Skip to content

YANG–ZHANG VOLATILITY

Intuição

O estimador Yang–Zhang combina informação de:

  • variação entre barras (open_t vs close_{t-1}),
  • retorno intrabar (close_t vs open_t),
  • range intrabar (via termo Rogers–Satchell).

Como feature, ele tende a capturar regimes de volatilidade usando mais informação do que retornos close-to-close.

Definição

Seja:

  • o_t = ln(open_t / close_{t-1})
  • c_t = ln(close_t / open_t)
  • RS_t = ln(high_t/open_t)*ln(high_t/close_t) + ln(low_t/open_t)*ln(low_t/close_t)

A variância Yang–Zhang em uma janela n é:

YZ_var = Var(o_t) + k * Var(c_t) + (1-k) * E[RS_t]

com:

k = 0.34 / (1.34 + (n+1)/(n-1))

E a volatilidade é sqrt(YZ_var).

Uso

from quantmaster.features.volatility import yang_zhang_volatility

df["yz"] = yang_zhang_volatility(df, window=20)

API

Source code in src/quantmaster/features/volatility.py 
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
def yang_zhang_volatility(
    data: pd.DataFrame,
    *,
    window: int = 20,
    open_col: str = "open",
    high_col: str = "high",
    low_col: str = "low",
    close_col: str = "close",
) -> pd.Series:
    window = validate_positive_int(window, name="window")
    if window < 2:
        raise ValueError(f"window must be >= 2, got {window}")

    validate_columns(data, required=(open_col, high_col, low_col, close_col))

    o = pd.to_numeric(data[open_col], errors="coerce").astype(float)
    h = pd.to_numeric(data[high_col], errors="coerce").astype(float)
    l = pd.to_numeric(data[low_col], errors="coerce").astype(float)
    c = pd.to_numeric(data[close_col], errors="coerce").astype(float)

    o = o.where(o > 0)
    h = h.where(h > 0)
    l = l.where(l > 0)
    c = c.where(c > 0)

    prev_c = c.shift(1)

    o_ret = np.log(o / prev_c)
    c_ret = np.log(c / o)

    sigma_o2 = o_ret.rolling(window).var(ddof=1)
    sigma_c2 = c_ret.rolling(window).var(ddof=1)

    log_ho = np.log(h / o)
    log_hc = np.log(h / c)
    log_lo = np.log(l / o)
    log_lc = np.log(l / c)
    rs = log_ho * log_hc + log_lo * log_lc
    sigma_rs2 = rs.rolling(window).mean()

    k = 0.34 / (1.34 + (window + 1) / (window - 1))
    yz_var = sigma_o2 + k * sigma_c2 + (1.0 - k) * sigma_rs2

    out = np.sqrt(yz_var)
    out.name = f"yang_zhang_volatility_{window}"
    return out