pfhedge.nn.functional.d1

pfhedge.nn.functional.d1(log_moneyness, time_to_maturity, volatility)

Returns \(d_1\) in the Black-Scholes formula.

\[d_1 = \frac{s}{\sigma \sqrt{t}} + \frac{\sigma \sqrt{t}}{2}\]

where \(s\) is the log moneyness, \(t\) is the time to maturity, and \(\sigma\) is the volatility.

Note

Risk-free rate is set to zero.

Parameters

• log_moneyness (torch.Tensor or float) – Log moneyness of the underlying asset.

• time_to_maturity (torch.Tensor or float) – Time to maturity of the derivative.

• volatility (torch.Tensor or float) – Volatility of the underlying asset.

Returns

torch.Tensor