BinaryBS function

Binary option valuation with Black-Scholes (BS) model

S3 object pricing model for a binary option. Two types of binary options are priced: 'cash-or-nothing' and 'asset-or-nothing'.

BinaryBS(o = OptPx(Opt(Style = "Binary")), Q = 1,
  Type = c("cash-or-nothing", "asset-or-nothing"))

Arguments

• o: An object of class OptPx
• Q: A fixed amount of payoff
• Type: Binary option type: 'Cash or Nothing' or 'Asset or Nothing'. Partial names are allowed, eg. 'C' or 'A'

Returns

A list of class Binary.BS consisting of the input object OptPx and the appended new parameters and option price.

Examples

(o = BinaryBS())$PxBS

#This example should produce price 4.33 (see Derivagem, DG201.xls)
o = Opt(Style="Binary", Right='Call', S0=50, ttm=5/12, K=52)
o = OptPx(o, r=.1, vol=.40, NSteps=NA)
(o = BinaryBS(o, Q = 10, Type='cash-or-nothing'))$PxBS

BinaryBS(OptPx(Opt(Style="Binary"), q=.01), Type='asset-or-nothing')
BinaryBS(OptPx(Opt(Style="Binary", S0=100, K=80),q=.01))
o = Opt(Style="Binary", Right="Put", S0=50, K=60)
BinaryBS(OptPx(o,q=.04), Type='asset-or-nothing')

Author(s)

Xinnan Lu, Department of Statistics, Rice University, Spring 2015

References

Hull, John C., Options, Futures and Other Derivatives, 9ed, 2014. Prentice Hall. ISBN 978-0-13-345631-8, http://www-2.rotman.utoronto.ca/~hull/ofod/index.html. pp.606-607