PhD Defense in Lyon

Today, I will go to Lyon for the PhD defense of Edouard Debonneuil (that will be on Monday morning) His thesis is on financial impacts of mortality improvements Several models and scenarios are considered… Probably more on that very interesting (and important) topic soon.

Fin de l’excursion en Suisse Suite au cours du début de la semaine, je vais passer quelques jours à Lausanne, visiter Florian, avant d’aller sur Lyon en début se semaine prochaine. Mais pas d’exposé de prévu pour l’instant… Climate change and insurance I will be in Lyon next Monday to give a talk on “Modeling heat-waves: return period for non-stationary extremes” in a workshop entitled “Changement climatique et gestion des risques“. An interesting reference might be some pages from Le Monde (2010). The talk will be more a discussion about modeling series of temperatures (daily temperatures). A starting point might be the IPCC Third Assessment graph which illustrates the effect on extreme temperatures when (a) the mean temperature increases, (b) the variance increases, and (c) when both the mean and variance increase for a normal distribution of temperature.

I will add here some code used to generate some graphs I will comment. The graph below it the daily minimum temperature,

D=as.Date(as.character(TEMP\$DATE),"%Y%m%d")
T=TEMP\$TN/10
day=as.POSIXlt(D)\$yday+1
an=trunc(TEMP\$DATE/10000)
plot(D,T,col="light blue",xlab="Minimum
daily temperature in Paris",ylab="",cex=.5)
abline(R,lwd=2,col="red") We can clearly see an increasing linear trend. But we do not care (too much) here about the increase of the average temperature, but more dispersion, and tails. Here are decenal box-plots or quantile-regressions library(quantreg)
PENTESTD=PENTE=rep(NA,99)
for(i in 1:99){
R=rq(T~D,tau=i/100)
PENTE[i]=R\$coefficients
PENTESTD[i]=summary(R)\$coefficients[2,2]
}
m=lm(T~D)\$coefficients
plot((1:99)/100,(PENTE/m-1)*100,type="b")
segments((1:99)/100,((PENTE-2*PENTESTD)/m-1)*100,
(1:99)/100,((PENTE+2*PENTESTD)/m-1)*100,
col="light blue",lwd=3)
points((1:99)/100,(PENTE/m-1)*100,type="b")
abline(h=0,lty=2,col="red")

In order to get a better understanding of the graph above, here are slopes of quantile regressions associated to different probabilities, The annualized maxima (of minimum temperature, i.e. warmest night of the year) i.e. the regression of yearly maximas. tail index of a Generalized Pareto distribution Instead of looking at observation over a century (the trend is obviously linear), we can focus on seaonal behavior,

B=data.frame(Y=rep(T,3),X=c(day,day-365,day+365),
A=rep(an,3))
library(quantreg)
library(splines)
Q50=rq(Y~bs(X,10),data=B,tau=.5)
Q95=rq(Y~bs(X,10),data=B,tau=.95)
Q05=rq(Y~bs(X,10),data=B,tau=.05)
YP95=predict(Q95,newdata=data.frame(X=1:366))
YP05=predict(Q05,newdata=data.frame(X=1:366))
I=(T>predict(Q95))|(T<predict(Q05))
YP50=predict(Q50,newdata=data.frame(X=1:366))
plot(day[I],T[I],col="light blue",cex=.5)
lines(1:365,YP95[1:365],col="blue")
lines(1:365,YP05[1:365],col="blue")
lines(1:365,YP50[1:365],col="blue",lwd=3) with on red series from 1900 till 1920, and on purple from 1990 till 2010. If we remove the linear trend, and the seasonal cycle, here are the residuals, assume to be stationary, on during the year Obviously, something has been missed, The graph below is the volatility of the residual series, within the year, Instead of looking at volatility, we can focus on tails, with tail index per month,

mois=as.POSIXlt(D)\$mon+1
Pmax=Dmax=matrix(NA,12,2)
for(s in 1:12){
X=T3[mois==s]
FIT=gpd(X,5)
Pmax[s,1:2]=FIT\$par.ests
Dmax[s,1:2]=FIT\$par.ses
}
plot(1:12,Pmax[,1],type="b",col="blue",
ylim=c(-.6,0))
segments(1:12,Pmax[,1]+2*Dmax[,1],1:12,Pmax[,1]-
2*Dmax[,1],col="light blue",lwd=2)
points(1:12,Pmax[,1],col="blue")
text(1:12,rep(-.5,12),c("JAN","FEV","MARS",
"AVR","MAI","JUIN","JUIL","AOUT","SEPT",
"OCT","NOV","DEV"),cex=.7) At the end of the talk, I will also mention multiple city models, e.g. Paris and Marseille, If we look at residuals (once we have removed the linear trend and the seasonal cycle) we observe some positive dependence In order to study (strong) tail dependence, define for lower left tail and for upper right tail, where is the survival copula associated to , i.e. and  It looks like there is no tail dependence (in the uper tail). But it is also possible to study weaker tail dependence, through and  Slides can be visualized below, I will upload them soon,

A few days in France Next week, I will spend a few days in France, in Lyon first, and then in Paris. I will try to post the slides and the code that I will use during my talk in Lyon (workshop on climate change) and also some codes on vine copulas (used to get a better understanding of that tool before the PhD defense of Pierre-André).

Category-based Tail Comovement Christophe gave a talk at EM Lyon at the end of February at the Journées de Finance Inter-Ecoles de Commerce 2010 (here), about “Category-Based Tail Comovement“. I have uploaded Christophe’s slides here. The abstract of the joint paper (writen also with Emilios Galariotis) is the following, traditional financial theory predicts that comovement in asset returns is due to fundamentals. An alternative view is that of Barberis and Shleifer (2003) and Barberis, Shleifer and Wurgler (2005) who propose a sentiment based theory of comovement, delinking it from fundamentals. In their paper they view comovement under the prism of the standard Pearsons correlation measure, implicitly excluding extreme market events, such as the latest financial crisis. Poon, Rockinger and Tawn (2004) have shown that under such events di¤erent types of comovement or dependence may co-exist, and make a clear distinction between the four types of dependence: perfect dependent, independent, asymptotically dependent and asymptotically independent. In this paper we extend the sentiment based theory of comovement so as to cover the whole spectrum of dependence, including extreme comovement such as the one that can be observed in nancial crises. One of the key contributions of this paper is that it formally proves that assets belonging to the same category comove too much in the tail and reclassifying an asset into a new category raises its tail dependence with that category“. 