putCallParity: Put-Call Parity

In NMOF: Numerical Methods and Optimization in Finance

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. (2011) Numerical Methods and Optimization in Finance. Elsevier. http://www.elsevierdirect.com/product.jsp?isbn=9780123756626

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)

Example output

[1] TRUE
[1] TRUE
$value
[1] 9.420463

$impliedVol
[1] 0.1999826

[1] TRUE
[1] TRUE

NMOF documentation built on May 2, 2019, 6:39 p.m.