naginterfaces.library.specfun.opt_bsm_price¶
- naginterfaces.library.specfun.opt_bsm_price(calput, x, s, t, sigma, r, q)[source]¶
opt_bsm_price
computes the European option price given by the Black–Scholes–Merton formula.For full information please refer to the NAG Library document for s30aa
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/s/s30aaf.html
- Parameters
- calputstr, length 1
Determines whether the option is a call or a put.
A call; the holder has a right to buy.
A put; the holder has a right to sell.
- xfloat, array-like, shape
must contain , the th strike price, for .
- sfloat
, the price of the underlying asset.
- tfloat, array-like, shape
must contain , the th time, in years, to expiry, for .
- sigmafloat
, the volatility of the underlying asset. Note that a rate of 15% should be entered as .
- rfloat
, the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as .
- qfloat
, the annual continuous yield rate. Note that a rate of 8% should be entered as .
- Returns
- pfloat, ndarray, shape
contains , the option price evaluated for the strike price at expiry for and .
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: and .
- (errno )
On entry, .
Constraint: and .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- Notes
opt_bsm_price
computes the price of a European call (or put) option for constant volatility, , and risk-free interest rate, , with possible dividend yield, , using the Black–Scholes–Merton formula (see Black and Scholes (1973) and Merton (1973)). For a given strike price, , the price of a European call with underlying price, , and time to expiry, , isand the corresponding European put price is
and where denotes the cumulative Normal distribution function,
and
The option price is computed for each strike price in a set , , and for each expiry time in a set , .
- References
Black, F and Scholes, M, 1973, The pricing of options and corporate liabilities, Journal of Political Economy (81), 637–654
Merton, R C, 1973, Theory of rational option pricing, Bell Journal of Economics and Management Science (4), 141–183