Discounting future casflows with chainladder

[johalnes]

Hi,

Working on a demo to see if we can change from ResQ to this package together with notebooks or Streamlit. Mostly super simple to follow the documentation, and the package has developed nicely since last time I took a look some years ago! Really impressive 😄

The one thing I somewhat struggle with is getting discount factors in an easy fashion. Using the package sample data

sample = cl.load_sample('tail_sample')
sample['rbns'] = sample['incurred'] - sample['paid']
dev = cl.TailCurve(attachment_age=48,projection_period=0).fit_transform(sample)

Using Tailcurve for smoothing effect, and it's nice to get same dimensions as input triangle.

My issue now is that I'll like to get the payment patterns from paid, and discount the RBNS with some interest curve, specified from EIOPA in my case. To do this I'll like to only look at remaining part of the payment pattern for each accident year. But using diff I get a dispatch errror from keepdims.

I also tried a bit with pct_change, but I think it's an error with pct_chg should be pct_change.

I've added this to discussion instead of issue, beacuse I've got the impression that you have thought most thing over some times during this development and that maybe there is something clever that I may have missed? What would be your suggestion for discounting future cashflows?

Please let me know if I should add diff and pct_change to issue, and I'll try to implement a fix 😄

My solution is then to leave the safe space within chainladder and converts to pandas.

dev['payment_pattern']=(dev.ldf_['paid']/dev.cdf_['paid'])
payment_pattern=dev['payment_pattern'].to_frame().diff(axis=1).fillna(dev['payment_pattern'].to_frame())*np.flip(dev.nan_triangle)
payment_pattern.div(payment_pattern.sum(axis=1),axis=0)

	12	24	36	48	60	72	84	96	108	120
2000-01-01	nan	nan	nan	nan	nan	nan	nan	nan	nan	1
2001-01-01	nan	nan	nan	nan	nan	nan	nan	nan	0.369578	0.630422
2002-01-01	nan	nan	nan	nan	nan	nan	nan	0.365194	0.234611	0.400195
2003-01-01	nan	nan	nan	nan	nan	nan	0.358266	0.234357	0.150558	0.256819
2004-01-01	nan	nan	nan	nan	nan	0.347421	0.233797	0.152937	0.0982507	0.167595
2005-01-01	nan	nan	nan	nan	0.330703	0.232528	0.15648	0.10236	0.0657589	0.112171
2006-01-01	nan	nan	nan	0.305562	0.229653	0.161476	0.108665	0.0710827	0.0456655	0.0778955
2007-01-01	nan	nan	0.264291	0.224805	0.168958	0.118799	0.079946	0.0522962	0.0335965	0.0573084
2008-01-01	nan	0.228429	0.203919	0.173453	0.130363	0.0916623	0.0616841	0.0403503	0.0259221	0.0442175
2009-01-01	0.290062	0.16217	0.14477	0.123141	0.0925495	0.0650745	0.0437918	0.0286462	0.0184031	0.0313917

And my next step would probably be flatting it into sql and join technical provisions by year and interest rate by development.

[jbogaardt]

Hi @johalnes . This sounds cool, Not having access to proprietary reserving software, its difficult for me to know the gaps that may exist in chainladder.

I'm not familiar with European regs, so I could be off the mark here, but I typically use the Chainladder.full_triangle_ to get patterns.

import chainladder as cl

sample = cl.load_sample('tail_sample')
sample['rbns'] = sample['incurred'] - sample['paid']


pipe = cl.Pipeline([
    ('dev', cl.Development()),
    ('tail', cl.TailCurve(attachment_age=48, projection_period=0)),
    ('model', cl.Chainladder())])

pipe.fit(sample['paid'])

increm_future_paid = (pipe.named_steps.model.full_triangle_.cum_to_incr() - sample['paid'].cum_to_incr())
increm_future_paid_pct = increm_future_paid / increm_future_paid.sum('development')

As far as discounting goes, there is a trend method. It's not my favorite method because its a bit confusing to use. Still I don't think it will give you what you need because we don't have a good solution for the timing of cashflows in the tail. chainladder assumes the cashflows at ultimate happen something like 150 years in the future which creates crazy results if you apply a discount factor. This is something we need to improve on.

For the sake of demonstration, (ignoring the cashflows at ultimate), the trend method could be used for discounting as follows:

discounted_increm_future_paid_pct  = increm_future_paid_pct.iloc[..., :-1].trend(
    0.05, axis='valuation', start=sample.valuation_date, end=sample.valuation.max())

discounted_increm_future_paid_pct

This may be way off base from your original question, if so, happy to take another stab at it with follow-up questions.