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age 26
visits member for 1 year, 9 months
seen Jun 30 '13 at 15:29

Apr
3
comment Obtaining a consistent covariance matrix for stochastic volatility processes
I thought of using a constant correlation matrix and generating covariance matrix using this and individual volatilities. But I think you should let the correlation changes too when the stochastic volatility changes. For instance, when stock A becomes highly volatile probably its correlation structure breaks down and becomes uncorrelated. In a nutshell, how would you reconcile your estimated volatility models in a covariance matrix.
Apr
3
comment Obtaining a consistent covariance matrix for stochastic volatility processes
I know it should be positive definite. My question is that how should I make sure the stochastic volatility models that I estimate for individual stocks does not disturb positive definite character of the matrix. Assume stock A,B are Garch(1,1) while stock C has constant volatility. As I perceived from Hull book this might make the covariance matrix inconsistent ( non-positive definite).
Mar
29
comment How to derive the implied probability distribution from B-S volatilities?
The first derivative also gives the CDF at 5 points, right? what are the advantages of using second derivative?
Mar
22
comment Credit risk data
Thank you I found them right there
Mar
21
comment Central Limit Theorem and Lévy processes
I am not persuaded yet. For instance, I believe that VG process has first 4 moments and is self-decomposable, so each T can be devided to T/N intervals with characteristic function of power T/N. you can increase N enough to get CLT for any length of T so the process should be gaussian but it is VG. What am I missing?
Mar
21
comment Central Limit Theorem and Lévy processes
Right, I have an elementary understanding of these processes so correct me if I am wrong. The only condition for the iid distributions is having finite variance, so for example VG process has finite variance and it is self-decomposable ( so you can divide it to N iid over a period). Why it is not normal? I mean should not it contradict itself?
Mar
21
comment Central Limit Theorem and Lévy processes
let me reword my question, I am still not convinced in that how central limit theorem fails for all those Levy processes which have not normal distribution ( VG process as an example). I believe CLT needs many i.i.d distributions to be summed. Self-decomposablity says for time T you can break it down to sum of N many T/N distributions. So I say that how sum of these N i.i.d is not normal?
Mar
21
comment Correlation decay in lognormal distribution
Sorry that's right. Variance increase with square root of time.
Mar
15
comment Correlation decay in lognormal distribution
Yes that is completely right. So my question is that GBM is a self decomposable process by itself but integrating such correlation structure makes the joint process sensitive to desicretization. so if you are simulating a spread option the price you get is dependent on how you discretize your model. Is not it right? and
Mar
15
comment Correlation decay in lognormal distribution
I understand the mean of the process changes but why variance? I think below answer is complete and the way I think about it is that assume the prices are equal at the beginning they have different volatilities and some correlation when time passes prices diverge most of the times as they are not perfectly correlated and even in that case variances are different so after a while because the base prices get far and far although the returns are still correlated as past but the prices lose their correlations
Mar
14
comment Correlation decay in lognormal distribution
I looked at the correlation of the stock prices themselves. For returns I believe the correlation stays constant and there is no problem. I just calculated correlation for different lengths of time using the covariance formula of the multivariate lognormal distribution. en.wikipedia.org/wiki/…
Mar
14
comment Correlation decay in lognormal distribution
You are right. I was thinking in a daily basis or Monte Carlo simulation context. So the process is not self decomposable? does not it make problem? because all other parameters and also brownian motion itself is not sensitive on the way you discretize that
Dec
2
comment How to improve the Black-Scholes framework?
Right, it's a really nice method. Beside enabling you to consider any distribution for underlying price, I think you can use a transform to analyize historical data and fit an appropriate characteristic function to the data. However, I am still confused how can you change from an actual measure to a risk neutral one using this method.
Nov
18
comment Missing factor in the factor model
This is a predictive model, I am locked to the factors are available in the preceding period. However, I added index returns it could not help the model as I expected.
Nov
18
comment Missing factor in the factor model
send me your contact if you would like to take a look at the data. They are monthly returns of S&P100.
Nov
17
comment Missing factor in the factor model
Right John. I introduced N dummy variables for each period to isolate the time-factor, R squared increased from 0.1 to 0.22 which confirms your hypothesis. I also was thinking to take a shorter period of time. Right now I am running the model for 43 months ending this October, but this force the Beta to be stationary over almost 4 years, which might not be necessary in practical usage of the model. Do you have any comments. about the missing factor, I have no idea how to identify that factor, I should try PCA, but interpreting that factor is another pain in bott.