Changes

Author: jaehyukchoi

pkg/NAMESPACE

@@ -4,3 +4,5 @@ export(BachelierImpvol)
 export(BachelierPrice)
 export(BlackScholesImpvol)
 export(BlackScholesPrice)
+export(CEV)
+export(SabrHagan2002)

pkg/R/bachelier_impvol.R

@@ -1,4 +1,4 @@
-#' Calculate normal model implied vol
+#' Calculate Bachelier model implied volatility
 #'
 #' @param type option type either 'call' or 'put'
 #' @param price Price

pkg/R/bachelier_price.R

@@ -1,4 +1,4 @@
-#' Calculate normal model option price
+#' Calculate Bachelier model option price
 #'
 #' @param type option type either "call" or "put"
 #' @param price Price

pkg/R/blackscholes_impvol.R

@@ -1,4 +1,4 @@
-#' Calculate Black-Scholes-Merton implied vol
+#' Calculate Black-Scholes implied volatility
 #'
 #' @param type option type either 'call' or 'put'
 #' @param price Price

pkg/R/blackscholes_price.R

@@ -1,4 +1,4 @@
-#' Calculate Black-Scholes-Merton option price
+#' Calculate Black-Scholes option price
 #'
 #' @param type option type either 'call' or 'put'
 #' @param spot current stock price

pkg/R/cev.R

@@ -1,9 +1,24 @@
+#' Constant Elasticity Of Variance (CEV) model option price
+#'
+#' @param strike
+#' @param spot
+#' @param forward
+#' @param t.exp
+#' @param sigma
+#' @param beta
+#' @param r
+#' @param div
+#' @param type
+#'
+#' @return
+#' @export
+#'
+#' @examples
 CEV <- function(
-  strike, spot, t.exp=1, sigma=0.01, vov=0, rho=0, beta=0.5,
+  strike, spot, forward = spot*exp((r-div)*t.exp),
+  t.exp=1, sigma=0.01, 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

pkg/R/sabr_hagan2002.R

@@ -1,9 +1,26 @@
+#' Hagan approximation for the SABR model
+#'
+#' @param strike
+#' @param spot
+#' @param forward
+#' @param t.exp
+#' @param sigma
+#' @param vov
+#' @param rho
+#' @param beta
+#' @param r
+#' @param div
+#' @param type 'BlackScholes', 'call', 'put'
+#'
+#' @return Black-Scholes volatility (type="BlackScholes") or option price ("call" or "put")
+#' @export
+#'
+#' @examples
 SabrHagan2002 <- function(
-  strike, spot, t.exp=1, sigma=0.01, vov=0, rho=0, beta=1,
+  strike, spot, forward = spot*exp((r-div)*t.exp),
+  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)
@@ -20,10 +37,9 @@ SabrHagan2002 <- function(
   zz <- powFwdStrk*logFwdStrk*vov/sigma  # need to make sure sig > 0
   yy <- sqrt(1 + zz*(zz-2*rho))
 
-  xx_zz <- rep(0, length(strike))
+  rho2 <- rho*rho
+  xx_zz[I] = 1 + (zz/2)*(rho + zz*((rho2-1/3) + (5*rho2-3)/4*rho*zz))
 
-  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)
@@ -33,7 +49,7 @@ SabrHagan2002 <- function(
 
   if(type=="BlackScholes"){
     return(volBlks)
-  } else if(type=="call" || type=="put") {
+  } else if(type=="call" | type=="put") {
     p <- BlackScholesPrice(
       type=type, spot=spot, strike=strike, t.exp=t.exp, sigma=volBlks,
       r=r, div=div