This example shows how to compute gap option prices using the Black-Scholes option pricing model. Consider a gap call and put options on a nondividend paying stock with a strike of 57 and expiring on January 1, 2008. On July 1, 2008 the stock is trading at 50. Using this data, compute the price of the option if the risk-free rate is 9%, the strike threshold is 50, and the volatility is 20%.
Interest-rate term structure (annualized and continuously compounded),
specified by the RateSpec obtained from intenvset. For
information on the interest-rate specification, see intenvset.
Data Types: struct
StockSpec — Stock specification for underlying asset structure
Stock specification for the underlying asset. For information on the stock
specification, see stockspec.
stockspec handles several
types of underlying assets. For example, for physical commodities the price
is StockSpec.Asset, the volatility is
StockSpec.Sigma, and the convenience yield is
StockSpec.DividendAmounts.
Data Types: struct
Settle — Settlement or trade date serial date number | date character vector
Settlement or trade date for the basket option, specified as an
NINST-by-1 vector of serial date
numbers or date character vectors.
Data Types: double | char | cell
Maturity — Maturity date serial date number | date character vector
Maturity date for the basket option, specified as an
NINST-by-1 vector of serial date
numbers or date character vectors.
Data Types: double | char | cell
OptSpec — Definition of option character vector with values 'call' or
'put' | cell array of character vectors with values 'call' or
'put'
Definition of the option as 'call' or
'put', specified as an
NINST-by-1 vector.
Data Types: char | cell
Strike — Pay-off strike value vector
Pay-off strike value, specified as an
NINST-by-1 vector.
Data Types: double
StrikeThreshold — Strike values that determine if the option pays off vector
Strike values that determine if the option pays off, specified as an
NINST-by-1 vector.
A gap option is a digital option in which
one strike decides if the option is in or out of money and another strike decides
the size the size of the payoff.
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