Statistical & Financial Consulting by Stanford PhD
CASE STUDIES

Below are excerpts from several projects addressed lately. The projects are chosen to give an idea of the span of my consulting activity. The projects differ in complexity and pertain to different areas of statistics and finance. Each time the formulation of the project and the provided solution are heavily rephrased and cut to preserve client's confidentiality, unless posting the original version is authorized by the client. Unfortunately, the most interesting projects cannot be exposed, as the clients prefer to keep them fully confidential. Most of the work done for financial companies and online businesses falls into this category.

After browsing through the case studies, please make sure to read the detailed description of the services offered in the areas of statistical consulting and financial consulting: home page, types of service, experience and payment options.

FINANCE, NEW YORK

It is well-known that the dynamics of many financial time series exhibit discontinuities. Relationships between the key factors which are true today may not be true tomorrow. The moments when the key relationships change are called the times of "structural change". Apply the Hidden Markov Model methodology to identify the structural change moments for the USD/EUR exchange rate. The analysis must be exploratory and robust. As such, it should not employ very complicated models relying on too many assumptions.
Solution (includes analysis in Matlab)

STATISTICS, HOUSTON

Compare performance of several well-established model selection methods. The methods are lasso, forward / backward stepwise selection based on p-values, forward / backward stepwise selection based on Akaike information criterion, forward / backward stepwise selection based on Bayesian information criterion and forward / backward stepwise selection based on cross-validation. Use several performance metrics including root-mean-square error and percentage of correctly identified true predictors.
Solution (includes analysis in R)

MEDICINE, NEW YORK

Using the data on more than 8,000 patients, determine if a particular type of treatment helps in reducing the hemoglobin A1C level in human body. High level of hemoglobin A1C is associated with diabetes.
Solution (includes analysis in SPSS)

SOCIOLOGY, LONDON

Using the database of more than 1,000 respondents, study a particular characteristic of social activity. Use the wide-spread, informal definition of this characteristic to see how it can be defined in terms of variables in the data set. Split the residents by location and a particular legal status. Perform analysis separately in each of the resulting groups, whenever possible. Determine which factors influence the given characteristic of social activity. As factors consider demographics, family status as well as several indicators of income and intelligence.
Solution (includes analysis in SPSS)

STATISTICS, NEW YORK

Implement estimation of the following nonlinear regression model using a fast and stable algorithm:

$Y = B_1 \Bigl( 1 - \frac{1}{\sqrt{1 + 2 B_2 X}} \Bigr) + \varepsilon.$

Solution (includes Matlab code)

FINANCE, CHICAGO

Price a vanilla put option and compute its Greeks under the CEV model for the underlying:

$dS_t = r S_t dt + \sigma S_t^\alpha dW_t.$

Use the Crank-Nicolson scheme.
Solution (includes Matlab code)

STOCHASTIC PROCESSES, LOS ANGELES

The arrival of new customers is modeled in the following way. Let Xt be a continuous time Markov chain, which occupies state i at time 0. Conditional on all the future dynamics of Xt, process Nt is a Poisson process with intensity λt = r(Xt). Here r() is some non-negative function. Each new arrival of a customer is given by a jump of process Nt... Derive a differential equation for the probability of no customers arriving before time t. This equation can be solved by finite difference methods later on. Solution

STATISTICS IN SPORTS, MELBOURNE

Review a research article on applications of extreme value theory in sports. Solution

Run intervention analysis on the price of stock M: model a function of the price as ARIMA with outliers and interventions.
Solution (includes analysis in SAS)

STATISTICS, PITTSBURGH

If you break a stick uniformly in two places, you will be left with three segments. Write an algorithm for computing the probability that the three segments form a triangle. This algorithm is supposed to employ Metropolis - Hastings ideas and serve as an independent verification of our theoretical calculations. Solution

STATISTICS, SAN FRANCISCO

Implement reduced rank regression as a simple R function.
Solution (includes R code)

MATLAB, BOSTON

The temperature distribution in a thin metal plate with constant temperatures on each side can be modeled using a two-dimensional grid. The number of points in the grid is specified, as are the constant temperatures on the four sides. The temperature of an interior point equals the average of the four adjacent temperatures. Each time the temperature of an interior point changes, the temperatures of the adjacent points change. These changes continue until a thermal equilibrium is achieved and all temperatures become constant... Implement the calculation of the equilibrium temperature in the grid.
Solution (includes Matlab code)

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