## Archive for the 'Columbia' Category

Nov 08, 2008 in Book, CFA, Columbia, Copulas, Hedge Funds, Interview Prep, Interview Questions, Investment Banking, Markets, Mathematics, Tech Tricks, Time Series Links

### Applied Functional Analysis

Sep 11, 2008 in Columbia, Free Online Books

This is great, free textbook Applied Analysis by John Hunter, Bruno Nachtergaele
here.Â Â  The book covers the topics:

Metric and Normed Spaces
Continuous Functions
The Contraction Mapping Theorem
Topological Spaces
Banach Spaces
Hilbert Spaces
Fourier Series
Bounded Linear Operators on a Hilbert Space
The Spectrum of Bounded Linear Operators
Linear Differential Operators and Green’s Functions
Distributions and the Fourier Transform
Measure Theory and Function Spaces
Differential Calculus and Variational Methods

### Memorial Day

May 26, 2008 in Columbia, Credit Derivatives

Good grief!Â  Here I am on Memorial Day stuck with two massive assignments in credit derivatives which require simulation in matlab.Â  A friend emailed me about something and I was going through some old notes from a class I took atÂ the University of Chicago (Financial Math program) taught by the illustrious Jack Cowan

As I was going through the notes, I saw some old matlab homework I’d done.Â  I didn’t even remember this, it was some kind of neural network code.Â  And at the top of the homework I had written, “Memorial Day 1999”.Â  Good grief!Â  Here it is 9 years later and I am still doing matlab on Memorial Day.Â  Guess it’s my Memorial Day tradition.Â  Hey, who needs parades and picnics when you can be coding up some matlab simulations.

### Martingale

May 25, 2008 in Columbia, Credit Derivatives

“I’ve never seen a martingale, I never hope to see one.Â  But I can tell you anyhow, I’d rather see than be one.”

Once I finish this massive set of homework for credit derivatives (two days into it and I am only on about item #5 of 15 for one homework, have not even started the second assignment!) I hope I never have to see a martingale again in my life.Â Â  (That’s affine martingale you’ve got there, missy.)Â

### Commencement!

May 23, 2008 in Columbia

Commencement was excellent!Â  Thank you, Columbia and Columbia Video Network!Â  Now on to the PhD…

http://www.columbia.edu/cu/ceremonies/commencement/docs/events/commencement/index.html

### Columbia Online Learning Information Session

Mar 22, 2008 in Columbia

Upcoming Online Information Sessions:
JoinÂ us to find out general information about Columbia Video Network. Sessions are held each week. Sign up for one of the sessions below.
Monday, June 2, 2008, 2:00 PM EDT. Click here to register for the Monday session.

Wednesday, June 4, 2008, 2:00 PM EDT. Click here to register for the Wednesday session.

### Matlab Code for Monte Carlo Simulation of Hedging Strategy

Feb 24, 2008 in Columbia, Matlab

This simple matlab code was for one of the homework problems. I wanted to generate n monte carlo paths, but have each one colored at random. I could modify this to rank order the final values and color accordingly, but was in a hurry to submit it. This code calculates the P&L from hedging at implied volatility but the underlying converges to realized volatility. Â
clf
num_paths = 100; % number of paths to average
hold on
kfrac = 0.95 ; % K = 95% of stock
rf = 0.10; % risk free rate, per annum
sig_i = 0.10; % implied volatility per annum
sig_r = 0.30; % realized volatility per annum
d = 0; % dividend yield, percent
T = 0.5; % time to expiry, years
num_days = 250; %number of days in year
mu = 0; % drift, percent per annum
S0 = 100; % initial stock price
%% assume stock price follows GBM dS = mu S dt + sigma*S*dZ where dZ is a
%% draw from standard normal distribution
hedging_frequency = 1; % hedging frequency in days, so 1 corresponds to daily
dt = hedging_frequency/(T*num_days); %% eg 1/250 for daily over a one year period
t = [0:hedging_frequency:T*num_days];
%% evolve stock price according to GBM
S=zeros(j,T*num_days);
gamma = S; %% initialization
profit = S;
totalprofit = zeros(1,num_paths);
for j=1:num_paths
profit(1,j) = 0;
S(1,j) =S0;
d1 = (log(1/kfrac)+(rf-d+0.5*sig_i^2*T))/(sig_i*sqrt(T));
gamma(1) = exp(-d1^2/2)/(S(1)*sig_i*sqrt(2*pi*T));
for i = 1:T*num_days-1
S(i+1,j) =S(i,j)*exp((rf-1/2*sig_i^2)*dt + sig_i*randn*sqrt(dt));
tau = T*num_days – i*dt;
d1 = (log(1/kfrac)+(rf-d+0.5*sig_i^2*tau))/(sig_i*sqrt(tau));
gamma(i+1,j) = exp(-d1^2/2)/(S(i,j)*sig_i*sqrt(2*pi*tau));
profit(i+1,j) =profit(i,j)+ gamma(i,j)*S(i,j)^2*(sig_r^2-sig_i^2)*1/T*exp(-rf*tau);
end

plot(S(:,j),’Color’,[0.01+.99*abs(rand),0.01+.99*abs(rand),0.01+.99*abs(rand)])
%%title(‘Simulated Stock Price paths by GBM’);
totalprofit(j) = 1/2*profit(i,j);
end
mean(totalprofit)
%%printf(‘Average expected profit = \$%n’,mean(profit))

### Derman and the Volatility Finger

Feb 24, 2008 in Columbia

A downside of listening to lectures on the go is that you can get so caught up in them, you miss your stop.Â  That happened to me the other night when I was so fascinated by a point Derman was making on smile-consistent models that I missed my stop and ended up having to walk home almost 5 miles because I was too stubborn to wait for the train going back to where I could make the right connection.Â

### Another tip for Cramming in that Study Time

Feb 24, 2008 in Columbia

It’s not that I like to multitask but I have to multitask.Â  I don’t want to give up my morning swim, so I ordered a waterproof video iPod case from h20audio so I can study while I swim.Â I haven’t tested it yet but plan on it soon.

### A Sweet Treat

Feb 24, 2008 in Columbia

I just came across this album while – what else – procrastinating instead of studying. It makes a great accompaniment to Derman homework, though. Check it out: www.songsforicecreamtrucks.com.
I guarantee this will put a smile on your face, even in the dead of winter when you are really behind in homework. (What else is new?)