letter. So further, I look on the same page there was actually a footnote, which I copied down. So the footnote about why it's called kappa at Morgan Stanley. Kappa is also called vega by some uneducated traders at the Salomon Brothers. That's where I came from. I just joined. They have mistaken vega as a Greek letter after gambling at Vegas. So anyway, so that was my first day. So obviously, I learned how to call kappa very quickly, because I came from Salomon Brothers. And I called it kappa in the last 17 years, but you will hear people calling it vega. Obviously, I have probably more people calling it the vega. But anyway, so that's my first day at Morgan Stanley. But why did I tell you the story? What point I try to make? So this story is actually-- when you think about it, mathematical or quantitative finance is a rather new field. A lot of these terms were newly introduced. And the pricing model of options, as you know, was introduced in the Black-Scholes in the '70s, or some of the ground work may be done a bit earlier. But it's not like finance was a quantitative profession to start with. So what we witness in the last 30 years was really a transformation of the trading profession coming from mostly under-educated traders. Some of them typically joined the firms in the mail room and became trader later on. That's typical career path. And to nowadays, if you walk on the trading floor, you talk to the traders, most of them have advanced degrees and quite a few of them have very high training in mathematics and computer science. So what has changed over the last 20 or 30 years? I myself, personally, was probably one of the data point experiencing this change. And I certainly didn't expect I would be doing this when I was at MIT, but I did that in the last 20 years. So the point I'm trying to tell you is, before you dive into any details of mathematics or any concept in finance in this class, just bear in mind, this is a field developed in the last mostly 30 years, or even shorter. And what you really need to ask questions is-- it's not really is it right or wrong in mathematics, is it right or wrong in physics? So, how the concepts are established and defined and verified. Because this is a field-- the transformation about the participants, products, models, methodology, everything are changing very rapidly. Even nowadays, they're still changing. So with that, I will give you some background on how the financial markets actually started, and that's really the history part of this industry. So, when we talk about markets, we know in early days people need to exchange goods. You have something I don't have, I have something you don't have, so there's exchanges. Then it becomes centralized. There are stock exchanges, futures exchanges all over the world where these products will be listed as securities on these exchanges. That's one way of trading, which is centralized. Obviously, in the last 10, 15 years, now we have ECNs, electronic platforms. Trade over-- you know, even larger volume of those trades. So, financial products is really just one form of trading. There are many other ways of trading aside from exchanges. One of them, which is called OTC, is over-the-counter, meaning two counterparties agree to do a trade without really subject to the exchange rules, or the underlying trading agreement does not have to be a securitized product, or standardized, or whatever ways you define it. And the different regions have different exchanges and markets, as well. And they typically specialize in local products, local company stocks, local bonds, and local currencies. So, there are many different forms. So again, what's in common? That's the question you need to ask. Also, you don't know the specifics. And the currencies, money itself, are also traded. And that's where different currencies issued by different countries. So, when we talk about trading stocks-- there are also people trade baskets of stocks, trade groups of stocks together, and that's stock index or indices. So, there are different products. How the stock get listed on the stock exchange? It goes through IPO-- Initial Public Offering process.