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finance PhD student


Apr
6
comment How to price this option without using BS framework
Two period binomial? If stock goes to H or D, then price of the replicating portfolio is (1 - D) / (H - D).
May
30
comment How to perform risk factor calculation?
I think all of the theories have zero intercepts (i.e., only one risk-free rate)? Empirically you include the intercept to avoid forcing $\alpha_i = 0$ so that you can test if there is a return not correlated with the risk factors.
Nov
30
comment zero-sum active management riddle
(As well, I would guess that the Roll critique of these pricing models is particularly strong in these less-sophisticated markets.)
Nov
30
comment zero-sum active management riddle
@QuantGuy -- Other than the case of value-weighted portfolios and value-weighted market factor (i.e., CAPM), I don't know of a requirement for $\sum_i w_i \alpha_i = 0$ and $\sum_i w_i \beta_i = 1$, where $w_i$ is the value weighting for each portfolio $i$.
Nov
29
comment How to generate a random price series with a specified range and correlation with an actual price?
How? Try AAPL and MSFT. There are about 5000 more.
Nov
18
comment Convexity of BS Equation for Call and Put
My first stop is checking $Call(\cdot, \lambda \sigma^2_1 + (1 - \lambda) \sigma^2_2) \leq \lambda Call(\cdot, \sigma^2_1) + (1 - \lambda)Call(\cdot, \sigma^2_2)$.
Nov
14
comment How to check if a timeseries is stationary?
@Dail -- There are a variety of tests, but Wald tests that all coefficients are jointly zero is probably the easiest. I searched for how to do this in R, but wasn't too successful. You will likely have to grab a text book and code the tests yourself. (I switched to Stata for most analyses because hypothesis testing is so much easier).
Nov
14
comment How to check if a timeseries is stationary?
@SKRX -- Yes, thanks. I should have included more commentary. He asked how to fit a GARCH model in R, so I gave some code. Once he determines the best-fitting GARCH model with ll, ic, and ssr, he can perform joint tests on the GARCH model coefficients.
Nov
14
comment How GARCH/ARCH models are useful to check the volatility?
The plots are helpful, but to determine if the GARCH model fits, you should use statistics. Look at the log-likelihood, sum-of-squared-residuals, and information criteria across various specifications to see which fits best. Then perform joint test of the GARCH coefficients. If you fail to reject that all coefficients are jointly zero, then you don't need a GARCH model.
Nov
14
comment How GARCH/ARCH models are useful to check the volatility?
fitted.values has +/- sigt (why isn't clear to me). You want to plot the positive sigt versus some time index. Something like this: y <- arch_model$fitted.values[, 1] then x <- seq(1, length(y)) then plot(x, y).
Nov
14
comment How to check if a timeseries is stationary?
@Dam -- I will post some code in an answer.
Nov
13
comment Any recommendations for textbooks for an undergraduate course in mathematical finance?
Are MFE/MSCF students not well-prepared? I would guess that you'll find the right level in Shreve's two book series. If these kids are really that tough, then use Duffie's. Although if these kids don't have exposure to the concepts in finance, then you may be best of with Hull's book and beefing up the math where necessary.
Nov
13
comment How to check if a timeseries is stationary?
@Dam -- You can reject the unit root and still have time-varying volatility. Maybe you want to fit an ARCH model?
Nov
13
comment How to check if a timeseries is stationary?
I agree with the Phillips-Perron test. The Augmented Dickey-Fuller test is not robust to the selection of the number of lags. The KPSS test differs from these two tests in its null hypothesis, which is trend stationarity.
Sep
2
comment Garch modelling on Stata
@sheegaon -- Good point. But it's a RTFM answer (or a LMGTFY answer) that doesn't add much to either community. I will see if the QF community closes.
Aug
15
comment How many explanatory variables is too many?
@gsk3 -- But I do see your point, in a specified range of regressors, for your use the multicollinearity isn't the end of the world.
Aug
15
comment How many explanatory variables is too many?
@gsk3 -- Read the next two bullets. Causality doesn't matter in sample, but it does matter out of sample. That slideshow is a good find -- Wooldridge, Cameron & Trivedi, etc, don't devote any attention to multicollinearity.
Aug
15
comment How many explanatory variables is too many?
@gsk3 -- You are right that you must test sub-samples, but the holdout sample won't necessarily catch multicollinearity. Using the ridiculous humidity example, because the humidity at Broadway and 34 is practically the same as the humidity at Broadway and Wall, there are a lot of linear combinations that sum to $\epsilon > 0$. In this example the multicollinearity would be obvious because $\beta_{midtown} \approx -1 \times \beta_{downtown}$, but if you're in the habit of having too many regressors, then it may not be easy for you to identify. You need to test adding & removing regressors.
Aug
15
comment Is there a quantitative finance ranking system for universities?
We will see how the community responds to your rephrasing, but this is likely a better question for advisor (you said you were a PhD student, correct?). Even if someone finds a ranking system, I would take it with a large grain of salt. Rankings for UG/MBA programs work because they have huge numbers of applicants and graduates (and graduates only care about USN&WR rankings), but when it comes to PhD and beyond, it is probably best to know the research and meet the researchers, then make a more subjective decision.
Aug
15
comment How many explanatory variables is too many?
@gsk3 -- And this wouldn't set the upper limit on the number of factors/regressors. I could add humidity downtown and humidity midtown as regressors in my model and "improve" its explanatory power, although these almost certainly have no impact on my model. Because these are collinear, I could get economically and statistically significant coefficients on these factors, even though a change in humidity has no impact on the market.