1. Introduction, Financial Terms and Concepts

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 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 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 okay is it okay yeah

and uh 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 as you know in this classroom and so last year dr vasily estrella and i i'm by the way i'm jake shaw and that's dr vasily and we were the main instructors last year now we doubled it up to four main instructors uh that's dr peter campston and dr chong bong

lee the reason we doubled up the main instructors is we have newly added math lectures mostly focusing on from linear algebra probability to statistics and some stochastic calculus so give you the foundation to understand the mass will be used in those examples uh in the lecture taught by the practitioners from the industry and the purpose of this course is really to give you a sampling manual to see how mathematics is applied in modern finance and help you to decide if this is a field that you would be uh okay you heard that and uh so

hopefully this will give you enough information to decide this is the field you 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 worked at morgan stanley someone worked at elsewhere and so that's that's really the goal and uh at the same time obviously you will further solidify your math knowledge and learn on a new content and we put the pre-requisite uh about the math part a bit later uh so i will use today's first lectures time to

give you an introduction really to prepare you some basic background knowledge about the financial markets um some terminologies will be used which you may not have heard before so before i get into the introduction i mean 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 and so i know roughly what kind of background and uh where you are so how many undergraduate students are here so i would say eighty percent okay statistics that's a how many graduate students are

here just to verify okay yeah that's about right 20 and uh how many students are in finance and business major just one okay and how many of you are in math major most of you okay how many of you are engineering major okay i feel how many of you actually are from uh uh other universities so okay 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 right 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 and but uh my um i forgot to mention that even that but i'm affiliated with both the math department and the sloan school here so um 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 and the easiest way

is really just to send us emails and which you will find from the class website so anyway today yes yeah we all have mit emails which are listed on the website yep and uh obviously we have offices here you can easily stop by peter and june boone'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 the quiz at the end don't worry it's not a real quiz i'm just going to

ask you some questions you can raise your hand and give your answer but let me start with uh my story this is actually my personal story uh i i want to tell you why i tell the story later but the story actually was in the mid 90s i just left solomon 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 and so i turned around i asked my

desk quant i said where is the vega report okay so let me show you so that's the story so and i'm obviously not going to tell you the story of pi or life of pi right that's not a financial story or the rest of the story alpha beta delta gamma theta which you'll learn from peter and chumbo and varsity's classes so i'm going to talk about vega so so by the way before i tell you the story what's unique about vega on this list it's not a greek letter that's right okay so i turned around

asking mike that's quan as where's the vega report but how many of you actually know what vega is okay a lot of people know so anyway i'm not gonna it's just for the people who haven't heard about before is a measurement about a book or portfolio or position sensitivity to volatility right so what is the volatility which again you will learn more in the rigorous terms what's 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 okay just that's all you need to know right now i'm not going to ask you questions later so my desktop look at me said you know this is supposed to be options trading desk so he looked at me kind of puzzled so instead of answering my question he handed over me a training manual for new employees and new analysts so i opened the trading training manual and looked it through i actually found my answer so actually at the moment stanley this is not called a vega it's called kappa so now remember it's called a

kappa kappa is actually greek letter so further i look at on the same page there was actually a footnote which i copied down so the footnote about why it's called kappa at the at morgan stanley kappa is also called vega by some uneducated traders at the solomon 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 uh call kappa very quickly because i came from solomon brothers and uh i called kappa

in the last 17 years but you will hear people calling the vega obviously probably more people counting the vega but anyway so that's my first day at moon stanley but why did i tell you this story right what point i try to make so this story is actually when you think about it mathematical or quantitative finance is that rather new field a lot of these terms were newly introduced and the pricing model of options as you know right was introduced in at the black shows in the 70s or some of the groundwork maybe down bit

earlier but it's not like finance was a quantitative profession to start with so what we witnessed in the last 30 years was really a transformation of trade of the trading profession coming from mostly undereducated 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 look at the trade you talk to the traders most of them have advanced degrees and quite a few of them have very you know high training in mathematics and computer science

so what has changed over the last 20 or 30 years i mean i myself personally you know was probably one of the data points experiencing this change and you know i certainly didn't expect i will be doing this when i was at mit but i did that in the last you know 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 the right or wrong in mathematics is it right or wrong in physics so how the concepts are established or defined and verified because this is a field the transformation about the participants products models methodology everything are changing very rapidly even nowadays still changing so with that i will give you some background of how the financial markets are actually started and that's really the history part of this uh this industry so when we talk about markets we know in early days right people need to

exchange goods you have something i don't have i have something you don't have so there's exchanges right then it becomes centralized there are stock exchanges futures exchanges all over the world then 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 electro electronic platforms trade over you know even larger volume of those trades so financial products is really just one form of trading and when you think about i mean 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 securitize the product or standardized or you know whatever ways you defined 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 also traded right so and that's where different the uh currencies issued by different countries so when we talk about trading stocks also people trade baskets of stocks trade groups of stocks together and that's stock index or indices so that there are different products now how the stock gets listed on the stock exchange they go through ipo initial public offering process so when a company changes from private to public it goes through this ipo process it's called primary market primary listing and once the stock is listed on exchange and it

becomes traded in the market we call it secondary trading so that's not that after the primary market and the equity or stock is one form of trading or one form of financial products what are other forms loans actually that products are more generic than equity products when you started thinking about what is really the what is really finance is about it's really about someone has money someone doesn't someone has money to land out someone needs to borrow money so that's loan loan is really a private agreement between two counterparties or multiple counterparties when you securitize

them it becomes bonds and uh when you look at bonds every government right issue large sovereign debt the u.s government has large outstanding u.s treasury debt bonds notes bills and corporates have issued a lot of that product as well they borrow money when they need to build a new factory or expand universities borrow money right when mit needs to build a new building you know some of the money will make come from the endowment support some will come from you know some other form of research budget or some will come from you know that financing

right just borrow from the public local governments states right counties even right so they have various forms so that's that product commodities actually you know metal energy agriculture uh products or traded right mostly in the futures format and some in physical format meaning you take deliveries when you actually buy and sell you build a warehouse to take them your you know ship tanks right to store above the ocean and the real estates you buy and sell houses you know 2008 financial crisis if you read about it this has a lot to do with the real

estate market the mortgages and asset-backed securities and so i'm not trying to give you all the definition dumping the information on you but i like you at least you're hearing at once today and then you have more interest you can read on the side so asset-backed securities is when you have an asset you basically issue a debt with the asset backing it and how how do you rate the assets risk level and what's the income stream cash flow and during before 2008 financial crisis as you heard large amount of cmbs commercial basically is a commercial

real estate backed uh you know securities mortgage securities and the residential as well and further of all these you heard probably a lot about the derivative products so that started with swaps options and the structured products you become more tailor-made for either investors or borrowers to structure the products in a way to suit their needs and some of the the complexity of those structured products you know become quite high and the mathematics involved in pricing them and the risk management become rather challenging so let me coming back to the players in the market one large

sector of player one large type of player is really bank so there are essentially after 1933 uh glass-steagall uh legislation there were two main types of banks one is called commercial bank the other is investment bank commercial bank is supposedly you're taking deposits and lend out the money and doing you know more commercial services investment bank supposed to focus on the capital markets raising capital trading and asset management but obviously after 1999 there's a you know the glass-steagall was repealed right there's no longer that some people blame that and probably for a very good reason

for the cause of 2008 financial crisis but i want to tell you how current the investment banks are organized so i mean vasily just mentioned he works in a fixed income right and so banks typically organized by you know institutional business and asset management so within the institutional client business it has typically three main parts fixed income which trade the debt and the derivative products equity trade stocks and the derivative products and ibd stands for investment banking division which really covers corporate finance raising capital listing a stock ipo and merger and acquisition and advisory so

that's that's how banks are organized outside banks other players basically the asset managers are obviously a very big force in the financial markets so the question a lot of people ask is is this a zero-sum game right i'm sure you you heard this many times so in the financial markets some people win some people lose i mean a lot of times it depends on specific products you trade the market you're in it is a lot of times you know pretty net zero but why why do we need financial markets right i mean this this comes

back to what i described before because something existed actually there's a need for it it's really the need to bridge between the lenders and the borrowers that's really coming down to the essential relationship so investors who have money need have better yield or better return better interest in the current environment when you have a savings account you know you don't really earn much at all and so you would have to take more risk to generate more return or you have a longer horizon cds or other type of products or trade stocks right so that's when

somebody has money when you trade stocks you're essentially you know you're buying a stock you give the money somewhere supposedly you know go to the company the company use the money uh you know to generate a better return and for the borrowers whoever needs money they need to have access to the capital right so they obviously different borrowers have different risks some people borrow money never return right so or never generate any returns or never even return the principle and so the trade between lenders and the borrowers is again essentially the main driver of the

financial markets so a few more words about market participants so banks and so-called dealers play the role of market making what is market making so when you or some end user go to the market wants to buy or sell you typically if there's no market you don't really find the match and some of the the products you want to buy or sell may not necessarily be liquid so the dealers step in the middle make your price say okay you want to buy or sell i can tell you you know this stock i make your price

you know 99 cents and that's my bid 95 cents that's my offer right so that's the price i'm willing to buy or sell so that's called they but what the result of the trade the dealer actually takes the other side of your trade so they take principal risk in this case so that's the difference between dealers and the brokers so brokers don't really take principal risks if you want to buy some buy something or sell something if i'm a broker so i don't make your price i go to the market makers i actually put two

people together to kind of a matchmaking make that trade happen so i earned a commission so that's a broker's role so obviously there are individual investors retail investors same meaning mutual funds who actually manage public investors money typically in a long only format meaning their loan means you buy something so you don't really sure sell a particular security insurance companies has large asset they need to generate return generate cash flow to meet the liability needs so they need to invest and the pension funds same thing as inflation goes higher they need to pay out more

to the retirees so where do you get a return right sovereign wealth fund similarly endowment funds they all have this same situation have capital needs to deploy and make better return so there's other type of players hedge funds so how many of you have heard hedge funds okay good almost everyone okay so i'm not the and peter mentioned he used to work at a hedge fund so and um so there are different types of strategies which i will dive into a bit more but hedge fund played a role in the market they basically find opportunities

to profit from inefficient market positioning or pricing right so they have different strategies and the private equity i mean different type of funds they basically look to take a pr invest in companies and uh you know either take them private or invest in the private uh equity forum to hopefully improve the company's profitability and then catch up and governments obviously have a huge impact on the market so we know in the financial crisis government intervened and not only that at the normal market condition government always have a very large impact on the market because they

are the policy makers they decide the interest rate and interest rate curve and the different policies they push out obviously will generate different outlook for the future markets therefore profitability then the corporate hedges and the liabilities when corporates borrow money they create some risk so they need to be sensitive to the market changes so to summarize the types of trading the first type is really just hedging that means you're not proactively adding risk to what you have you already have some exposure let's say just give you an example let's say you borrow money you bought

a house you have mortgage and uh so let's say it's a you know uh floating rate mortgage payments and you're worried about the interest rate going higher right so you can lock that rate in into the fixed rate format or you can find ways to to hedge your exposure or your corporate has a large income coming from europe so you have euros coming in but you're not sure if euro will trade stronger to the u.s dollar in the future or trade weaker right if you trade it will be if you think it will be stronger

you just leave it but if you think it will will trade weaker so you may want to hedge it meaning you want to sell euro and buy us dollars and so that's the hedging type the second type as i mentioned is a market maker so market maker also takes principle risk but the main source of profit is really to earn the bid offer i gave you the example of 90 cents a bit 95 cents offer so that's what the market maker is trying to profit from but obviously they have residual risks sitting on the book

not every trade is matched so how to optimize those group of trades that's what market maker is doing most of the banks dealers are market makers i mean in the new um regulation obviously proprietary trading is some you know expand right and so the third type is really the proprietary trader the risk taker so these are the hedge funds or some portfolio managers they need to focus on generating return and with control the risk so that's where the beta and offer the concept comes in so if you're a portfolio manager i mean some people say

you don't really you know don't worry don't go pick any stocks just by s p 500 index fund you know very cheap you can pay very little cost to do it that's true so but if you want to beat the s p 500 index let's assume we call it s p 500 index fund is asset b so the return of that off b that's the return of that index then you have a portfolio a you you time series of return of you asset a obviously you can do linear regression by your a lot of your

math major here and you can find a correlation between those two time series so that how the two returns are are related in a simplified form so you can say this actually somehow it came out it's supposed to be alpha and a beta but it turned out to be uh you know the the letters but so in the short description beta is really kind of you know just think as uh the correlated move with the the other asset alpha is really the the you know the difference in return uh it's a format you want to

beat smp 500 so you want basically have certain tracking of this index but you want to return more on top of that so let me just go in details of how each type of trade actually occurs so when we talk about hedging i mentioned the currency example let me give you another example a lot of people issue bonds or issue debt so this example i'm going to give you is let's think about australian corporate because interest rate in australia is higher than in japan so typically people like to borrow money in japan because you pay

smaller interest and you invest it in australia you earn higher interest rate so let me ask you a question who can tell me why don't people just do that all day long just borrow from japan and invest in australia then that interest rate i'm giving you an example of a difference is about three and a half percent for the ten year roughly you know ten years uh swap rates why don't yeah go ahead right because you invest in the australia aussie right australian dollar the australian dollar may become weaker to the yen you may lose

all your profit or even more right and further if everybody plays the same game then and when you try to exit you you have the adverse impact of your trade so let's say you you think that's the right time to do it but then at one time you wake up you said huh i think too many people are doing this i want to hedge myself so what do you do yep so you try to lock in right so basically you you sell the australian dollars by the japanese yen or on the interest rate terms you

say you you basically pay the house australian dollar in the swap lag and the receive yen so that in the you this involves foreign exchange trade interest rate swap and the cross currency swap so your answer about currency forward is roughly right but it obviously involves a bit more in actual execution so let's just give you an example even you are not a finance guy you know you work in a corporate you just do input export or building a factory or you know you have to know actually what the exposure is so risk management nowadays

becomes pretty widespread responsibility it's not just of you know the corporate treasury's responsibility so that's on the hedging side obviously if you're um intel for example right you sell a lot of chips uh overseas and your income actually intel does have a lot of overseas income sitting outside the states so the exposure to them is if the exchange rate fluctuates dollar becomes a lot stronger they actually lose money so they need to think about you know how to hatch the revenue produced overseas and uh obviously if you are import exporters that's even more apparent and

if you're in entering the merger deal you one company is buying another you need to hedge your potential currency exposure and your interest rate exposure and whatever is on on the on assets or the liability of the balance sheet you need to have your exposure so we talked about the hedging activity let's talk about a bit of market making so if it's a simple transparent product everybody pretty much knows where the price is right so if you buy apple stock i think a lot of people know pretty much what it is you may even have

it on your cell phone right know where that stock is but if it's not transparent so what do you do so if i instead of asking you where apple is probably you're going to tell me 4.95 today okay yeah but if i ask you instead what is the call option on apple stock in the you know two months time i'll give you a strike let's say 500. right so you're probably less transparent so that market maker comes in to provide that liquidity and then takes the risk they manage the book by balancing those greeks which

i mentioned earlier delta which describes the kind of the linear relationship of this whole book to the underlying stock or underlying whatever currency that's called the delta gamma is really the change of the portfolio take the derivative to the to the delta or to the underlying spot so that's the second order derivative right the delta is the first order so gamma you take so now you have curvature or convexity coming in and theta is really you know on nothing changes in the market nothing changes in your position how your trading book is carrying or bleeding

away money and we talk about the volatility exposure with vega and on top of that what are the tail risks you know how do what other events can actually get you into big trouble right so people use value at risk so you will hear this var concept in some of the lectures and which is also obviously a very important concept and i think peter will uh or tumor would probably peter will teach uh then capital right uh how much capital you're using it becomes a very important issue nowadays and balance sheet again you have asset

your liability how how do you leverage how much leverage you have before the crisis for example a lot of the banks leverage up 40 times meaning when you have one dollar you have a 40 exposure so when the market moves a little you get wiped out that's that's really what amplified in the 2008 financial crisis and how do you measure the the asset in balance sheet when you have derivatives right rather than straightforward notional so a lot of quantitative type of people like to focus a bit more on the risk taking side because people heard

stories about the successful cases of some hedge funds using high math right they generate very impressive returns uh they seem to have an edge so a lot of people focus on trading strategies right so that that's that falls into the category of proprietary trading or risk taking so that you can just simply doing directional trading strategies just go long or sure the stock right that's very simple you know they are the so-called gut traders gut feeling go with your gut you don't even think he said i'm eating i'm eating um you know uh curry today

so i i go long i'm eating rice tomorrow so i go short so this arbitrage arbitrage is really to find the relationships between prices and try to profit from uh those relationship uh missed pricing this is actually very interesting this um not many people focus on arbitrage you know because when a lot of people are gut traders you essentially just watch your own market you don't really care what's going on if you trade gold uh in the states i mean obviously the gold prices happen in asia and in europe matters right so you because you're

trading the same thing if they're not priced the same way you can profit from the difference and uh that's just a simple example but a spot price versus forward price that's a deterministic relationship it's a mathematical relationship if that relationship breaks down you can also profit so there are many examples of mathematical relationship which gives you the arbitrage opportunity i mean the other type is called value trade or relative value strategies you instead of you know think there's a deterministic temporary mathematical relationship you look at the longer term in horizon trying to determine what is

really the underlying value of a particular instrument then trade on the relative value obviously there are successful value investors out there and the systematic trader builds computer models one example is train the following right so just follow the price trend i mean that used to be a effective uh strategy for some time but when a lot of people doing the same thing that becomes much less effective or momentum same things stat up right finding statistics statistical relationship among large number of stocks then you know trade at the higher frequency and fundamental analysis you're really trying

to understand what's going on in the world what is the trade balance what is the earning potential of a you know of a company what's the trade balance of a country what is the policy change what does it mean when federal reserve announced they're going to taper the quantitative easing right what's why stock market sold off in the last couple months especially why stocks in india brazil indonesia sold out more right why is that so you know it goes through those fundamental analysis uh and there are special situations some companies are going through uh particular

uh difficulties assets are priced very cheaply so there are firms out there i mean you probably heard you know bain capital and many others right they focus on these private equity and special situation opportunities so what has what have all these to do with mathematics right where does math come in how do you use math so i want to give you some aspects of that so from my personal experience i joined the market really started working on pricing models so that's the first area so math is very effective because when you your bank your or

your corporate you want to buy some financial instruments you have to know where is the price it's easy to observe a stock in the market but when it comes to more complex products they just take one step full or forward on the complexity which is option you have to know how to press an option so that's where the math comes in right you actually have to be able to solve differential equations to get a you know model price then you obviously adjust to the your assumptions to fit into the market so pricing model which uh

vasily and many of his colleagues can tell you more which is very much a very interesting and challenging area how do you price all these instruments and when i say pricing it's not in the narrow definition of just coming up as a price when you build a pricing model you also generate the risk parameters of these instruments and how do you risk manage them so that comes the second part so math is very useful in risk management which i will give you some uh another quiz questions after this slide when you can see that risk

management itself is very challenging it's not a purely mathematical question but yet math plays a very important role to quantify how much exposure you have then the third is trading strategies again i think a lot of people with mass background or in general people are looking for the so-called holy grail trading strategies just almost like perpetual motion machines right people looking for 100 years ago you just turn it on it makes money by itself you go to sleep you go on vacation you come back you have more in your bank account obviously that's not going

to happen the robe the robo trader a robotic trader is the dream it has its place or its use but it's a fast evolving market you have to constantly you know upgrade your research and uh adjust your strategies there's no such thing you can build and leave it alone it runs for itself forever but i just want to mention that because maybe towards the end of the term you will feel i came up with this brilliant trading strategy i think it's going to make money forever please let me know first so um i want to

leave some time to vasily actually he he can give you some examples of projects of last year's students who actually came to this class and did some real application at morgan stanley but before i hand over to vasily let me ask you some questions i just want to give not really to quiz you just give you the sense how math and intuition and judgment can come into the same place so let me first give you examples i call risk aversion so you you are facing two choices choice a and choice b choice a b you

have 80 chance to lose 500 you have 20 chance to win five hundred dollars it's pretty clear right that's it that's choice a well choice b you basically just lock in you have 100 chance to lose 280 dollars let me ask you for whoever likes to choose a choice a please raise your hand about six out of say let's call it the 50. okay so can i ask you why you think choice a makes sense so i know it's a lower expected value but i i just kind of enjoy right because you don't want to

lock in that 280 loss right that way you still have 20 chance to win so okay uh for the wines raise the hand for choices are there any other reasons same reason okay okay i assume the rest of you will choose choice b unless you neither okay how many of you choose choice b okay choice b okay and are they anybody think neither is right so maybe you have no you have to choose okay no you have to choose okay so either choice a or choice b so let me just talk a little bit about

this again i'm not trying to tell you which one is right but let's just share my thoughts how to look at these why i call risk aversion right so this is a very common human behavior when you go to the market you buy a stock when the stock goes up makes big money the natural tendency for especially someone is new to the market is to let's take take profit let's sell oh i made a thousand dollars i made five hundred dollars let's go you know have a nice meal or you know whatever i buy a

ipad but when the stock loses money what's the natural tendency that's i think natural tendency a lot of people will keep it i think if you have the discipline to get out that's great and that's you know i i mean trading is really all about how where do you how do you risk manage you know have a discipline and how to manage your losses right the natural tendency a lot of people say well i think there's a chance 20 chance to come back i'm going to make 500 more right why do i want to lock

in to stop myself out at 280 right so even though the expected value as a lot of people i think a lot of people said you know you lose expected value which is three hundred dollars in choice a but you would still you know not to choose choice b because they're unlocking the 280 loss again i'm not trying to inject the idea to you of which one is right or wrong but think about it right so that's really the common behavior which mathematically may not make sense but that's a lot of people still would like

to do right and also really when you think about it was depends on your situation and uh if you can let's say you think the market i mean i'll give you the stock example again if you're not purely following the discipline of stop loss but you just think you know the fundamental picture has changed you really don't think the stock is should go up anymore obviously at whatever level you should get out right regardless how much loss you're locking and uh but if you if you think the fundamental story is still very sound you should

think about as if you don't have a position what do you want to do next so but anyway mathematically i just want to see it's actually i think i guess this is mit so many people think mathematically you know you would actually choose choice b because that's low expectation which makes sense but i think if you ask a larger audience i think you probably a lot of people don't really want to choose choice b because they don't want locking the loss now let me change the question a little bit so choice a becomes instead of

the 80 chance to lose now you have 80 chance to win 500 and 20 chance to lose 500 choice b you have 100 chance to win 280 who chooses who would choose choice a again minority of this audience let's say less than 10 percent okay who would choose choice b the rest of it okay all right um can someone uh choose choice a give me a argument why would you yeah um okay yep anyone wants to give me a reason for choice b higher shop yep okay well let me just leave it here again i

think we can talk a bit more along in the class i mean the last day of the class hopefully we have much deeper discussion on this it's not unique the answer okay i think it can go either way i mean as as you said if your bank account balance is let's say you're a freshman student your bank account is uh uh eight hundred dollars your choice will be very different from someone has a hundred thousand dollars in his bank account okay and uh also your risk tolerance right how much you can you can tolerate but

i'm not going to give you say this is right or wrong but with that let me move on and give you some homework so before i give you the homework i want to make a few more comments so do people always learn from the experiences you think you know in science right we collect evidence we build models we first understand the physics we build mathematic models then we verify in physics doing experiments but is that the same investigation process process in finance i mean market cycles are typically very long but people tend to have show

the memories is so how do people really learn from the experience it's a very interesting question and the very natural tendency is to extrapolate historical experience what happened in 2008 people still remember what happened in 1970s maybe some people still remember what happened 100 years ago right so people tend to extrapolate join conclusions from very recent experience and deterministic relationship versus statistical relationship is very interesting as well when you try to trade on those how do you really build models i mean is the market really efficient right i mean what is really what part is

efficient you know how do you really apply those theories in your day-to-day uh risk management or training activities and sometimes people tend to oversimplify right just say oh i can model this you know this is one important parameter i just take that so i just give you all the warnings that again very young new field and largely often this is art than science so keep that in mind even though we're talking about mathematics in finance math is very powerful and useful in finance so learn the math learn the finance first but keep those questions along

the way when you are learning during this class okay so suggested the homework optional just i mentioned a lot of terminologies uh today go to the course website read what we have put up for the financial glossary right so if you still have things you don't understand make compile your own list of financial concepts which you can search on the web or even ask us but i encourage you to do that it will prepare you well so that's really uh and the read other materials on the on the course web so we got uh maybe

how about this we still got about 15 minutes or 10 or 12 minutes left so i passed it to vasili now maybe we can leave five minutes for some questions yeah okay yeah just mention that that apple trade is now at 494.4 when you were saying it was at 88. all right so yeah just a couple examples well first of all no offense to a few people who wear who wear but i just wanted to to give an example of uh yeah thanks because he was working in in our group and it just will give

you an idea of what uh what a little bit of an idea what what we will be talking about and what actually we do in the daily life or uh what an intern or somebody who comes to work in this industry could do and one project is which tushan worked was on estimating uh the noisy derivative the derivative is called delta delta is usually a first derivative to a function and as we'll see in the class quite often to to obtain a price you you do it through monte carlo meaning running a lot of pass

and then averaging along along them so it is statistical methods so obviously there there is a noise to to your answer every time so if you want to to differentiate this function and get the derivative uh then this derivative will be quite noisy and so instead of getting the the true derivative you might obtain something quite different from two derivative just because there is a confidence interval around any any point and obviously there is a trade-off here as well because you can run more paths throw more computational power and which will reduce your confidence interval

you you will know uh better where where you are more precise uh or the other uh solution could be if you know that your your function is not too concave and reasonably flat you might move uh the uh do the numerical differentiation on wider interval basically reducing the significance of the error right and you would hope to arrive to a better approximation so obviously there is somewhere balance and the question was uh how uh is there an optimal shift size to obtain to to get the derivative and that's what oh oh oh the slight good

corrupted right uh so the oh there was a quite a bit of mathematics involved and minimization and optimization there was an answer and that's actually what we finally arrived at and that's some some two example but still it shows you that if you use constant size and not optimal size that that would be your numerical derivative of this of this blue function while the uh while if you use the optimal shift size which which duration computed it would be much smoother and much better so that's one example uh and that's what he did and we

actually are implementing it in our systems and plan uh plan to use it in in practice another project uh was actually quite different and it was about electronic trading and basically uh how to better predict prices of uh of cro of currencies and exchange rate funny enough it was on ruble uh ruble us dollar because it was actually aimed for for our moscow office uh and um basically what we had we had the noisy observation of broker data uh and they it it was not it was coming on a different non uh on uniform times

basically at random times so uh we decided to use kalman filter and um to uh and uh to study how it can predict and yeah that's one of uh of the nice graphs dusan produced which which again uh will be we will use this the strategy and this the column filters which he constructed in our in our e-trading platform in moscow all right so uh that's just a couple of examples which i wanted to give you and as a preview what we will be talking in the class uh they uh just remind so the website

is fully functional uh i put syllable we put syllables there a a short list of literature uh the we will be posting a lot of materials there uh most probably mostly most lectures will be published there jake's slides are there already so uh any questions uh handbag uh there's some signup sheets right so we like to get your emails so we can uh put you on the website for the further announcements but you can also you know add yourself yes i believe but it's probably easier if you put your email on the signup sheet so

we can uh yeah but but please please visit and and sign up yeah because there will be announcements to the class all right thank you very much