Put-Call Parity
Put–call parity
putCallParity(what, call, put, S, X, tau, r, q = 0, tauD = 0, D = 0)
what |
character: what to compute. Currently only |
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 |
Put–call parity only works for European options. The function is
vectorised (like vanillaOptionEuropean), except for
dividends.
Numeric vector.
Enrico Schumann
Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. https://www.elsevier.com/books/numerical-methods-and-optimization-in-finance/gilli/978-0-12-815065-8
Schumann, E. (2019) Financial Optimisation with R (NMOF Manual). http://enricoschumann.net/NMOF.htm#NMOFmanual
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.