New functions

Author: jaehyukchoi

pkg/R/cev.R

@@ -0,0 +1,21 @@
+CEV <- function(
+  strike, spot, t.exp=1, sigma=0.01, vov=0, rho=0, beta=0.5,
+  r = 0, div = 0, type="call"
+){
+  forward = spot*exp((r-div)*t.exp)
+
+  betac <- 1 - beta
+  scale <- (betac*sigma)^2*t.exp
+  strike_cov = strike^(2*betac) / scale # strike change of variable
+  forward_cov = forward^(2*betac) / scale # forward change of variable
+  df <- 1/betac
+
+  iscall = (type=="call")
+
+  term1 <- stats::pchisq(strike_cov, df=df+2, ncp=forward_cov, lower.tail=!iscall)
+  term2 <- stats::pchisq(forward_cov, df=df, ncp=strike_cov, lower.tail=iscall)
+
+  price <- ifelse(iscall, 1, -1)*exp(-r*t.exp)*(forward*term1 - strike*term2)
+
+  return(price)
+}

pkg/R/sabr_hagan2002.R

@@ -0,0 +1,43 @@
+SabrHagan2002 <- function(
+  strike, spot, t.exp=1, sigma=0.01, vov=0, rho=0, beta=1,
+  r = 0, div = 0, type="BlackScholes"
+){
+
+  forward = spot*exp((r-div)*t.exp)
+  betac <- 1 - beta
+  powFwdStrk <- (forward*strike)^(betac/2)
+  logFwdStrk <- log(forward/strike)
+  logFwdStrk2 <- logFwdStrk^2
+
+  pre1 = powFwdStrk*( 1 + betac^2/24 * logFwdStrk2*(1 + betac^2/80 * logFwdStrk2) )
+
+  pre2alp0 <- (2-3*rho^2)*vov^2/24
+  pre2alp1 <- vov*rho*beta/4/powFwdStrk
+  pre2alp2 <- betac^2/24/powFwdStrk^2
+
+  pre2 <- 1 + t.exp*( pre2alp0 + sigma*(pre2alp1 + pre2alp2*sigma) )
+
+  zz <- powFwdStrk*logFwdStrk*vov/sigma  # need to make sure sig > 0
+  yy <- sqrt(1 + zz*(zz-2*rho))
+
+  xx_zz <- rep(0, length(strike))
+
+  I <- (abs(zz) < 1e-5)
+  xx_zz[I] = 1 + (rho/2)*zz[I] + (1/2*rho^2-1/6)*zz[I]^2 + 1/8*(5*rho^2-3)*rho*zz[I]^3
+  I <- (zz >= 1e-5)
+  xx_zz[I] = log( (yy[I] + (zz[I]-rho))/(1-rho) ) / zz[I]
+  I <- (zz <= -1e-5)
+  xx_zz[I] = log( (1+rho)/(yy[I] - (zz[I]-rho)) ) / zz[I]
+
+  volBlks = sigma*pre2/(pre1*xx_zz) # blks vol
+
+  if(type=="BlackScholes"){
+    return(volBlks)
+  } else if(type=="call" || type=="put") {
+    p <- BlackScholesPrice(
+      type=type, spot=spot, strike=strike, t.exp=t.exp, sigma=volBlks,
+      r=r, div=div
+    )
+    return(p)
+  }
+}