# LK: Likelihood factorization of Lin and Ke (2011) - LK... In InfoTrad: Calculates the Probability of Informed Trading (PIN)

## Description

The function calculates the likelihood factorization of Lin and Ke (2011) and computes paramaters for estimation of PIN value.

## Usage

 `1` ```LK(data, fixed = c(FALSE, FALSE, FALSE, FALSE, FALSE)) ```

## Arguments

 `data` Data frame with 2 variables `fixed` Initial values for parameters in the following order: alpha, delta, mu, epsilon_b, epsilon_s

## Details

In order to use LK's return in optimization functions, please omit second argument. With this way, LK will return a function instead of a value. Moreover, argument for data must be a data frame with 2 columns that contain numbers. Not any other type.

## Value

 `LK_out` Returns an optim() object including parameter estimates for the likelihood factorization of Lin and Ke (2011)

## Warning

This function does not handle NA values. Therefore the datasets should not contain any missing value

## Author(s)

Duygu Celik and Murat Tinic

## References

Lin, H.W.W. and Ke, W.C. A computing bias in estimating the probability of informed trading. Journal of Financial Markets, 14(4), pp.625-640, 2011.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41``` ``` # Sample Data # Buy Sell #1 350 382 #2 250 500 #3 500 463 #4 552 550 #5 163 200 #6 345 323 #7 847 456 #8 923 342 #9 123 578 #10 349 455 Buy<-c(350,250,500,552,163,345,847,923,123,349) Sell<-c(382,500,463,550,200,323,456,342,578,455) data=cbind(Buy,Sell) # Initial parameter values # par0 = (alpha, delta, mu, epsilon_b, epsilon_s) par0 = c(0.5,0.5,300,400,500) # Call LK function LK_out = LK(data) model = optim(par0, LK_out, gr = NULL, method = c("Nelder-Mead"), hessian = FALSE) ## Parameter Estimates model\$par[1] # Estimate for alpha # [1] 0.480277 model\$par[2] # Estimate for delta # [1] 0.830850 model\$par[3] # Estimate for mu # [1] 315.259805 model\$par[4] # Estimate for eb # [1] 296.862318 model\$par[5] # Estimate for es # [1] 434.3046 ## Estimate for PIN (model\$par[1]*model\$par[3])/((model\$par[1]*model\$par[3])+model\$par[4]+model\$par[5]) # [1] 0.178391 #### ```

### Example output

```Attaching package: 'InfoTrad'

The following object is masked from 'package:base':

print

There were 31 warnings (use warnings() to see them)
[1] -118808167
[1] 210730213
[1] 441.6373
[1] 266.348
[1] 437.4163
[1] 1
```

InfoTrad documentation built on Aug. 21, 2017, 9:02 a.m.