From gi1242+944 at cmu.edu Tue Oct 19 22:11:55 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Tue, 19 Oct 2021 22:11:55 -0400 Subject: [944] 46-944 Course info and website. Message-ID: Hi All, Just a short message saying that you're registered for MSCF 944, and I've signed you up for the class mailing list. All info about the class can be found on the class webstie: https://www.math.cmu.edu/~gautam/sj/teaching/2021-22/944-scalc-finance1/ (If you lose this link, just Google me, and there's a link from my web page.) I will not use Canvas. For the first week please look at the videos in the Stochastic Calculus Self Study, Modules 1 through 7. Due to time constraints, we will not go over this in too much detail in class, and I will expect some familiarity with probability. Watching these videos will help. Lecture notes: I've posted lecture notes online from the last time I taught this course (2019). Unfortunately since then there were a few changes made to the MSCF curriculum. Thus the beginning of the course will be a bit different from the lecture notes. In a few weeks I will catch up and then follow the lecture notes; though I might not get through all the material. In lieu of updating the lecture notes, I will post slides from my lectures. These slides are a bit different from the standard power-points that are usually used for presentations. They typically contain a few lines of text, and *statements* of problems, not solutions or justification. I will write on the slides by hand during class, and post both the annotated slides and the un-annotated slides. See you Thursday, Best, Gautam -- Q: What kind of ghosts haunt chemistry faculties? A: Methylated Spirits! From gi1242+944 at cmu.edu Thu Oct 21 18:14:28 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Thu, 21 Oct 2021 18:14:28 -0400 Subject: [944] TA Session Tomorrow, and Midterm date Message-ID: Hi All, Reminder: Your TA Shukun will go over the basics of probability, arbitrage free pricing, and do lots of examples of conditional expectation in the recitation tomorrow. It's at 2:00PM tomorrow (Friday), and will be held every week at that time. Also, as I mentioned in class, there is a chance that the midterm will be delayed by a lecture or two, depending on whether or not I have had time to deal with It?'s formula. I will confirm the date on Tuesday Nov 2nd. The notes from class today are online. (It looks like my computer will not connect to the projector, so in future I'll see if I can at least print the slides larger.) GI -- Where there's a will there are five hundred relatives. From gi1242+944 at cmu.edu Thu Oct 21 22:26:18 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Thu, 21 Oct 2021 22:26:18 -0400 Subject: [944] Homework 1 Message-ID: Hi All, Homework 1 is online. It is due one week from today, before the start of class (10:10AM). As I mentioned in class, doing problems is the best way to understand the material. Some of the problems (Q1(f), in particular) will require you to spend some time thinking about it; no formula we know (so far) can be blindly used to get the answer... Please collaborate, and seek out help! Use the homework as an opportunity to learn and master the material. (However be sure you write up your own solutions, independently; and only turn in solutions you understand completely.) Best, Gautam PS: Both of us will have office hours next week, and I will post times on the website later today. -- As far as the laws of mathematics refer to reality, they are not certain. And as far as they are certain, they do not refer to reality. -- Einstein From gi1242+944 at cmu.edu Sun Oct 24 21:09:19 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Sun, 24 Oct 2021 21:09:19 -0400 Subject: [944] Office hours, and references Message-ID: Hi All, 1. Shukun and I will both have office hours Tuesday afternoon on Zoom It looks like this was the only free time that intersects with our schedules and the MSCF schedules... (for the second half of the course, when homework is due Tuesdays, we will change our office hour schedule). The connection info and times are posted on the website. 2. I got the multi-period asset pricing notes from Dima Kramov, and posted them online. 3. Steve Shreve's stochastic calculus notes are also a useful resource; there available to you on Canvas (and one kind soul already posted a link to it on the discussion board). I'm hoping my laptop will connect on Tuesday; but if it doesn't I've made my font sizes bigger so hopefully things are a bit more readable when I print my slides. Best, Gautam PS: If you have any math questions, please use the discussion board. -- Why were the Star Wars movies released in the order 4,5,6,1,2,3,7,8,9? Because in charge of the sequence Yoda was. From gi1242+944 at cmu.edu Thu Oct 28 19:56:44 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Thu, 28 Oct 2021 19:56:44 -0400 Subject: [944] HW2 Message-ID: Hi ALl, Homework 2 is online. It's due one week from today. Solutions to homework 1 will go up after the 24h late deadline has passed (sometime tomorrow). Best, Gautam -- When a clock is hungry, it goes back four seconds. From gi1242+944 at cmu.edu Tue Nov 2 16:28:33 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Tue, 2 Nov 2021 16:28:33 -0400 Subject: [944] Midterm Message-ID: Hi All, To confirm what I said in class today: 1. The midterm will proceed on schedule (Tue Nov 16, lecture 8). I will be able to finish It?'s formula lecture 6, and do a bit of review lecture 7. I'll send the full details of the midterm (with midterms from previous years) after lecture 6, when I have finished It?'s formula. 2. New York students: I usually like to come to NY and spend a week there. But due to COVID I've declined all travel invitations until January. So my apologies -- I won't see you in person this year; but we can Zoom for office hours ?. (Also, when you come to class, there are portions of the room that are not shown to me by default; if you could sit where I can see you, it helps; wherever you were sitting today was good.) Best, Gautam -- We are Pentium of Borg: Division is futile - you will be approximated. From gi1242+944 at cmu.edu Thu Nov 4 14:37:38 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Thu, 4 Nov 2021 14:37:38 -0400 Subject: [944] HW3 + HW1 grades Message-ID: Hi All, HW3 is online, due one week from today. You can view your graded HW1 on gradescope. If you want overall statistics, and a rough indication of where you stand in class, you can view this on the class website. (Click the "your grades" link). Please look over solutions to homework 1; I leave regrade requests open for a week on homework, so in case there was some work of yours that was overlooked, file a regrade request within a week. Best, Gautam -- A conjecture is something that is true but a proof isn't written down. And a theorem is something that is written down and might not be true. From shukunl at andrew.cmu.edu Fri Nov 5 19:02:12 2021 From: shukunl at andrew.cmu.edu (Shukun Long) Date: Fri, 5 Nov 2021 19:02:12 -0400 Subject: [944] A minor mistake in today's recitation Message-ID: Hi all, Sorry I made a silly mistake in today's recitation when I was trying to give you an intuition that finite first variation implies zero quadratic variation. Please see the correction in the attached pdf file. I appreciate the student who pointed this out after class, and sorry again for confusing some of you. Best regards, Shukun -------------- next part -------------- An HTML attachment was scrubbed... URL: -------------- next part -------------- A non-text attachment was scrubbed... Name: correction.pdf Type: application/pdf Size: 91894 bytes Desc: not available URL: From gi1242+944 at cmu.edu Tue Nov 9 09:47:42 2021 From: gi1242+944 at cmu.edu (Gautam Iyer via mscf-944) Date: Tue, 9 Nov 2021 09:47:42 -0500 Subject: [944] Midterm Message-ID: Dear All, Your midterm will be Tue Nov 16th, in class. It will be closed book, and cover everything up to and including It?'s formula. (I will finish this up in class today and only do examples / review before the midterm). The exam will cover everything we have done so far in class. I will not ask proofs. The proofs I do in class, or ask you to do on the homework are only to help you understand the material better. All questions on your midterm will ask you to "compute something", and will have a clear answer (either numerical or symbolic). I have put up the midterms from the last two years online. As you can see from them, there are a few questions that you can do directly from the basics (compute conditional expectations, It? decomposition, quadratic variation, etc.). There is usually a question or two that requires you to think creatively before you can do the computation. Please note: In previous years, I did not do the Binomial model in this course. Accordingly previous years exams do not have the Binomial model on it; your exam may have a question involving the Binomial model. I will put an *OPTIONAL* homework up on Thursday; this only has practice problems to help you get a feel for using It?'s formula and related material. I have also put up solutions to previous years midterms. I strongly recommend you DON'T look at them, and try the midterms yourself in a mock exam setting, and then check your answers later. In previous years many students underestimated the midterm, partly because looking at previous midterms in the comfort of your own home, with no time limit, access to solutions, friends who know the material and the internet makes it easier. Your midterm will be closed book, in class with a time limit. I hope my email is sufficient warning that you won't underestimate the midterm. Best, Gautam -- They say hard work never hurt anybody, but why take the chance. From gi1242+944 at cmu.edu Tue Nov 9 15:50:51 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Tue, 9 Nov 2021 15:50:51 -0500 Subject: [944] Midterm (calculator policy) In-Reply-To: References: Message-ID: Hi All, This year I will allow the use of calculators on the midterm. (I have never allowed it in the past, as you typically don't need it for the continuous time problems. But it's helpful to have for the discrete time problems.) My policy will be the same as what you had in Fixed income: You may use a calculator on the exam. However, no devices that have electronic communications capabilities are allowed (includes phones, watches and laptops). No calculators that can store or read PDF files / word documents are allowed. Best, Gautam -- Name one nice thing about Windows? It doesn't just crash, it displays a dialog box and lets you press 'OK' first. From gi1242+944 at cmu.edu Thu Nov 11 19:48:31 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Thu, 11 Nov 2021 19:48:31 -0500 Subject: [944] Optional homework Message-ID: Hi All, I put up an optional homework. It is never due. The problems are good practice on many of the concepts you've learned so far. Since previous years exams did not have any problems on the discrete time models, I included a few problems on this. I put up answers to some of those problems. No solutions or answers will be given to the others, as some of them will be on your next homework. Best, Gautam PS: As usual, solutions to HW3 will post sometime tomorrow (after the late deadline passes) -- FATAL ERROR! SYSTEM HALTED! - Press any key to do nothing... From gi1242+944 at cmu.edu Fri Nov 12 20:22:05 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Fri, 12 Nov 2021 20:22:05 -0500 Subject: [944] Midterm (office hours) In-Reply-To: References: Message-ID: Hi All, Next week there will be no office ours on Tuesday. Instead we will have office hours at the following times: 11:45AM--12:45pm (Gautam) 5:00PM--6:00PM (Shukun) Both office hours will be on Zoom. If you've tried a problem and want to know where you've gone wrong, either scan it in and share screen, or join the Zoom call with a tablet. Finally, as a reminder: Please post all math questions on the discussion board, and not email. Best, Gautam -- He who laughs last is at 300 baud. From gi1242+944 at cmu.edu Fri Nov 12 20:31:25 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Fri, 12 Nov 2021 20:31:25 -0500 Subject: [944] Midterm (office hours) In-Reply-To: References: Message-ID: Clarification: Office hour times are on MONDAY. GI On Fri, Nov 12, 2021 at 08:22:05PM -0500, Gautam Iyer wrote: > Date: Fri, 12 Nov 2021 20:22:05 -0500 > From: Gautam Iyer > To: mscf-944 at lists.andrew.cmu.edu > Subject: Re: [944] Midterm (office hours) > > Hi All, > > Next week there will be no office ours on Tuesday. Instead we will have > office hours at the following times: > > 11:45AM--12:45pm (Gautam) > 5:00PM--6:00PM (Shukun) > > Both office hours will be on Zoom. If you've tried a problem and want to > know where you've gone wrong, either scan it in and share screen, or > join the Zoom call with a tablet. > > Finally, as a reminder: Please post all math questions on the discussion > board, and not email. > > Best, > > Gautam > > -- > He who laughs last is at 300 baud. > _______________________________________________ > mscf-944 mailing list > mscf-944 at lists.andrew.cmu.edu > https://lists.andrew.cmu.edu/mailman/listinfo/mscf-944 -- Mac OS X. Because making Unix user-friendly is easier than debugging Windows. From gi1242+944 at cmu.edu Mon Nov 15 13:24:15 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Mon, 15 Nov 2021 13:24:15 -0500 Subject: [944] 2016 midterm, and office hour notes Message-ID: Hi All, I just posted the notes from office hours today online. Some of you asked about solutions to the 2016 midterm. I'm not sure I have permission to release them -- but instead I wrote down the answers to all questions at the end of my office hour notes. GI -- Top Ten New Intel Slogans For The Pentium: 1.9999103517 We're Looking for a Few Good Flaws From gi1242+944 at cmu.edu Tue Nov 16 19:37:28 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Tue, 16 Nov 2021 19:37:28 -0500 Subject: [944] Midterm, office hours, etc. Message-ID: Hi All, 1. For future exams I've asked MSCF to keep a few spare calculators handy, just in case you forgot yours 2. Your next homework is online. It is due Tue 11/23. (All subsequent homework will be assigned Tuesday and due the following Tuesday.) 3. Because of the change in the homework deadline, we are moving our office hours: Monday 11:45PM--1:00PM (me, on Zoom) Monday 5:30PM--7:00PM (Shukun, on Zoom) 4. Your midterm and solution are online. We hope to have it graded by the weekend, and I'll post more about grades once it's graded. 5. There were a few common mistakes we found so far; there were also a few tricks that some of you didn't use. I can go over them on Friday (instead of the recitation) if you are interested. If yes, please express your interested here: https://zym.math.cmu.edu/t/zoom-session-friday/749 (Note -- there will be no recitation Friday; and if I hold a Zoom session it will be at 1:30PM and not 2:00PM.) GI -- "He's BREAD, Jim." -- Dr. McCoy after a tragic transporter accident while visiting planet Pillsbury. From gi1242+944 at cmu.edu Thu Nov 18 17:57:42 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Thu, 18 Nov 2021 17:57:42 -0500 Subject: [944] HW deadline, and error at end of class Message-ID: Hi All, A few students requested moving the homework deadline in order to allow more time between office hours and the due date (and to avoid conflicts with your other deadlines). Accordingly I can change all following homework to be due Wed 8PM instead. Please note -- I have another appointment after class on Tuesdays, so I have to leave by about 12:05. So if you have questions about the homework due Wednesday you may not be able to ask me on Tuesday. (But you can during office hours on Monday, of course.) In class today I made a mistake at the end: For the proof of theorem 8.4, you need to start out choosing 1. X_0 = f(0, S_0) 2. ?_t = ?_x f(t, S_t) (I made the second choice in class, but not the first.) Now if you follow through the calculations at the end you get d( e^{-rt} f(t, S_t) ) = d (e^{-rt} X_t ) Combined with our choice 1, this implies X_t = f(t, S_t). Setting t = T implies X_T = f(T, S_T) = g(S_T), which is the payoff of the security. This implies X is a replicating portfolio. I will go over this again at the beginning of class Tuesday. (Hand written notes online have been corrected, but the video will be wrong obviously.) Tomorrow at 1:30 I will go over parts of the midterm / talk about general shortcuts. I have until 2:30, so if you have questions tomorrow feel free to ask. (Note this will be on Zoom, and not in person) Best, Gautam -- When a clock is hungry, it goes back four seconds. From gi1242+944 at cmu.edu Sat Nov 20 12:48:29 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Sat, 20 Nov 2021 12:48:29 -0500 Subject: [944] Midterm grades Message-ID: Hi All, Your midterm is now graded, and your scores should be accessible to on the class website. The grade cutoffs are APPROXIMATELY: 20: Approximately bottom end of A- 15: Approximately bottom end of B- 10: Approximately bottom end of C- 5: Approximately bottom end of D Please note that the quartiles, and your percentile rank are for your information only; I do not use them to assign letter grades. There were 12 students who got a perfect score, which is excellent. VIEWING YOUR MIDTERMS: Pittsburgh students, please ask Sara/Mike. NY students, please ask Diffy. Remote students: We will email you next week. Important: You may view exams in the respective office (or scan them on your phone). However, following MSCF policy, if you take them out of the office you may not request regrading of any problems. REGRADING POLICY: If you believe a particular question has been graded incorrectly, then you must do so in writing by email, or by leaving a post-it note on the front of the exam indicating which question you want re-graded. Please do NOT include any explanation or message. Your grade will be solely based on our interpretation of what is written on the exam, and not on any explanation you provide outside the exam. We will cover up the original grade, and independently regrade the requested question. The new grade will replace your old grade, EVEN IF IT IS LOWER. I strongly recommend you read and understand the solutions posted online before requesting a regrade, because your grade could become lower. Best, Gautam -- 665.9238429876 - Number of the Pentium Beast From gi1242+944 at cmu.edu Mon Nov 22 10:37:13 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Mon, 22 Nov 2021 10:37:13 -0500 Subject: [944] Reminder: New office hour times In-Reply-To: References: Message-ID: Hi All, Because of the new HW dates (Assigned Tue, Due following week), we moved our office hours: Monday 11:45PM--1:00PM (me, on Zoom) Monday 5:30PM--7:00PM (Shukun, on Zoom) Also, today I will have to leave early (12:40) for a doctors appointment. Best, Gautam -- He often broke into song because he couldn't find the key. From gi1242+944 at cmu.edu Tue Nov 23 16:20:06 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Tue, 23 Nov 2021 16:20:06 -0500 Subject: [944] HW6 Message-ID: Hi All, Homework 6 is online. Due to the change in due dates, if you're still doing homework 5 (due tomorrow), please be aware that it's not in "current homework" anymore. Homework 6 is due Wednesday next week. You will have one last homework assigned Tuesday after break. Solutions to HW5 will post sometime Thursday (after the late deadline). Best, Gautam PS: Those of you reviewing your exam and requesting regrades: Please do so by Friday next week. I plan to collect all requests on Friday next week. -- 'Common' Proof Techniques: 14. Proof by eminent authority -- "I saw Karp in the elevator and he said it was probably NP-complete." From gi1242+944 at cmu.edu Tue Nov 30 19:52:44 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Tue, 30 Nov 2021 19:52:44 -0500 Subject: [944] Last homework Message-ID: Hi All, In light of your final Dec 9th, I shortened the last homework by making two problems optional. I am making it due before class on Tuesday Dec 7th, and removing the 24h late period for this homework. This way I will post solutions immediately on Dec 7th. If you are still doing HW6 (due tomorrow), please note that the "current homework" link on the website now points to HW7 (due next week). On Thursday class, I will post previous finals and solutions. I will construct the risk neutral measure on Thursday; and will spend Tuesday next week doing a review. I will also see what we can do in terms of extra office hours next week before the final and send you an email. Best, Gautam -- Reading while sunbathing makes you well-red. From gi1242+944 at cmu.edu Thu Dec 2 16:21:18 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Thu, 2 Dec 2021 16:21:18 -0500 Subject: [944] Final + end course notes Message-ID: <20211202212118.GD19279@andrew.cmu.edu> Hi All, 1. In recitation tomorrow, Shukun will re-derive the Black Scholes formula from the risk neutral pricing formula. (This was the last theorem I didn't have time to prove.) He'll also do some other examples of multi-dimensional It?, + risk neutral pricing / etc. 2. Please fill out faculty course evaluations, I value your feedback. Two incentives: 1. If 75% of you fill out course evaluations, I will release your grades as soon as they are available. If not, I will only release them at the very end of the grading period. 2. The steering committee has asked that we allot time *DURING CLASS* for you to fill out course evaluations; If the response rate is less than 75% by Tuesday, I will allot time DURING THE REVIEW SESSION for you to fill out FCEs. Here's the link to the FCE site: https://cmu.smartevals.com 3. Tuesday next week will only be a review. Previous years finals and solutions are online. I'll put up a few review problems, and I'll go over as many as I have time for. I will stay until 12:30 after class Tuesday if anyone still has questions/stamina. We will hold the same office hours on Monday next week. Best, Gautam -- 'Experience' -- A comb life gives you after you lose your hair. From gi1242+944 at cmu.edu Mon Dec 6 19:18:57 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Mon, 6 Dec 2021 19:18:57 -0500 Subject: [944] Review session + FCE reminder Message-ID: HI All, 1. If you tried the 2016 final from last years website, I wrote the answers to it in the notes from today's office hours. (I'm not sure I have permission to host complete solutions.) 2. I put up a few problems for tomorrows review session; feel free to give some of them a shot. I might not have time to get through all, so if you have preferences on which to do, just let me know in class. (I'll also add a problem or two on discrete time models later.) 3. Please fill out FCEs, I value your feedback. Incentives: a. Warm fuzzy feeling that you helped me ?. b. If there's a 75% response rate you get grades early. c. I'll stop sending reminders ? Note, the steering committee has asked us to give time *during class* for you to fill out FCEs. If the response rate is below 75%, I will give you 15 minutes during the review session to fill FCEs, leaving us even less time for review... Best, Gautam -- We are Pentium of Borg: Division is futile - you will be approximated. From shukunl at andrew.cmu.edu Tue Dec 7 16:35:04 2021 From: shukunl at andrew.cmu.edu (Shukun Long) Date: Tue, 7 Dec 2021 16:35:04 -0500 Subject: [944] Extra Office Hour Message-ID: Hi all, I will hold an extra office hour 2pm - 3pm tomorrow. The Zoom link is the usual one. Best, Shukun -------------- next part -------------- An HTML attachment was scrubbed... URL: From gi1242+944 at cmu.edu Wed Dec 8 15:01:22 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Wed, 8 Dec 2021 15:01:22 -0500 Subject: [944] Memorizing formule / formula sheets Message-ID: <20211208200122.GI22727@andrew.cmu.edu> Hi All, A few of you have asked me about having a formula sheet, and whether we need to memorize formula X for the final. 1. I was asked by a steering committee member a few years ago to make the final closed book, no formula sheet. This is because you can't take formulae sheets to interviews. (If this is no longer relevant, I'll change my policy based on the steering committees recommendation.) 2. Please use your best judgement on what formulae you memorize / not. There are quite a few formulae we've used many times in class. I recommend either knowing them, or knowing something that allows you to derive them quickly. The more of them you know thoroughly, the better equipped you will be for the final. Best, Gautam -- Asked if he believes in one God, a mathematician answered: "Yes, up to isomorphism." From gi1242+944 at cmu.edu Wed Dec 8 22:27:52 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Wed, 8 Dec 2021 22:27:52 -0500 Subject: [944] Final time Message-ID: Hi All, I thought I would send a reminder letting you know that the final is at 10:00AM (not 10:10AM). Good luck, and see you tomorrow. GI -- Your mouse has moved. Windows must be restarted for the change to take effect. Reboot now? [ OK ] From gi1242+944 at cmu.edu Tue Dec 14 16:13:53 2021 From: gi1242+944 at cmu.edu (Gautam Iyer) Date: Tue, 14 Dec 2021 16:13:53 -0500 Subject: [944] Final grades Message-ID: Hi All, Your final is graded and the overall performance was very good. Your grades will be available on S3 shortly, and your score on the final will be available on canvas. The approximate grading scale for the final was: 85%: Approximately bottom end of A- 65%: Approximately bottom end of B- 50%: Approximately bottom end of C- I computed your final grades using the weights described on the class website, after normalizing your exam/homework scores, and assessing any late penalties. Please ignore any percentile ranks / statistics you see on Gradescope / the class website. They are for your information only; I do not use them. Seven students got a perfect score, which is excellent! Everyone who got lower than a B- will have a chance to increase their grade (up to a maximum of B- ) by taking the makeup final / second chance exam. I will contact these students via email later tonight. VIEWING YOUR FINALS: Pittsburgh students: They will be with Sara in the MSCF office. NY students, it will be in Diffy's office. You may view them in the respective office, or scan them on your phone. However, following MSCF policy, if you take them out of the office you may not request regrading of any problems. I suggest you take a picture of your exam, and view it at leisure, leaving your original with Diffy/Sara. REGRADING POLICY: If you believe a particular question has been graded incorrectly, then you must do so in writing by email, or by leaving a post-it note on the front of the exam indicating which question you want re-graded. Please do NOT include any explanation or message. Your grade will be solely based on our interpretation of what is written on the exam, and not on any explanation you provide outside the exam. We will cover up the original grade, and independently regrade the requested question. The new grade will replace your old grade, EVEN IF IT IS LOWER. I strongly recommend you read and understand the solutions posted online before requesting a regrade, because your grade could become lower. Overall, I hope you enjoyed this Mini as much as I enjoyed interacting with you, and I wish you success in your future careers. Of course, this isn't entirely a selfless wish -- since one of you will almost certainly be working for a bank that manages my retirement someday... :) Best, Gautam -- 'Dopeler Effect' -- The tendency of stupid ideas to seem smarter when they come at you rapidly.