qdpmc.model.market_process.BlackScholes

class qdpmc.model.market_process.BlackScholes(r, q, v, day_counter=252)[source]

Bases: object

A Black-Scholes process. A Black-Scholes market has two securities: a risky asset and a risk-free bond.

Dynamics of the asset price is driven by a geometric Brownian motion:

\[\mathrm{d}S_t=r S_t\mathrm{d}t + \sigma S_t \mathrm{d}W_t\]

and the log-return follows

\[\mathrm{d}\left(\mathrm{log}{S_t}\right)= (r-q-\frac{\sigma^2}{2})\mathrm{d}t+\sigma\mathrm{d}W_t\]

where the drift (under the risk-neutral measure) is the risk-free rate.

Parameters regarding market dynamics are set here before implementing Monte Carlo simulation.

Parameters

  • r (scalar) – The instantaenous risk-free rate.

  • q (scalar) – The continuous yield.

  • v (scalar) – The diffusion parameter.

  • day_counter (int) – An integer that controls the numder of trading days in a year. Default is 252.

Methods

__init__(r, q, v[, day_counter])

Attributes

coordinator