Spread option pricing method by Bjerksund & Stensland (2014)

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

Usage

SpreadBjerksund2014(
  strike = 0,
  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

strike

(vector of) strike price

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

Bjerksund, P., & Stensland, G. (2014). Closed form spread option valuation. Quantitative Finance, 14(10), 1785–1794. doi:10.1080/14697688.2011.617775

Examples

FER::SpreadBjerksund2014((-2:2)*10, 100, 120, 1.3, 0.2, 0.3, -0.5)
#> [1] 22.131720 17.183042 12.989742  9.544319  6.806126