I have to complete an assignment in Rstudio but I'm pretty new to it:
Compute the first order greeks (delta, vega, theta, rho, lambda, epsilon) for a plain vanilla European option using R.
I have generated the code to price the option both with Montecarlo and Binary Tree, but I have no idea how to proceed. On the internet, I found codes to generate the Greeks with the Black-Scholes model, but it's not exactly what I'm looking for.
My teacher suggested doing it with the definition of derivative.
Could someone help me?
Related
Recently I have been trying to use an optimizer to make feature selections for clustering. I need a fitness function to tell the optimizer which feature set is better. So I refer to the criteria mentioned in the book "Introduction to Statistical Pattern Recognition 2nd Ed chapter 10,10.2- Keinosuke Fukunaga". The content is shown below.
I have found a function(ScatterMatrices()) in Matlab to calculate the value J. As shown below.
However, I didn't find any function similar to ScatterMatrices() in Matlab. I would appreciate it if you could help me🙏.
withinSS: Within-class Sum of Squares Matrix
"Calculates within-class sum of squares and cross product matrix (a.k.a. within-class scatter matrix)"
Which is available in the archive Index of /src/contrib/Archive/DiscriMiner
How do I install a package that has been archived from CRAN
I have used the function hw to analyze a time series
fcast<-hw(my_series,h=12,level=95,seasonal="multiplicative",damped=TRUE,lambda=NULL)
By looking at the fcast$model$par I observe the values of alpha, beta, gamma, phi, and the initial states.
I've also looked at the contents of fcast$model$states to see the evolution of all the values. I've tried to reproduce the results in Excel in order to understand the whole procedure.
To achieve the same values of b (trend) as in fcast$model$states I observe that I have to use a formula like the one in the bibliography about the Holt-Winters method:
b(t)=beta2*(l(t)-l(t-1)+(1-beta2)*phi*b(t-1)
But, if in fcast$model$par beta=0.08128968, I find that in order to achieve the same results I have to use beta2=0.50593541.
What's the reason for that? I don't see any relationship between beta and beta2.
I have also found that in order to get the same forecast as the one obtained with the hw function I have to use the following formulas once the data are finished:
l(t)=l(t-1)+b(t-1)
b(t)=phi*b(t-1)
^y(t)=(l(t-1)+b(t-1))*s(t-m)
I haven't found any bibliography on this forecasting phase, explaining that some parameters are no longer used. For instance, in this case phi is still used for b(t), but not used anymore for l(t).
Can anyone refer to any bibliography where I can find this part explained?
So in the end I've been able to reproduce the whole set of data in Excel, but there's a couple of steps I would like to understand better.
Thank you!!
I am trying to fit my data using the fitdist() function from the fitdistrplus package in R. I succeeded using a normal and a lognormal distribution via key words 'norm' and 'lnorm' which I found via searching online.
I was not able to get other distributions working; the help of fitdist() says:
distr: A character string "name" naming a distribution for which the corresponding density function dname, the corresponding distribution function pname and the corresponding quantile function qname must be defined, or directly the density function.
I checked and when entering ?norm or ?norm into the R command line, neither function norm() nor lnorm() is found. This confuses me totally.
When I try for example fitdist(data, 'poisson'), I get the following error message:
Error in fitdist(data$time, "poisson") :
The dpoisson function must be defined
I am somewhat a noob in R, can anybody give a hint?
norm() in R is a different function to compute norms of a matrix, so not directly related to the normal distribution.
?Normal brings up the documentation related to the normal distribution, and you'll see the 4 functions dnorm, pnorm, qnorm and rnorm belonging to this family.
If you look at ?Lognormal you'll see the same convention with the typical 4 functions.
More generally, you can look-up ?Distributions, which links all of them. There you can see that the keyword for the poisson distribution should actually be pois.
I want to estimate the forward looking version of the Taylor rule equation using the iterative nonlinear GMM:
I have the data for all the variables in the model, namely (inflation rate), (unemployment gap) and (effective federal funds rate) and what I am trying to estimate is the set of parameters , and .
Where I need help is in the usage of the gmm() function in the {gmm} R package. I 'think' that the parameters of the function that I need are the parameters:
gmm(g, x, type = "iterative",...)
where g is the formula (so, the model stated above), x is the data vector (or matrix) and type is the type of GMM to use.
My problem is with the data matrix parameter. I do not know the way in which to construct it (not that I don't know of matrices in R and all the examples I have seen on the internet are not similar to what I am attempting to do here. Also, this is my first time using the gmm() function in R. Is there anything else I need to know?
Your help will be much appreciated. Thank you :)
I am trying to manually calculate the standard error of the constant in an ARIMA model, if it is included. I have referred to Box and Jenkins (1994) text, specially Section 7.2, but my understanding is that the methods mentioned here calculates the variance-covariance matrix for the ARIMA parameters only, not the constant. Tried searching on the Internet, but couldn't find any theory. Software like Minitab, R etc. calculate this, so I was wondering what is the way? Can someone provide any pointer(s) on this topic?
Thanks.
arima() will fit a regression model with ARMA errors. The constant is treated as the coefficient of a regression variable consisting only of 1s. So you need the covariance matrix of the regression coefficients which is usually calculated separately from the covariance matrix of the ARMA coefficients. Look at Section 8.3 of Hamilton's "Time series analysis"
One of the nicest things about R is that you can access a lot of the source code to R itself from within the environment. If you simply type arima at the command prompt, you get the high-level source code for the arima() function. I got several pages of code here, when I tried it.
You do miss out on anything implemented internally within the R executable in native code, but often the high-level code tells you everything you want to know.
Perhaps a shift of perspective can solve this problem.
Rather than seeing the constant as something special, just consider the problem without constant and with a variable that is a vector of ones.