putCallParity {NMOF}

Put-Call Parity

Description

Put–call parity

Usage

  putCallParity(what, call, put, S, X, tau, r, q = 0, tauD = 0, D = 0)

Arguments

what

character: what to compute. Currently only call or put are supported.

call

call price

put

put price

S

underlier

X

strike

tau

time to expiry

r

interest rate

q

dividend rate

tauD

numeric vector: time to dividend

D

numeric vector: dividends

Details

Put–call parity only works for European options. The function is vectorised (like vanillaOptionEuropean), except for dividends.

Value

Numeric vector.

Author(s)

Enrico Schumann

References

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. doi:10.1016/C2017-0-01621-X

Schumann, E. (2023) Financial Optimisation with R (NMOF Manual). http://enricoschumann.net/NMOF.htm#NMOFmanual

Examples

S <- 100; X <- 100; tau <- 1; r <- 0.02; q <- 0.0;
vol <- 0.3; D <- 20; tauD <- 0.5
call <- vanillaOptionEuropean(S, X, tau, r, q, vol^2,
                              tauD = tauD, D = D, type = "call")$value
put  <- vanillaOptionEuropean(S, X, tau, r, q, vol^2,
                              tauD = tauD, D = D, type = "put")$value

## recover the call from the put (et vice versa)
all.equal(call, putCallParity("call", put = put,  S=S, X=X, tau=tau,
                              r=r, q=q, tauD=tauD, D=D))
all.equal(put, putCallParity("put",  call = call, S=S, X=X, tau=tau,
                             r=r, q=q, tauD=tauD, D=D))


## Black--Scholes--Merton with with 'callCF'
S <- 100; X <- 90; tau <- 1; r <- 0.02; q <- 0.08
v <- 0.2^2  ## variance, not volatility

(ccf <- callCF(cf = cfBSM, S = S, X = X, tau = tau, r = r, q = q,
                 v = v, implVol = TRUE))
all.equal(ccf$value,
          vanillaOptionEuropean(S, X, tau, r, q, v, type = "call")$value)
all.equal(
  putCallParity("put", call=ccf$value, S=S, X=X, tau=tau, r=r, q=q),
  vanillaOptionEuropean(S, X, tau, r, q, v, type = "put")$value)