Binary_BOPM function

Binary option valuation vialattice tree (LT) implementation

Compute option price via binomial option pricing model (recombining symmetric binomial tree)

Binary_BOPM(o = OptPx(Opt(Style = "Binary")), Type = c("cash-or-nothing",
  "asset-or-nothing"), Q = 1000, IncBT = FALSE)

Arguments

• o: OptPx object
• Type: Binary option type: 'cash-or-nothing' or 'asset-or-nothing'
• Q: A fixed amount of payoff
• IncBT: TRUE/FALSE, indicates whether to include the full binomial tree in the returned object

Returns

original OptPx object with Px.BOPM property and (optional) binomial tree IncBT = FALSE: option price value (type double, class numeric) IncBT = TRUE: binomial tree as a list (of length (o$n+1) of numeric matrices (2 x i). Each matrix is a set of possible i outcomes at time step i columns: (underlying prices, option prices)

Examples

(o = Binary_BOPM())$PxBT

o = OptPx(o=Opt(Style='Binary'))
(o = Binary_BOPM(o, Type='cash', Q=100, IncBT=TRUE))$PxBT

o = OptPx(Opt(Style='Binary'), r=0.05, q=0.02, rf=0.0, vol=0.30, NSteps=5)
(o = Binary_BOPM(o, Type='cash', Q=1000, IncBT=FALSE))$PxBT

o = OptPx(o=Opt(Style='Binary'), r=0.15, q=0.01, rf=0.05, vol=0.35, NSteps=5)
(o = Binary_BOPM(o,Type='asset',Q=150, IncBT=FALSE))$PxBT

o = OptPx(o=Opt(Style='Binary'), r=0.025, q=0.001, rf=0.0, vol=0.10, NSteps=5)
(o = Binary_BOPM(o, Type='cash', Q=20, IncBT=FALSE))$PxBT