QFRM (version 1.0.1)

RainbowBS: Rainbow option valuation via Black-Scholes (BS) model

Description

Rainbow Option via Black-Scholes (BS) model

Usage

RainbowBS(o = OptPx(Opt(Style = "Rainbow")), S1 = 100, S2 = 95, D1 = 0, D2 = 0, sigma1 = 0.15, sigma2 = 0.2, rho = 0.75, Type = c("Max", "Min"))

Arguments

o

An object of class OptPx

S1

A spot price of the underlying security 1 (usually S1)

S2

A spot price of the underlying security 2 (usually S2)

D1

A percent yield per annum from the underlying security 1

D2

A percent yield per annum from the underlying security 2

sigma1

a vector of implied volatilities for the associated security 1

sigma2

a vector of implied volatilities for the associated security 2

rho

is the correlation between asset 1 and asset 2

Type

Rainbow option type: 'Max' or 'Min'.

Value

A list of class RainbowBS consisting of the original OptPx object and the option pricing parameters S1, Type, isMax, and isMin as well as the computed price PxBS.

Details

Two types of Rainbow options are priced: 'Max' and 'Min'.

References

Zhang Peter G., Exotic Options, 2nd ed, 1998.

Examples

(o = RainbowBS())$PxBS

  o = OptPx(Opt(Style = 'Rainbow',  Right = "Put"), r = 0.08)
  RainbowBS(o, S1=100, S2=95, D1=0,D2=0,sigma1=0.15,sigma2=0.2, rho=0.75,Type='Min')

  o = OptPx(Opt(Style = 'Rainbow', K = 102, ttm = 1, Right = "Put"), r = 0.08)
  RainbowBS(o, S1=100, S2=95, D1=0,D2=0,sigma1=0.15,sigma2=0.2, rho=0.75,Type='Min')

  o=OptPx(Opt(Style = 'Rainbow', K = 102, ttm = 1, Right = "Put"), r = 0.08)
  RainbowBS(o, S1=100, S2=95, D1=0,D2=0,sigma1=0.15,sigma2=0.2, rho=0.75,Type='Max')

  o=OptPx(Opt(Style = 'Rainbow', K = 102, ttm = 1, Right = "Call"), r = 0.08)
  RainbowBS(o, S1=100, S2=95, D1=0,D2=0,sigma1=0.15,sigma2=0.2, rho=0.75,Type='Min')

  o=OptPx(Opt(Style = 'Rainbow', K = 102, ttm = 1, Right = "Call"), r = 0.08)
  RainbowBS(o, S1=100, S2=95, D1=0,D2=0,sigma1=0.15,sigma2=0.2, rho=0.75,Type='Max')