Margrabe's formula for exhange option price

The payout of the exchange option is max(S1_T - S2_T, 0) where S1_T and S2_T are the prices at expiry T of assets 1 and 2 respectively.

Usage

SwitchMargrabe(
  spot1,
  spot2,
  texp = 1,
  sigma1,
  sigma2,
  corr,
  intr = 0,
  divr1 = 0,
  divr2 = 0,
  cp = 1L,
  forward1 = spot1 * exp(-divr1 * texp)/df,
  forward2 = spot2 * exp(-divr2 * texp)/df,
  df = exp(-intr * texp)
)

Arguments

spot1

(vector of) spot price of asset 1

spot2

(vector of) spot price of asset 2

texp

(vector of) time to expiry

sigma1

(vector of) volatility of asset 1

sigma2

(vector of) volatility of asset 2

corr

correlation

intr

interest rate

divr1

dividend rate of asset 1

divr2

dividend rate of asset 2

cp

call/put sign. 1 for call, -1 for put.

forward1

forward price of asset 1. If given, overrides spot1

forward2

forward price of asset 2. If given, overrides spot2

df

discount factor. If given, df overrides intr

Value

option price

References

Margrabe, W. (1978). The value of an option to exchange one asset for another. The Journal of Finance, 33(1), 177–186.

See also

SpreadKirk

Examples

FER::SwitchMargrabe(100, 120, 1.3, 0.2, 0.3, -0.5)
#> [1] 12.98974