Function fit_two_normal_mixture_em

crates/openquant/src/bet_sizing.rs:435–512

(
    samples: &[f64],
    fit_runs: usize,
    epsilon: f64,
    max_iter: usize,
)

///
/// # Errors
///
/// [`BetSizingError::PriceDivergenceOutOfRange`] if `price_div` is outside `[-1, 1]`.
pub fn get_w_power(price_div: f64, m_bet_size: f64) -> Result<f64, BetSizingError> {
    if !(-1.0..=1.0).contains(&price_div) {
        return Err(BetSizingError::PriceDivergenceOutOfRange { value: price_div });
    }
    let w_calc = (m_bet_size / price_div.signum()).ln() / price_div.abs().ln();
    if w_calc < 0.0 {
        return Ok(0.0);
    }
    Ok(w_calc)
}

/// Sigmoid target position `trunc(m(forecast - market) * max_pos)` (AFML Snippet 10.4).
pub fn get_target_pos_sigmoid(
    w_param: f64,
    forecast_price: f64,
    market_price: f64,
    max_pos: f64,
) -> f64 {
    (bet_size_sigmoid(w_param, forecast_price - market_price) * max_pos).trunc()
}

/// Power-curve target position `trunc(m(forecast - market) * max_pos)`.
///
/// # Errors
///
/// [`BetSizingError::PriceDivergenceOutOfRange`] if `forecast_price - market_price` is
/// outside `[-1, 1]`.
pub fn get_target_pos_power(
    w_param: f64,
    forecast_price: f64,
    market_price: f64,
    max_pos: f64,
) -> Result<f64, BetSizingError> {
    Ok((bet_size_power(w_param, forecast_price - market_price)? * max_pos).trunc())
}

/// Averages `inv(k / max_pos)` over the positions `k` passed through on the way from `pos`
/// to `t_pos`: `pos + sgn, pos + 2 sgn, ..., t_pos`, with `sgn` the sign of `t_pos - pos` and
/// both truncated to whole units. `NaN` when the truncated positions are equal.
fn limit_price_traversal(t_pos: f64, pos: f64, max_pos: f64, inv: impl Fn(f64) -> f64) -> f64 {
    let target = t_pos.trunc() as i64;
    let current = pos.trunc() as i64;
    if target == current {
        return f64::NAN;
    }
    let sgn = (target - current).signum();
    let steps = (target - current).abs();
    let total: f64 = (1..=steps).map(|i| inv((current + sgn * i) as f64 / max_pos)).sum();
    total / steps as f64
}

/// Sigmoid breakeven limit price for moving from `pos` to `t_pos` with forecast `f`, width
/// `w` and maximum position `max_pos` (AFML Snippet 10.4, extended to every direction).
///
/// Both positions are truncated to whole units. With `sgn` the sign of `t_pos - pos`, the
/// result is the mean of [`inv_price_sigmoid`]`(f, w, k / max_pos)` over the positions