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  • 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.