3.6.38. sdepy.bscall¶
-
class
sdepy.
bscall
(k, t, *, x0=1., r=0., q=0., sigma=1.)[source]¶ Black-Scholes call option value.
Parameters: - k : array-like
Strike.
- t : array-like
Time to maturity.
- x0 : array-like
Initial value of underlying security.
- r : array-like
Risk-free rate.
- q : array-like
Dividend yield of underlying security.
- sigma : array-like
Volatility of underlying security.
Returns: - array
Risk neutral valuation at time s=0 of an European call option paying
max(x(t) - k, 0)
at maturity, where the pricex(s)
of the underlying security follows a lognormal process withx(0) = x0
and volatilitysigma
.
See also
Notes
bscall(k, t, x0, r, q, sigma)
returns:bscall_value = x0*exp(-q*t)*norm.cdf(d1) + k*exp(-r*t)*norm.cdf(d2)
where
cdf
isscipy.stats.norm.cdf
andd1, d2 = bsd1d2(k, t, x0, r, q, sigma)
are given as:d1 = (log(x0/k) + (r - q + sigma**2/2)*t)/(sigma*sqrt(t)) d2 = d1 - sigma*sqrt(t)
Attributes: - params
Methods
__call__