path: root/R/distrib.R

## todo:
## -investigate other ways to interpolate the random severities on the grid
## I'm thinking that at eah severity that we add to the distribution, round it down
##  and keep track of the missing mass: namely if X_i=S_i w.p p_i, then add
## X_i=lu*floor(S_i/lu) with probability p_i and propagate
## X_{i+1}=S_{i+1}+(S_i-lu*floor(S_i/lu)) with the right probability
## - investigate truncated distributions more (need to compute loss and recov distribution
## separately, for the 0-10 equity tranche, we need the loss on the 0-0.1 support and
## recovery with 0.1-1 support, so it's not clear that there is a big gain.
## - do the correlation adjustments when computing the deltas since it seems to be
## the market standard

#' Gauss-Hermite quadrature weights
#'
#' \code{GHquad} computes the quadrature weights for integrating against a
#' Gaussian distribution.
#'
#' if f is a function, then \eqn{\sum_{i=1}^n f(Z_i)w_i \approx
#' \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty f(x)e^{-\frac{x^2}{2}}\,dx}.
#' @param n Integer, the number of nodes
#' @return A list with two components:
#'  \item{Z}{the list of nodes}
#'  \item{w}{the corresponding weights}
#'
GHquad <- function(n){
    n <- as.integer(n)
    Z <- double(n)
    w <- double(n)
    result <- .C("GHquad", n, Z=Z, w=w)
    result[[1]] <- NULL
    return(result)
}

#' Loss distribution of a portfolio
#'
#' \code{lossdistrib} computes the probability distribution of a sum
#' of independent Bernouilli variables with unequal probabilities
#' (also called the Poisson-Binomial distribution).
#'
#' We compute the probability distribution of \eqn{S = \sum_{i=1}^n X_i}
#' where \eqn{X_i} is Bernouilli(\eqn{p_i}). This uses the simple recursive
#' algorithm of Andersen, Sidenius and Basu
#' @param p Numeric vector, the vector of success probabilities
#' @return A vector q such that \eqn{q_k=\Pr(S=k)}
lossdistrib <- function(p){
    ## basic recursive algorithm of Andersen, Sidenius and Basu
    n <- length(p)
    q <- rep(0, (n+1))
    q[1] <- 1
    for(i in 1:n){
        q[-1] <- p[i]*q[-(n+1)]+(1-p[i])*q[-1]
        q[1] <- (1-p[i])*q[1]
    }
    return(q)
}

#'Convolution of two discrete probability distributions
#'
#' This is the probability of the sum of the two random variables
#' assuming they are independent.
#' @param dist1 Numeric vector of probabilities
#' @param dist2 Numeric vector of probabilities
#' @return Convolution of the two vectors
convolve <- function(dist1, dist2) {
    n1 <- length(dist1)
    n2 <- length(dist2)
    dist1 <- c(dist1, rep(0, n2-1))
    dist2 <- c(dist2, rep(0, n1-1))
    Re(fft(fft(dist1) * fft(dist2), inverse=T))/length(dist1)
}

#' Loss distribution of a portfolio
#'
#' \code{lossdistrib.fft} computes the probability distribution of a sum
#' of independent Bernouilli variables with unequal probabilities
#' (also called the Poisson-Binomial distribution).
#'
#' We compute the probability distribution of \eqn{S = \sum_{i=1}^n X_i}
#' where \eqn{X_i} is Bernouilli(\eqn{p_i}).
#' This uses the FFT, thus complexity is of order \eqn{O(n \log(n))},
#' compared to \eqn{O(n^2)} for the recursive algorithm.
#' @param p Numeric vector, the vector of success probabilities
#' @return A vector such that \eqn{q_k=\Pr(S=k)}
lossdistrib.fft <- function(p) {
    ## haven't tested when p is not a power of 2.
    if(length(p) == 1){
        c(1-p, p)
    }else {
        convolve(lossdistrib.fft(p[1:(length(p)/2)]),
                 lossdistrib.fft(p[-(1:(length(p)/2))]))
    }
}

#' Loss distribution of a portfolio
#'
#' \code{lossdistrib2} computes the probability distribution of a sum
#' of independent Bernouilli variables with unequal probabilities.
#'
#' We compute the probability distribution of \eqn{L = \sum_{i=1}^n w_i S_i X_i}
#' where \eqn{X_i} is Bernouilli(\eqn{p_i}). If \code{defaultflag} is TRUE, we
#' compute the distribution of \eqn{D = \sum_{i=1}^n w_i X_i} instead.
#' This a recursive algorithm with first order correction for discretization.
#' Complexity is of ordier \eqn{O(nN)}, so linear for a given grid size.
#' @param p Numeric, vector of default probabilities
#' @param w Numeric, vector of weights
#' @param S Numeric, vector of severities
#' @param N Integer, number of ticks in the grid
#' @param defaultflag Boolean, if TRUE, we compute the default distribution
#' (instead of the loss distribution).
#' @return a Numeric vector of size \code{N} computing the loss (resp.
#' default) distribution if \code{defaultflag} is FALSE (resp. TRUE).
lossdistrib2 <- function(p, w, S, N, defaultflag=FALSE){
    n <- length(p)
    lu <- 1/(N-1)
    q <- rep(0, N)
    q[1] <- 1
    for(i in 1:n){
        if(defaultflag){
            d <- w[i] /lu
        }else{
            d <- S[i] * w[i] / lu
        }
        d1 <- floor(d)
        d2 <- ceiling(d)
        p1 <- p[i]*(d2-d)
        p2 <- p[i] - p1
        q1 <- c(rep(0,d1), p1*q[1:(N-d1)])
        q2 <- c(rep(0,d2), p2*q[1:(N-d2)])
        q <- q1 + q2 + (1-p[i])*q
    }
    q[length(q)] <- q[length(q)]+1-sum(q)
    return(q)
}

#' Loss distribution truncated version
#'
#' \code{lossdistrib2.truncated} computes the probability distribution of a sum
#' of independent Bernouilli variables with unequal probabilities up
#' to a cutoff N.
#'
#' This is actually slower than \code{lossdistrib2}, but in C this is
#' twice as fast. For high severities, M can become bigger than the cutoff, and
#' there is some probability mass escaping.
#' @param p Numeric, vector of default probabilities
#' @param w Numeric, vector of weights
#' @param S Numeric, vector of severities
#' @param N Integer, number of ticks in the grid
#' @param cutoff Integer, where to stop computing the exact probabilities
#' @return a Numeric vector of size \code{N} computing the loss distribution
lossdistrib2.truncated <- function(p, w, S, N, cutoff=N){
    n <- length(p)
    lu <- 1/(N-1)
    q <- rep(0, cutoff)
    q[1] <- 1
    M <- 1
    for(i in 1:n){
        d <- S[i] * w[i] / lu
        d1 <- floor(d)
        d2 <- ceiling(d)
        p1 <- p[i]*(d2-d)
        p2 <- p[i] - p1
        q1 <- p1*q[1:min(M, cutoff-d1)]
        q2 <- p2*q[1:min(M, cutoff-d2)]
        q[1:min(M, cutoff)] <-  (1-p[i])*q[1:min(M, cutoff)]
        q[(d1+1):min(M+d1, cutoff)] <- q[(d1+1):min(M+d1, cutoff)]+q1
        q[(d2+1):min(M+d2, cutoff)] <- q[(d2+1):min(M+d2, cutoff)]+q2
        M <- M+d2
    }
    return(q)
}

#' Recovery distribution of a portfolio
#'
#' \code{recovdist} computes the recovery distribution of portfolio
#' described by a vector of default probabilities, and prepay probabilities.
#' \eqn{R=\sum_{i=1}^n w_i X_i} where \eqn{X_i=0} w.p. \eqn{1-dp_i-pp_i},
#' \eqn{X_i=1-S_i} with probability \eqn{dp_i}, and \eqn{X_i=1} w.p. \eqn{pp_i}
#'
#' It is a recursive algorithm with first-order correction. For a unit of loss
#' \eqn{lu}, each non-zero value \eqn{v} is interpolated on the grid
#' as the pair of values
#' \eqn{\left\lfloor\frac{v}{lu}\right\rfloor}  and
#' \eqn{\left\lceil\frac{v}{lu}\right\rceil} so that \eqn{X_i} has
#' four non zero values.
#' @param dp Numeric, vector of default probabilities
#' @param pp Numeric, vector of prepay probabilities
#' @param w Numeric, vector of weights
#' @param S Numeric, vector of severities
#' @param N Integer, number of ticks in the grid
#' @return a Numeric vector of size \code{N} computing the recovery distribution
recovdist <- function(dp, pp, w, S, N){
    n <- length(dp)
    q <- rep(0, N)
    q[1] <- 1
    lu <- 1/(N-1)
    for(i in 1:n){
        d1 <- w[i]*(1-S[i])/lu
        d1l <- floor(d1)
        d1u <- ceiling(d1)
        d2 <- w[i] / lu
        d2l <- floor(d2)
        d2u <- ceiling(d2)
        dp1 <- dp[i] * (d1u-d1)
        dp2 <- dp[i] - dp1
        pp1 <- pp[i] * (d2u - d2)
        pp2 <- pp[i] - pp1
        q1 <- c(rep(0, d1l), dp1 * q[1:(N-d1l)])
        q2 <- c(rep(0, d1u), dp2 * q[1:(N-d1u)])
        q3 <- c(rep(0, d2l), pp1 * q[1:(N-d2l)])
        q4 <- c(rep(0, d2u), pp2 *q[1:(N-d2u)])
        q <- q1+q2+q3+q4+(1-dp[i]-pp[i])*q
    }
    return(q)
}

#' Joint loss-recovery distributionrecursive algorithm with first order correction to compute the joint
#' probability distribution of the loss and recovery.
#'
#' For high severities, M can become bigger than N, and there is
#' some probability mass escaping.
#' @param p Numeric, vector of default probabilities
#' @param w Numeric, vector of weights
#' @param S Numeric, vector of severities
#' @param N Integer, number of ticks in the grid
#' @param defaultflag Logical, whether to return the loss or default distribution
#' @return q Matrix of joint loss, recovery probability distribution
#' colSums(q) is the recovery distribution marginal
#' rowSums(q) is the loss distribution marginal
lossdist.joint <- function(p, w, S, N, defaultflag=FALSE){
    n <- length(p)
    lu <- 1/(N-1)
    q <- matrix(0, N, N)
    q[1,1] <- 1
    for(k in 1:n){
        if(defaultflag){
            x <- w[k] / lu
        }else{
            x <- S[k] * w[k]/lu
        }
        y <- (1-S[k]) * w[k]/lu
        i <- floor(x)
        j <- floor(y)
        weights <- c((i+1-x)*(j+1-y), (i+1-x)*(y-j), (x-i)*(y-j), (j+1-y)*(x-i))
        psplit <- p[k] * weights
        qtemp <- matrix(0, N, N)
        qtemp[(i+1):N,(j+1):N] <- qtemp[(i+1):N,(j+1):N] + psplit[1] * q[1:(N-i),1:(N-j)]
        qtemp[(i+1):N,(j+2):N] <- qtemp[(i+1):N,(j+2):N] + psplit[2] * q[1:(N-i), 1:(N-j-1)]
        qtemp[(i+2):N,(j+2):N] <- qtemp[(i+2):N,(j+2):N] + psplit[3] * q[1:(N-i-1), 1:(N-j-1)]
        qtemp[(i+2):N, (j+1):N] <- qtemp[(i+2):N, (j+1):N] + psplit[4] * q[1:(N-i-1), 1:(N-j)]
        q <- qtemp + (1-p[k])*q
    }
    q[length(q)] <- q[length(q)]+1-sum(q)
    return(q)
}

lossdist.prepay.joint <- function(dp, pp, w, S, N, defaultflag=FALSE){
    ## recursive algorithm with first order correction
    ## to compute the joint probability distribition of the loss and recovery
    ## inputs:
    ##   dp: vector of default probabilities
    ##   pp: vector of prepay probabilities
    ##   w:  vector of issuer weights
    ##   S:   vector of severities
    ##   N: number of tick sizes on the grid
    ##   defaultflag: if true computes the default
    ## outputs
    ##   q: matrix of joint loss and recovery probability
    ##      colSums(q) is the recovery distribution marginal
    ##      rowSums(q) is the loss distribution marginal
    n <- length(dp)
    lu <- 1/(N-1)
    q <- matrix(0, N, N)
    q[1,1] <- 1
    for(k in 1:n){
        y1 <- (1-S[k]) * w[k]/lu
        y2 <- w[k]/lu
        j1 <- floor(y1)
        j2 <- floor(y2)
        if(defaultflag){
            x <- y2
            i <- j2
        }else{
            x <- y2-y1
            i <- floor(x)
        }

        ## weights <- c((i+1-x)*(j1+1-y1), (i+1-x)*(y1-j1), (x-i)*(y1-j1), (j1+1-y1)*(x-i))
        weights1 <- c((i+1-x)*(j1+1-y1), (i+1-x)*(y1-j1), (x-i)*(y1-j1), (j1+1-y1)*(x-i))
        dpsplit <- dp[k] * weights1

        if(defaultflag){
            weights2 <- c((i+1-x)*(j2+1-y2), (i+1-x)*(y2-j2), (x-i)*(y2-j2), (j2+1-y2)*(x-i))
            ppsplit <- pp[k] * weights2
        }else{
            ppsplit <- pp[k] * c(j2+1-y2, y2-j2)
        }
        qtemp <- matrix(0, N, N)
        qtemp[(i+1):N,(j1+1):N] <- qtemp[(i+1):N,(j1+1):N] + dpsplit[1] * q[1:(N-i),1:(N-j1)]
        qtemp[(i+1):N,(j1+2):N] <- qtemp[(i+1):N,(j1+2):N] + dpsplit[2] * q[1:(N-i), 1:(N-j1-1)]
        qtemp[(i+2):N,(j1+2):N] <- qtemp[(i+2):N,(j1+2):N] + dpsplit[3] * q[1:(N-i-1), 1:(N-j1-1)]
        qtemp[(i+2):N,(j1+1):N] <- qtemp[(i+2):N, (j1+1):N] + dpsplit[4] * q[1:(N-i-1), 1:(N-j1)]
        if(defaultflag){
            qtemp[(i+1):N,(j2+1):N] <- qtemp[(i+1):N,(j2+1):N] + ppsplit[1] * q[1:(N-i),1:(N-j2)]
            qtemp[(i+1):N,(j2+2):N] <- qtemp[(i+1):N,(j2+2):N] + ppsplit[2] * q[1:(N-i), 1:(N-j2-1)]
            qtemp[(i+2):N,(j2+2):N] <- qtemp[(i+2):N,(j2+2):N] + ppsplit[3] * q[1:(N-i-1), 1:(N-j2-1)]
            qtemp[(i+2):N,(j2+1):N] <- qtemp[(i+2):N, (j2+1):N] + ppsplit[4] * q[1:(N-i-1), 1:(N-j2)]
        }else{
            qtemp[, (j2+1):N] <- qtemp[,(j2+1):N]+ppsplit[1]*q[,1:(N-j2)]
            qtemp[, (j2+2):N] <- qtemp[,(j2+2):N]+ppsplit[2]*q[,1:(N-j2-1)]
        }
        q <- qtemp + (1-pp[k]-dp[k]) * q
    }
    q[length(q)] <- q[length(q)] + 1 - sum(q)
    return(q)
}

lossdistC <- function(p, w, S, N, defaultflag=FALSE){
    ## C version of lossdistrib2, roughly 50 times faster
    .C("lossdistrib", as.double(p), as.integer(length(p)),
       as.double(w), as.double(S), as.integer(N), as.integer(N), as.logical(defaultflag), q = double(N))$q
}

lossdistCZ <- function(p, w, S, N, defaultflag=FALSE, rho, Z){
    ##S is of size (length(p), length(Z))
    stopifnot(length(rho)==length(p),
              length(rho)==length(w),
              nrow(S)==length(p),
              ncol(S)==length(Z))
    .C("lossdistrib_Z", as.double(p), as.integer(length(p)),
       as.double(w), as.double(S), as.integer(N), as.logical(defaultflag),
       as.double(rho), as.double(Z), as.integer(length(Z)),
       q = matrix(0, N, length(Z)))$q
}

lossdistC.truncated <- function(p, w, S, N, T=N, defaultflag=FALSE){
    ## truncated version of lossdistrib
    ## q[i] is 0 for i>=T
    .C("lossdistrib_truncated", as.double(p), as.integer(length(p)),
       as.double(w), as.double(S), as.integer(N), as.integer(T), as.logical(defaultflag),
       q = double(N))$q
}

exp.trunc <- function(p, w, S, N, K){
    ## computes E[(K-L)^+]
    r <- 0
    .C("exp_trunc", as.double(p), as.integer(length(p)),
       as.double(w), as.double(S), as.integer(N), as.double(K), res = r)$res
}

rec.trunc <- function(p, w, S, N, K){
    ## computes E[(K-(1-R))^+] = E[(\tilde K- \bar R)]
    ## where \tilde K = K-sum_i w_i S_i and \bar R=\sum_i w_i R_i (1-X_i)
    Ktilde <- K-crossprod(w, S)
    if(Ktilde < 0){
        return( 0 )
    }else{
        return( exp.trunc(1-p, w, 1-S, N, Ktilde) )
    }
}

recovdistC <- function(dp, pp, w, S, N){
    ## C version of recovdist
    .C("recovdist", as.double(dp), as.double(pp), as.integer(length(dp)),
       as.double(w), as.double(S), as.integer(N), q = double(N))$q
}

lossdistC.prepay.joint <- function(dp, pp, w, S, N, defaultflag=FALSE){
    ## C version of lossdist.prepay.joint
    r <- .C("lossdistrib_joint", as.double(dp), as.double(pp), as.integer(length(dp)),
            as.double(w), as.double(S), as.integer(N), as.logical(defaultflag), q=matrix(0, N, N))$q
    return(r)
}

lossdistC.prepay.jointZ <- function(dp, pp, w, S, N, defaultflag = FALSE, rho, Z, wZ){
    ## N is the size of the grid
    ## dp is of size n.credits
    ## pp is of size n.credits
    ## w is of size n.credits
    ## S is of size n.credits by nZ
    ## rho is a vector of doubles of size n.credits
    ## Z is a vector of length nZ
    ## w is a vector if length wZ

    r <- .C("lossdistrib_joint_Z", as.double(dp), as.double(pp), as.integer(length(dp)),
            as.double(w), as.double(S), as.integer(N), as.logical(defaultflag), as.double(rho),
            as.double(Z), as.double(wZ), as.integer(length(Z)), output = matrix(0,N,N))
    return(r$output)
}

lossrecovdist <- function(defaultprob, prepayprob, w, S, N, defaultflag=FALSE, useC=TRUE){
    lossdistrib2 <- if(useC) lossdistC
    recovdist <- if(useC) recovdistC
    if(missing(prepayprob)){
        L <- lossdistrib2(defaultprob, w, S, N, defaultflag)
        R <- lossdistrib2(defaultprob, w, 1-S, N)
    }else{
        L <- lossdistrib2(defaultprob+defaultflag*prepayprob, w, S, N, defaultflag)
        R <- recovdist(defaultprob, prepayprob, w, S, N)
    }
    return(list(L=L, R=R))
}

lossrecovdist.term <- function(defaultprob, prepayprob, w, S, N, defaultflag=FALSE, useC=TRUE){
    ## computes the loss and recovery distribution over time
    L <- array(0, dim=c(N, ncol(defaultprob)))
    R <- array(0, dim=c(N, ncol(defaultprob)))
    if(missing(prepayprob)){
        for(t in 1:ncol(defaultprob)){
            temp <- lossrecovdist(defaultprob[,t], , w, S[,t], N, defaultflag, useC)
            L[,t] <- temp$L
            R[,t] <- temp$R
        }
    }else{
        for(t in 1:ncol(defaultprob)){
            temp <- lossrecovdist(defaultprob[,t], prepayprob[,t], w, S[,t], N, defaultflag, useC)
            L[,t] <- temp$L
            R[,t] <- temp$R
        }
    }
    return(list(L=L, R=R))
}

lossrecovdist.joint.term <- function(defaultprob, prepayprob, w, S, N, defaultflag=FALSE, useC=TRUE){
    ## computes the joint loss and recovery distribution over time
    Q <- array(0, dim=c(ncol(defaultprob), N, N))
    lossdist.joint <- if(useC) lossdistC.jointblas
    lossdist.prepay.joint <- if(useC) lossdistC.prepay.jointblas
    if(missing(prepayprob)){
        for(t in 1:ncol(defaultprob)){
            Q[t,,] <- lossdist.joint(defaultprob[,t], w, S[,t], N, defaultflag)
        }
    }else{
        for(t in 1:ncol(defaultprob)){
            Q[t,,] <- lossdist.prepay.jointblas(defaultprob[,t], prepayprob[,t], w, S[,t], N, defaultflag)
        }
    }
    return(Q)
}

dist.transform <- function(dist.joint){
    ## compute the joint (D, R) distribution
    ## from the (L, R) distribution using D = L+R
    distDR <- array(0, dim=dim(dist.joint))
    Ngrid <- dim(dist.joint)[2]
    for(t in 1:dim(dist.joint)[1]){
        for(i in 1:Ngrid){
            for(j in 1:Ngrid){
                index <- i+j
                if(index <= Ngrid){
                    distDR[t,index,j] <- distDR[t,index,j] + dist.joint[t,i,j]
                }else{
                    distDR[t,Ngrid,j] <- distDR[t,Ngrid,j] +
                        dist.joint[t,i,j]
                }
            }
        }
        distDR[t,,] <- distDR[t,,]/sum(distDR[t,,])
    }
    return( distDR )
}

shockprob <- function(p, rho, Z, log.p=F){
  ## computes the shocked default probability as a function of the copula factor
  ## function is vectorized provided the below caveats:
  ## p and rho are vectors of same length n, Z is a scalar, returns vector of length n
  ## p and rho are scalars, Z is a vector of length n, returns vector of length n
  if(length(p)==1){
    if(rho==1){
      return(Z<=qnorm(p))
    }else{
      return(pnorm((qnorm(p)-sqrt(rho)*Z)/sqrt(1-rho), log.p=log.p))
    }
  }else{
    result <- double(length(p))
    result[rho==1] <- Z<=qnorm(p[rho==1])
    result[rho<1] <- pnorm((qnorm(p[rho<1])-sqrt(rho[rho<1])*Z)/sqrt(1-rho[rho<1]), log.p=log.p)
    return( result )
  }
}

shockseverity <- function(S, Stilde=1, Z, rho, p){
  ## computes the severity as a function of the copula factor Z
  result <- double(length(S))
  result[p==0] <- 0
  result[p!=0] <- Stilde * exp( shockprob(S[p!=0]/Stilde*p[p!=0], rho[p!=0], Z, TRUE) -
           shockprob(p[p!=0], rho[p!=0], Z, TRUE))
  return(result)
}

dshockprob <- function(p,rho,Z){
    dnorm((qnorm(p)-sqrt(rho)*Z)/sqrt(1-rho))*dqnorm(p)/sqrt(1-rho)
}

dqnorm <- function(x){
    1/dnorm(qnorm(x))
}

fit.prob <- function(Z, w, rho, p0){
    ## if the weights are not perfectly gaussian, find the probability p such
    ## E_w(shockprob(p, rho, Z)) = p0
    if(p0==0){
        return(0)
    }
    if(rho == 1){
        distw <- distr::DiscreteDistribution(Z, w)
        return(distr::pnorm(distr::q(distw)(p0)))
    }
    eps <- 1e-12
    dp <- (crossprod(shockprob(p0,rho,Z),w)-p0)/crossprod(dshockprob(p0,rho,Z),w)
    p <- p0
    while(abs(dp) > eps){
        dp <- (crossprod(shockprob(p,rho,Z),w)-p0)/crossprod(dshockprob(p,rho,Z),w)
        phi <- 1
        while ((p-phi*dp)<0 || (p-phi*dp)>1){
            phi <- 0.8*phi
        }
        p <- p - phi*dp
    }
    return(p)
}

fit.probC <- function(Z, w, rho, p0){
    stopifnot(length(Z)==length(w))
    r <- .C("fitprob", as.double(Z), as.double(w), as.integer(length(Z)),
            as.double(rho), as.double(p0), q = double(1))
    return(r$q)
}

stochasticrecov <- function(R, Rtilde, Z, w, rho, porig, pmod){
    ## if porig == 0 (probably matured asset) then return orginal recovery
    ## it shouldn't matter anyway since we never default that asset
    if(porig == 0){
        return(rep(R, length(Z)))
    }else{
        ptilde <- fit.prob(Z, w, rho, (1-R)/(1-Rtilde) * porig)
        return(abs(1-(1-Rtilde) * exp(shockprob(ptilde, rho, Z, TRUE) - shockprob(pmod, rho, Z, TRUE))))
    }
}

stochasticrecovC <- function(R, Rtilde, Z, w, rho, porig, pmod){
    r <- .C("stochasticrecov", as.double(R), as.double(Rtilde), as.double(Z),
            as.double(w), as.integer(length(Z)), as.double(rho), as.double(porig),
            as.double(pmod), q = double(length(Z)))
    return(r$q)
}

BClossdist <- function(defaultprob, issuerweights, recov, rho, Z, w,
                       N=length(recov)+1, defaultflag=FALSE, n.int=500){

    if(missing(Z)){
        quadrature <- GHquad(n.int)
        Z <- quadrature$Z
        w <- quadrature$w
    }
    stopifnot(length(Z)==length(w),
              nrow(defaultprob) == length(issuerweights))

    ## do not use if weights are not gaussian, results would be incorrect
    ## since shockseverity is invalid in that case (need to use stochasticrecov)
    LZ <- matrix(0, N, length(Z))
    RZ <- matrix(0, N, length(Z))
    L <- matrix(0, N, ncol(defaultprob))
    R <- matrix(0, N, ncol(defaultprob))
    for(t in 1:ncol(defaultprob)){
        for(i in 1:length(Z)){
            g.shocked <- shockprob(defaultprob[,t], rho, Z[i])
            S.shocked <- shockseverity(1-recov, 1, Z[i], rho, defaultprob[,t])
            temp <- lossrecovdist(g.shocked, , issuerweights, S.shocked, N)
            LZ[,i] <- temp$L
            RZ[,i] <- temp$R
        }
        L[,t] <- LZ%*%w
        R[,t] <- RZ%*%w
    }
    list(L=L, R=R)
}

BClossdistC <- function(defaultprob, issuerweights, recov, rho, Z, w,
                        N=length(issuerweights)+1, defaultflag=FALSE){
    if(is.null(dim(defaultprob))){
        dim(defaultprob) <- c(length(defaultprob),1)
    }
    stopifnot(length(Z)==length(w),
              nrow(defaultprob)==length(issuerweights),
              nrow(defaultprob)==length(recov))
    L <- matrix(0, N, ncol(defaultprob))
    R <- matrix(0, N, ncol(defaultprob))
    rho <- rep(rho, length(issuerweights))
    r <- .C("BCloss_recov_dist", defaultprob, as.integer(nrow(defaultprob)),
            as.integer(ncol(defaultprob)), as.double(issuerweights),
            as.double(recov), as.double(Z), as.double(w), as.integer(length(Z)),
            as.double(rho), as.integer(N), as.logical(defaultflag), L=L, R=R)
    return(list(L=r$L,R=r$R))
}

BCER <- function(defaultprob, issuerweights, recov, K, rho, Z, w,
                 N=length(issuerweights)+1, defaultflag=FALSE){
    stopifnot(length(Z)==length(w),
              nrow(defaultprob)==length(issuerweights))

    rho <- rep(rho, length(issuerweights))
    ELt <- numeric(ncol(defaultprob))
    ERt <- numeric(ncol(defaultprob))
    r <- .C("BCloss_recov_trunc", defaultprob, as.integer(nrow(defaultprob)),
            as.integer(ncol(defaultprob)),
            as.double(issuerweights), as.double(recov), as.double(Z), as.double(w),
            as.integer(length(Z)), as.double(rho), as.integer(N), as.double(K),
            as.logical(defaultflag), ELt=ELt, ERt=ERt)
    return(list(ELt=r$ELt, ERt=r$ERt))
}