2.6.38. 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 price x(s) of the underlying security follows a lognormal process with x(0) = x0 and volatility sigma.

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 is scipy.stats.norm.cdf and d1, 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__