QuantCandy's Blog

Sundaram and Das, Derivatives
Contains:
Chapter 1: Futures and Options: An Overview
Chapter 3: Pricing Forwards and Futures I: The Basic Theory
Chapter 7: Options Markets
Chapter 8: Options: Payoffs & Trading Strategies
Chapter 9: No-Arbitrage Restrictions on Option Prices
Chapter 10: Early Exercise and Put–Call Parity

Here are some old, but hopefully still good, tutorials I wrote while teaching Mathematica. They are in pdf format, but if you want the notebook format, just email jennifer@quantcandy.com

Introduction to Mathematica – A Tutorial 

Illuminating Numerical Analysis Using Mathematica 

Mathematica and the Glass Tempering Process This is from a talk I gave at a Mathematica conference from my PhD research. 

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.

 
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))

A downside of listening to lectures on the go is that you can get so caught up in them, you miss your stop.  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. 

It’s not that I like to multitask but I have to multitask.  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. I haven’t tested it yet but plan on it soon.

It’s now February 22.  The CFA exam is 104 days away, according to the Schweser Countdown Clock.  If it really takes 250 hours to prepare, I have some serious work to do.   My strategy, since I already know the material but just need exam practice, is to buy the Schweser Secret Sauce, videos and Question bank.  I’ll study in between courses, work and all the rest of it.

Here are some interview questions:

Time Series
What is a stationary time series?
How do you handle non-constant volatility?
What is a logistic regression?
What is a moving average process?

See notes here and here

Credit Derivatives
I was on the subway the other day reading my textbook on Credit Derivatives and a random stranger asked “What is a Credit Derivative?” I thought this would make a great interview question, as I had about 60 seconds to try to come up with an answer before my stop.

Why do companies have their debt rated, but not their equity?

If you need help preparing for finance interviews, the following links may be helpful.

Vault Guide to Finance Interviews 7th Edition

Vault Finance Interviews Practice Guide, Daniel Montoya

Vault Guide to Advanced Finance and Quantitative Interviews

Heard on the Street: Quantitative Questions from Wall Street Interviews

Vault Guide to Resumes, Cover Letters & Interviewing

How to Ace the Brainteaser Interview, John Kador

What should you expect from a professional resume writer?
Deb Wheatman of Vault.com, ranked #1 in resume preparation services, says the following:

How can a résumé writer help you? Can someone learn enough about your background, skills and competencies in a phone conversation to write a compelling document that reveals your strengths and positions you for a new position with more responsibility making more money? Well, the answer is yes.

Writing a résumé is a skill requiring the ability to extract information about a client’s background and achievements, and conveying that information in a compelling way. A qualified writer should be able to quickly understand the contributions a client has made throughout their professional career to develop a strong, results oriented résumé. It should be noted however, that the responsibility for creating a winning document lies as much with the client as it does with the writer. The client must be able to articulate clearly and reference information that will enable the writer to draw substantial and meaningful conclusions. In turn, the writer should be able to ask the right questions, and paint an interesting picture. The process of writing a résumé should be interactive; that is, the client should be able to convey their experiences, and the writer should be able to provide an engaging portrait that will generate interest on behalf of a potential employer.

A phone or in-person consultation should take place so the writer and client are comfortable with each other. The client is responsible for conducting something of a fact-finding mission before engaging the services of a writer. I always recommend that an initial discussion take place to ensure the writer is familiar with a client’s industry. The ability to understand a client’s needs and professional experiences will facilitate an easy interaction, and establish a trusting relationship. The client will feel more secure that the writer understands his / her professional goals throughout the writing process.

There are no miracles. A writer can only create a winning document with the help of their client. The relationship a writer has with a client needs to be a partnership to ensure success – and ultimately enable the client to ‘feel the love’ when using the résumé as part of their overall job search strategy.

What should you expect from your writer? A number of things. A client should expect a thorough interview, an interactive process, and a well-written document that is free of spelling errors; grammatically correct; succinct, and interesting. It should not take two weeks to write a résumé. From the time the conversation with the client is held, the initial draft document should be produced two or three days later. The process should be iterative; the client should be given the opportunity to review the résumé, and have a follow-up call with the writer if necessary to make any corrections or adjustments. Naturally, it is best to establish the writing plan up front so there is an understanding of the process and expectations are set accordingly.

In such a competitive environment, a candidate with exceptional skills and a mediocre résumé will not be called for an interview, while that same candidate with a résumé that details accomplishments and skills will be well positioned to get the calls.

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?)

This term has come up in more than a few classes at Columbia.  I remember hearing it in the time series and continuous time finance courses, and now it rears it’s ugly head in Derman lecture 2, where he quotes from Fischer Black.   At this point I just had to know:  what IS a stylized fact?  Either something is a fact, or it is not.  Isn’t it? 

 This link has a good definition, and this one from Wharton  refers back to Rama Cont (prof for another class I am taking now.)  According to the first link, “That’s not true, but it’s a stylized fact.”.  So a stylized fact need not have high correlation with truth.  I think I get it …. Pats finished with a 19-0 season would be a stylized fact.  I guess.