2011 IIT Stuart Commencement Speech

I was the Student Commencement Speaker to the Class of 2011 at IIT Stuart School of Business, Chicago.  There were over 800+ people in the audience and it certainly did not help my case!  I had auditioned for this amazing opportunity competing against few others and what won the judges over was the humor and passion in my speech, delivered in an alien accent.  The speech was given on May 14th 2011. I am very thankful to the following people for their advice, comments, and above all, their patience in helping me improve my speech content.  To be frank, the delivered speech was an exponential improvement compared to my first draft!  So the people are: Abhishek Rai & Manisha Verma (Brother & Sister-in-Law), Gary Behrens (Toastmasters Group), Kent Bevel, Siddhesh Barot, Mrityunjay Sharma, Mike Stritch (Office Group), Huilan Jin, Adam Cebulski, Dana Bouche, (College Group/Staff), and of course...my parents!  ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Student Commencement Speech – Madhuresh ‘Maddy’ Rai Class of 2011 IIT Stuart School of Business Thank you Dean Kahalas.  That introduction is surely going on my Facebook! Good Afternoon Mr. Sandor, Board of Trustees, Professors, staff members, emotional guests, non-emotional guests, and above all, the Graduating Class of 2011!   Congratulations!! I am honored to be given this chance today.  My time at IIT Stuart has been ‘transformational’.  See, when I joined Stuart in the Fall of 2008, I was prepared for the technical challenges…but the cultural shift surprised me.  I can still remember how apprehensive I was during my first few months here.  In fact, on my first day in the US, there were 3 things (using fingers for counting) I just could not understand – Every, Single, Word.  I always thought I knew English well… until I met…Americans.  I learned when they smile at you and nod their heads , it usually means they have no idea what the heck you are saying!!!  But I worked on it...  I spent hours on the phone talking to people who just could not refuse me.  Thank you Chase and AT&T customer support!!! Our shared experiences have made us different from the people we were when we came to Stuart. We have learned from each other just as much as we have learned from our professors.  I have always believed we are the mini-ambassadors of the countries and cultures we represent.  I cannot tell you how many times people have approached me to talk about Slumdog Millionaire or their admiration for the Kamasutra.  Through some of you, I have come to enjoy Chinese cuisine.  I can today sing karaoke to a few Korean songs, and I now know enough Spanish to get in trouble!  Friends,  life outside is going to be tough.  There will be no take home tests, no rough drafts, no U-pass <show U-pass>, no student discounts, and worst of all… no free pizza!  We have to start afresh and find our new mentors again.  Yes, we all are unique…just like a million other graduates this year!  So we have to have to find our niche, and excel in the careers we choose.  And, I have absolutely no doubt in your ability to adapt and keep growing for the years to come.  If you ever get bogged down by new challenges… just remember this one thing from my speech… If you have a desire, your limitations won’t stop you.  In fact, they’ll push you harder to improve upon your strengths.  And trust me, you’ll find people around willing to help you…just like I did. I would also like to request you to take some time today and thank your parents or loved ones who have come here to support you on this special day.      My parents could not join me today but they are celebrating some 7,562 miles away in this direction <point in East direction!> I will always cherish my time here and I will never forget how funny you all look right now in these Harry-Potter gowns !!!   <open your arms to show the falling dress>.   I truly believe that Stuart’s education has made us a strategically competitive <make it funningly-sarcastic & look at Dean!> to go out and start new chapters of our lives.   There will be failures along the way, but just remember: Neither success not failure is ever Final! Good luck with your journeys and congratulations once again. Thank you. -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Jump – Diffusion Model

Jump – Diffusion Model 

The famous Black-Scholes model assumes a continuous change in the price of an asset. The prices change continuously to produce a lognormal distribution at any time in future. We know that there is enough evidence to suggest that the well-loved Geometric Brownian motion model for stock price behavior does not work well in practice. In particular, the financial instruments do not follow a lognormal random walk and the jumps can appear at any random time.

A model which has continuous price changes is known as Diffusion Model. When a diffusive model is overlaid with jumps, it becomes a Jump Diffusion Model (J-D from Scrubs!).  

Merton’s Mixed J-D Model does the same combining jumps with continuous changes. It incorporates small day-to-day diffusive movements together with larger randomly occurring jumps. Such an inclusion of jumps allows for more realistic crash scenarios such as what happened on 19^th & 20^th Oct. 1987. In the J-D model, the stock price S_t follows the random process – 

        dS_t / S_t  =  m dt  + s dW_t + (J-1) dN(t) 

where, m is the drift rate, s is the volatility, dWt gives the random walk (Wiener Process Wt), and ‘J-1’ is a Jump function which produces a jump from S to SJ. E[J-1] gives the expected relative jump size. 

        The last term represents the jumps. J is the jump size; a multiple of the stock price while N(t) is the number of jump events that have occurred upto time t. N(t) is assumed to follow Poisson Process, 

        

       P [N(t) = k] =  (λ t) k e– λt / k!  

Where,  

λ  :  average number of jumps per unit time.

k :  average jump size measured as a % of asset price. It is assumed to be drawn from a probability distribution in the model. 

The probability of a jump in time ∆t = λ ∆t. Therefore, average growth rate in asset price from the jump = λ k. Using this, the differential equation above can be simply rewritten as: 

        dS / S   =  (rfr - λ k)  dt  + s dz + dp

The jump size may follow any distribution, but a common choice is a log-normal distribution. It should be noted that the arrival of a jump is random and through the J-D model, it becomes a part of the stochastic differential equation for S. The uncertainty is now produced by 2 sources : 

• The already known s dz from the Brownian motion.
• (J-1) dN(t) corresponds to the exceptional and infrequent events. 

As we can see, when there are no jumps, the J-D model reduces to the Black Scholes Model, in which returns follow the Normal Distribution. A limitation of the J-D model is that it assumes constant volatility in the diffusive component, which results in unrealistic-looking behavior when the jumps are large. Since in reality, s tends to increase dramatically around the time the large jumps occur!

References:

 
D. J. Duffy, Num. Analysis of Jump Diffusion Models using PDE, DataSim
Wolfram Demonstration Projects, Distribution of Returns

Wolfram Demonstration Projects, Option Prices in Merton's J-D Model

J. C. Hull, Options, Futures, & Other Derivatives, Ed. 6th, Chap. 24

Pythagorean Triplets through MATLAB

1. Find Pythagorean Triplets  
                                                                       such that the 3rd number is within a Range

This code was created by me in order to find Pythagorean Triplets such that the Third number of the set lies in the given Range. Interestingly, multiples of 25 - 25, 50, etc are part of more than 1 triplet set and your code should be able to capture the same!

  

(I am taking the range as: 1100 to 1200)

% in MATLAB

% Show all the 3 numbers in the output

% Code created by Madhuresh Rai on Jan. 14th 2010

tic

lowerLimit = 1100 ; % Lower of the given range

upperLimit = 1200 ; % Higher of the given range

tempMat = lowerLimit:upperLimit ; 

% Initialize the matrix with nos. from the given range

initRow = 1 ;

pythTriplets = zeros(10,3) ; % Initializing the answer matrix

for i = 1:1:upperLimit

for j = i:1:upperLimit % Use of 'i' should be noted!

if tempMat ( sqrt(i*i + j*j) == tempMat ) % Logically

pythTriplets(initRow,:) = [i j sqrt(i*i + j*j)] ;

initRow = initRow + 1 ;

end

end

end

disp('The required pair of pythagorean triplets are given below:')

pythTriplets

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