putCallParity function

Put-Call Parity

Put--call parity

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.

Returns

Numeric vector.

References

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

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

Author(s)

Enrico Schumann

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)