SabrHagan2002 {FER}

Calculate the equivalent BS volatility (Hagan et al. 2002) for the Stochatic-Alpha-Beta-Rho (SABR) model

Description

Calculate the equivalent BS volatility (Hagan et al. 2002) for the Stochatic-Alpha-Beta-Rho (SABR) model

Usage

SabrHagan2002(
  strike = forward,
  spot,
  texp = 1,
  sigma,
  vov = 0,
  rho = 0,
  beta = 1,
  intr = 0,
  divr = 0,
  cp = NULL,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

strike

(vector of) strike price

spot

(vector of) spot price

texp

(vector of) time to expiry

sigma

(vector of) volatility

vov

(vector of) vol-of-vol

rho

(vector of) correlation

beta

(vector of) beta

intr

interest rate (domestic interest rate)

divr

convenience rate (foreign interest rate)

cp

call/put sign. NULL for BS vol (default), 1 for call price, -1 for put price.

forward

forward price. If given, forward overrides spot

df

discount factor. If given, df overrides intr

Value

BS volatility or option price based on cp

References

Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing Smile Risk. Wilmott, September, 84-108.

Examples

sigma <- 0.25
vov <- 0.3
rho <- -0.8
beta <- 0.3
texp <- 10
strike <- seq(0.1, 2, 0.1)
FER::SabrHagan2002(strike, 1, texp, sigma, vov, rho, beta)
FER::SabrHagan2002(strike, 1, texp, sigma, vov, rho, beta, cp=1)