├── .dockerignore ├── thumbnail.png ├── .gitignore ├── .streamlit └── config.toml ├── Dockerfile ├── pyproject.toml ├── README.md ├── requirements.txt ├── lib ├── surface.py ├── data.py └── plot.py ├── app.py ├── LICENSE └── uv.lock /.dockerignore: -------------------------------------------------------------------------------- 1 | .venv 2 | .git 3 | thumbnail.png 4 | -------------------------------------------------------------------------------- /thumbnail.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/joshuapjacob/crypto-volatility-surface/HEAD/thumbnail.png -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # python generated files 2 | __pycache__/ 3 | *.py[oc] 4 | build/ 5 | dist/ 6 | wheels/ 7 | *.egg-info 8 | 9 | # venv 10 | .venv 11 | -------------------------------------------------------------------------------- /.streamlit/config.toml: -------------------------------------------------------------------------------- 1 | [theme] 2 | base = "dark" 3 | 4 | [client] 5 | toolbarMode = "minimal" 6 | 7 | [server] 8 | baseUrlPath = "/crypto-volatility-surface" -------------------------------------------------------------------------------- /Dockerfile: -------------------------------------------------------------------------------- 1 | FROM python:3.12-slim-bookworm 2 | 3 | COPY --from=ghcr.io/astral-sh/uv:latest /uv /bin/uv 4 | 5 | ADD . /app 6 | 7 | WORKDIR /app 8 | 9 | RUN uv sync --frozen 10 | 11 | EXPOSE 8501 12 | 13 | ENTRYPOINT ["uv", "run", "streamlit", "run", "app.py", "--server.port=8501", "--server.address=0.0.0.0"] -------------------------------------------------------------------------------- /pyproject.toml: -------------------------------------------------------------------------------- 1 | [project] 2 | name = "crypto-volatility-surface" 3 | version = "0.1.0" 4 | description = "A dashboard to visualize cryptocurrency implied volatility surfaces constructed with option data from Binance." 5 | readme = "README.md" 6 | requires-python = ">=3.12" 7 | dependencies = [ 8 | "numpy>=2.1.0", 9 | "plotly>=5.24.0", 10 | "polars", 11 | "requests[socks]>=2.32.3", 12 | "scipy>=1.14.1", 13 | "streamlit", 14 | ] 15 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # [Crypto Volatility Surface](https://joshuapjacob.com/crypto-volatility-surface) 2 | 3 | A dashboard to visualize cryptocurrency implied volatility surfaces constructed with option data from Binance. 4 | 5 | ![Volatility Surface](./thumbnail.png) 6 | 7 | ## Run Locally 8 | 9 | ```bash 10 | uv run streamlit run app.py 11 | ``` 12 | 13 | If you are in a restricted location (like the United States) and use a proxy to access Binance, set a `BINANCE_PROXY` environment variable. 14 | 15 | ```bash 16 | # For example: 17 | BINANCE_PROXY="socks5://localhost:5000" 18 | ``` 19 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | # This file was autogenerated by uv via the following command: 2 | # uv pip compile pyproject.toml 3 | altair==5.5.0 4 | # via streamlit 5 | attrs==25.1.0 6 | # via 7 | # jsonschema 8 | # referencing 9 | blinker==1.9.0 10 | # via streamlit 11 | cachetools==5.5.1 12 | # via streamlit 13 | certifi==2025.1.31 14 | # via requests 15 | charset-normalizer==3.4.1 16 | # via requests 17 | click==8.1.8 18 | # via streamlit 19 | gitdb==4.0.12 20 | # via gitpython 21 | gitpython==3.1.44 22 | # via streamlit 23 | idna==3.10 24 | # via requests 25 | jinja2==3.1.6 26 | # via 27 | # altair 28 | # pydeck 29 | jsonschema==4.23.0 30 | # via altair 31 | jsonschema-specifications==2024.10.1 32 | # via jsonschema 33 | markdown-it-py==3.0.0 34 | # via rich 35 | markupsafe==3.0.2 36 | # via jinja2 37 | mdurl==0.1.2 38 | # via markdown-it-py 39 | narwhals==1.25.0 40 | # via 41 | # altair 42 | # plotly 43 | numpy==2.2.2 44 | # via 45 | # crypto-volatility-surface (pyproject.toml) 46 | # pandas 47 | # pydeck 48 | # scipy 49 | # streamlit 50 | packaging==24.2 51 | # via 52 | # altair 53 | # plotly 54 | # streamlit 55 | pandas==2.2.3 56 | # via streamlit 57 | pillow==11.1.0 58 | # via streamlit 59 | plotly==6.0.0 60 | # via crypto-volatility-surface (pyproject.toml) 61 | polars==1.21.0 62 | # via crypto-volatility-surface (pyproject.toml) 63 | protobuf==5.29.3 64 | # via streamlit 65 | pyarrow==19.0.0 66 | # via streamlit 67 | pydeck==0.9.1 68 | # via streamlit 69 | pygments==2.19.1 70 | # via rich 71 | pysocks==1.7.1 72 | # via requests 73 | python-dateutil==2.9.0.post0 74 | # via pandas 75 | pytz==2025.1 76 | # via pandas 77 | referencing==0.36.2 78 | # via 79 | # jsonschema 80 | # jsonschema-specifications 81 | requests==2.32.3 82 | # via 83 | # crypto-volatility-surface (pyproject.toml) 84 | # streamlit 85 | rich==13.9.4 86 | # via streamlit 87 | rpds-py==0.22.3 88 | # via 89 | # jsonschema 90 | # referencing 91 | scipy==1.15.1 92 | # via crypto-volatility-surface (pyproject.toml) 93 | six==1.17.0 94 | # via python-dateutil 95 | smmap==5.0.2 96 | # via gitdb 97 | streamlit==1.42.0 98 | # via crypto-volatility-surface (pyproject.toml) 99 | tenacity==9.0.0 100 | # via streamlit 101 | toml==0.10.2 102 | # via streamlit 103 | tornado==6.5.1 104 | # via streamlit 105 | typing-extensions==4.12.2 106 | # via 107 | # altair 108 | # referencing 109 | # streamlit 110 | tzdata==2025.1 111 | # via pandas 112 | urllib3==2.3.0 113 | # via requests 114 | -------------------------------------------------------------------------------- /lib/surface.py: -------------------------------------------------------------------------------- 1 | """Surface Construction""" 2 | 3 | import numpy as np 4 | import polars as pl 5 | from scipy.interpolate import RectBivariateSpline 6 | from scipy.optimize import least_squares 7 | 8 | 9 | def kernel_smoothing( 10 | X: np.ndarray, 11 | Y: np.ndarray, 12 | df: pl.DataFrame, 13 | h_x: float = 0.01, 14 | h_y: float = 0.1, 15 | ) -> np.ndarray: 16 | """ 17 | Construct kernel smoothed surface. 18 | 19 | Args: 20 | X (np.ndarray): Moneyness coordinate matrix. 21 | Y (np.ndarray): Horizon coordinate matrix. 22 | df (pl.DataFrame): Option data. 23 | h_x (float): Moneyness bandwidth. 24 | h_y (float): Horizon bandwidth. 25 | """ 26 | 27 | def kernel(dx, dy): 28 | exponent = (dx**2) / (2 * h_x) + (dy**2) / (2 * h_y) 29 | return np.exp(-exponent) / np.sqrt(2 * np.pi) 30 | 31 | # Vectorized! 32 | x = X.ravel().reshape(1, -1) 33 | y = Y.ravel().reshape(1, -1) 34 | dx = df["logMoneyness"].to_numpy().reshape(-1, 1) - x 35 | dy = np.log(df["daysToExpiry"].to_numpy().reshape(-1, 1) / y) 36 | w = df["weight"].to_numpy().reshape(-1, 1) * kernel(dx, dy) 37 | res = np.sum(df["markIV"].to_numpy()[:, np.newaxis] * w, axis=0) 38 | res /= np.sum(w, axis=0) 39 | Z = res.reshape(Y.shape) 40 | return Z 41 | 42 | 43 | def svi(X: np.ndarray, Y: np.ndarray, df: pl.DataFrame): 44 | """ 45 | Construct Stochastic Volatility Inspired (SVI) surface. 46 | 47 | Args: 48 | X (np.ndarray): Moneyness coordinate matrix. 49 | Y (np.ndarray): Horizon coordinate matrix. 50 | df (pl.DataFrame): Option data. 51 | """ 52 | 53 | def raw_svi(k, a, b, s, rho, m): 54 | return a + b * (rho * (k - m) + np.sqrt((k - m) ** 2 + s**2)) 55 | 56 | def fit(data): 57 | """For a given time slice, return fitted IV curve.""" 58 | log_moneyness = data[0].to_numpy() 59 | yrs_to_expiry = data[1][0] / 365 60 | mark_iv = data[2].to_numpy() 61 | weights = data[3].to_numpy() 62 | 63 | def residual(params): 64 | total_implied_var = raw_svi(log_moneyness, *params) 65 | iv = np.sqrt(total_implied_var / yrs_to_expiry) 66 | return (mark_iv - iv) * np.sqrt(weights) 67 | 68 | result = least_squares( 69 | fun=residual, 70 | x0=np.zeros(5), 71 | max_nfev=10_000, 72 | verbose=0, 73 | bounds=([-np.inf, 0, -1, -np.inf, 0], [np.inf, np.inf, 1, np.inf, np.inf]), 74 | ) 75 | 76 | return np.sqrt(raw_svi(X[0], *result.x) / yrs_to_expiry) 77 | 78 | # Fit for each time slice. 79 | res = ( 80 | df.group_by("daysToExpiry") 81 | .agg(pl.map_groups(["logMoneyness", "daysToExpiry", "markIV", "weight"], fit)) 82 | .sort("daysToExpiry") 83 | ) 84 | y_raw = res["daysToExpiry"].to_numpy() 85 | z_raw = res["logMoneyness"].explode().to_numpy() 86 | Z_raw = z_raw.reshape((len(y_raw), len(X[0]))).T 87 | 88 | # Interpolate over horizon with bivariate spline approximation. 89 | interpolate = RectBivariateSpline(X[0], y_raw, Z_raw, ky=2) 90 | Z = interpolate(X[0], Y[:, 0]).T 91 | return Z 92 | -------------------------------------------------------------------------------- /lib/data.py: -------------------------------------------------------------------------------- 1 | """Binance Option Data""" 2 | 3 | import os 4 | from datetime import datetime, timezone 5 | 6 | import polars as pl 7 | import requests 8 | import streamlit as st 9 | 10 | 11 | def get(path: str) -> dict: 12 | """Send GET request to Binance Options API and return the JSON response.""" 13 | 14 | resp = requests.get( 15 | f"https://eapi.binance.com/eapi/v1/{path}", 16 | proxies=dict(https=os.getenv("BINANCE_PROXY", "")), 17 | ) 18 | resp.raise_for_status() 19 | resp = resp.json() 20 | 21 | if "code" in resp and resp["code"] == 0: 22 | raise ConnectionError(resp["msg"]) 23 | 24 | return resp 25 | 26 | 27 | @st.cache_data( 28 | persist="disk", show_spinner="Updating option market data...", max_entries=1 29 | ) 30 | def load_data(now_ts: int, universe: list[str]) -> tuple[pl.DataFrame, datetime]: 31 | """ 32 | Load option data from Binance. 33 | 34 | Args: 35 | now_ts (int): Current timestamp (rounded to nearest hour). 36 | Only used by the caching mechanism. 37 | universe (list[str]): List of underlying symbols. 38 | 39 | Returns: 40 | tuple[pl.DataFrame, datetime]: Option data and update timestamp. 41 | """ 42 | 43 | MIN_IV = 0.01 44 | MAX_IV = 5 45 | MIN_DAYS_TO_EXPIRY = 10 46 | MAX_DAYS_TO_EXPIRY = 180 47 | MAX_LOG_MONEYNESS = 0.15 48 | 49 | # Get current exchange and symbol information. 50 | exchange_info = get("exchangeInfo") 51 | update_dt = datetime.fromtimestamp( 52 | exchange_info["serverTime"] / 1000, tz=timezone.utc 53 | ) 54 | symbol_df = ( 55 | pl.DataFrame( 56 | exchange_info["optionSymbols"], 57 | schema={ 58 | "symbol": str, 59 | "underlying": str, 60 | "expiryDate": pl.Datetime(time_unit="ms", time_zone="UTC"), 61 | "strikePrice": pl.Float32, 62 | "side": str, 63 | }, 64 | ) 65 | .with_columns(daysToExpiry=(pl.col("expiryDate") - update_dt).dt.total_days()) 66 | .filter( 67 | pl.col("daysToExpiry").is_between(MIN_DAYS_TO_EXPIRY, MAX_DAYS_TO_EXPIRY), 68 | pl.col("underlying").is_in(universe), 69 | ) 70 | ) 71 | 72 | # Get underlying index prices. 73 | underlying_df = ( 74 | symbol_df["underlying"] 75 | .unique() 76 | .to_frame() 77 | .with_columns( 78 | indexPrice=pl.col("underlying").map_elements( 79 | lambda x: float(get(f"index?underlying={x}")["indexPrice"]), 80 | return_dtype=pl.Float32, 81 | ) 82 | ) 83 | ) 84 | 85 | # Get option IVs and greeks. 86 | mark_df = pl.DataFrame( 87 | get("mark"), 88 | schema={ 89 | "symbol": str, 90 | "bidIV": pl.Float32, 91 | "askIV": pl.Float32, 92 | "markIV": pl.Float32, 93 | }, 94 | ).filter( 95 | pl.col("bidIV").is_between(MIN_IV, MAX_IV), 96 | pl.col("askIV").is_between(MIN_IV, MAX_IV), 97 | ) 98 | 99 | df = ( 100 | symbol_df.join(underlying_df, on="underlying") 101 | .join(mark_df, on="symbol") 102 | .sort(by=["underlying", "strikePrice", "daysToExpiry"]) 103 | .with_columns( 104 | logMoneyness=(pl.col("indexPrice") / pl.col("strikePrice")).log(), 105 | weight=1 / (1 + pl.col("askIV") - pl.col("bidIV")), 106 | ) 107 | .filter( 108 | # Ignore deep in-the-money options. 109 | pl.when(pl.col("side") == "CALL") 110 | .then((pl.col("logMoneyness") < MAX_LOG_MONEYNESS)) 111 | .otherwise((pl.col("logMoneyness") > -MAX_LOG_MONEYNESS)) 112 | ) 113 | ) 114 | 115 | return df, update_dt 116 | -------------------------------------------------------------------------------- /lib/plot.py: -------------------------------------------------------------------------------- 1 | """Volatility Surface Plots""" 2 | 3 | import numpy as np 4 | import plotly.graph_objs as go 5 | import polars as pl 6 | 7 | N_POINTS = 25 8 | 9 | 10 | def generate_figures( 11 | df: pl.DataFrame, surface_func: callable, *args 12 | ) -> list[go.Figure]: 13 | """ 14 | Generate volatility surface plots. 15 | 16 | Args: 17 | df (pl.DataFrame): Option data. 18 | surface_func (callable): Volatility surface construction function. 19 | *args: arguments to the the surface function. 20 | 21 | Returns: 22 | go.Figure: Plotly figure. 23 | """ 24 | 25 | universe = df["underlying"].unique().sort() 26 | max_tte = df.filter(pl.col("daysToExpiry") <= 180)["daysToExpiry"].max() 27 | x = np.linspace(-1, 1, N_POINTS) 28 | y = np.linspace(10, max_tte, N_POINTS) 29 | X, Y = np.meshgrid(x, y) 30 | cmin, cmax = df["markIV"].min(), df["markIV"].max() 31 | 32 | def generate_figure(underlying: str) -> go.Figure: 33 | """Generate volatility surface plot for a given underlying.""" 34 | udf = df.filter(pl.col("underlying") == underlying) 35 | fig = go.Figure() 36 | 37 | # Add surface. 38 | Z = surface_func(X, Y, udf, *args) 39 | fig.add_trace( 40 | go.Surface( 41 | x=X, 42 | y=Y, 43 | z=Z, 44 | coloraxis="coloraxis", 45 | opacity=0.9, 46 | contours=dict( 47 | z=dict(highlight=False), 48 | ), 49 | name="Surface", 50 | showlegend=True, 51 | hovertemplate=( 52 | "Log Moneyness: %{x:.2f}
" 53 | "Days To Expiry: %{y:d}
" 54 | "IV: %{z}" 55 | ), 56 | ), 57 | ) 58 | 59 | # Add scatter plot of options. 60 | for side, color in [("CALL", "#00CC96"), ("PUT", "#EF553B")]: 61 | filtered = udf.filter(pl.col("side") == side) 62 | fig.add_trace( 63 | go.Scatter3d( 64 | x=filtered["logMoneyness"], 65 | y=filtered["daysToExpiry"], 66 | z=filtered["markIV"], 67 | mode="markers", 68 | marker=dict(size=5, color=color), 69 | name=side, 70 | text=filtered["symbol"], 71 | hovertemplate="%{text}
IV: %{z}", 72 | showlegend=True, 73 | ), 74 | ) 75 | 76 | # Define layout. 77 | fig.update_layout( 78 | title=dict( 79 | text=underlying, 80 | x=0.5, 81 | y=0.95, 82 | xanchor="center", 83 | yanchor="top", 84 | ), 85 | height=600, 86 | margin=dict(l=0, r=0, t=0, b=0), 87 | coloraxis=dict( 88 | cmin=cmin, 89 | cmax=cmax, 90 | colorbar=dict(tickformat=",.0%", title="IV", thickness=10), 91 | colorscale="Viridis", 92 | ), 93 | legend=dict(y=0, itemsizing="constant"), 94 | scene=dict( 95 | xaxis=dict(title="Log Moneyness", range=[-1, 1], showspikes=False), 96 | yaxis=dict( 97 | title="Days To Expiry", range=[10, max_tte], showspikes=False 98 | ), 99 | zaxis=dict( 100 | title="Implied Volatility", 101 | tickformat=",.0%", 102 | showspikes=False, 103 | ), 104 | ), 105 | ) 106 | 107 | return fig 108 | 109 | return [generate_figure(underlying) for underlying in universe] 110 | -------------------------------------------------------------------------------- /app.py: -------------------------------------------------------------------------------- 1 | """Streamlit App""" 2 | 3 | from datetime import datetime, timezone 4 | 5 | import streamlit as st 6 | 7 | from lib.data import load_data 8 | from lib.plot import generate_figures 9 | from lib.surface import kernel_smoothing, svi 10 | 11 | UNIVERSE = ["BTCUSDT", "ETHUSDT"] 12 | 13 | st.set_page_config( 14 | page_icon=":material/candlestick_chart:", 15 | page_title="Crypto Volatility Surface", 16 | layout="wide", 17 | menu_items={}, 18 | ) 19 | 20 | # ------------------------------------------------------------------------------ 21 | 22 | st.title("Crypto Volatility Surface") 23 | st.markdown( 24 | """**A dashboard to visualize cryptocurrency implied volatility surfaces 25 | constructed with option data from Binance.**""" 26 | ) 27 | 28 | st.divider() # ---------------------------------------------------------------- 29 | 30 | cols = st.columns(2, gap="large") 31 | with cols[0]: 32 | st.markdown( 33 | r""" 34 | Implied volatility (IV) shows the market's expected volatility of an 35 | option's underlying over the life of the option. Not all options on the 36 | same underlying have the same IV. High IV results in higher premiums and 37 | vice versa. 38 | 39 | A [volatility surface](https://www.investopedia.com/articles/stock-analysis/081916/volatility-surface-explained.asp) 40 | is a three-dimensional plot of IVs of various options listed on the same 41 | underlying. It can be used to visualize the volatility smile/skew and 42 | term structure. We use cryptocurrency option data from Binance to 43 | construct volatility surfaces using two approaches: kernel smoothing and 44 | the Stochastic Volatility Inspired (SVI) parametrization. 45 | 46 | Cryptocurrency options listed on Binance are European-style. For each 47 | option, Binance uses the [Black-Scholes model](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model) 48 | to provide three different IVs: $\sigma^{\text{bid}}$, 49 | $\sigma^{\text{ask}}$, and $\sigma^{\text{mark}}$, calculated from the 50 | best bid, best ask, and midprice respectively. We use $\tau$ to denote 51 | the number of days to expiry. For an option with strike price $K$ and 52 | underlying spot price $S$, we define log moneyness $k = \log(S/K)$. 53 | """ 54 | ) 55 | st.markdown( 56 | r""" 57 | In both of our approaches, we also ignore deep in-the-money options and 58 | weight observed option data points with the following scheme: 59 | """ 60 | ) 61 | st.latex( 62 | r""" 63 | w = \frac{1}{1 + \left(\sigma^\text{ask} - \sigma^\text{bid}\right)} 64 | """ 65 | ) 66 | st.markdown( 67 | r""" 68 | This downweights options with higher IV spreads i.e. options with mark 69 | IVs that are less "agreed upon". 70 | """ 71 | ) 72 | 73 | with cols[1]: 74 | # Load option data (with caching). 75 | now_dt = datetime.now(tz=timezone.utc) 76 | now_hr_ts = (now_dt.timestamp() // 3600) * 3600 77 | df, update_dt = load_data(now_hr_ts, UNIVERSE) # Cache hit if same hour. 78 | min_ago = int(max((now_dt - update_dt).total_seconds() // 60, 0)) 79 | s = "" if min_ago == 1 else "s" 80 | st.markdown( 81 | f""" 82 | Option market data was last updated {min_ago} minute{s} ago at 83 | {str(update_dt)[:16]} UTC.""" 84 | ) 85 | st.dataframe(df, use_container_width=True) 86 | 87 | st.divider() # ---------------------------------------------------------------- 88 | 89 | st.header("Kernel Smoothing") 90 | cols = st.columns(2, gap="large") 91 | with cols[0]: 92 | st.markdown( 93 | r""" 94 | [Kernel smoothing](https://en.wikipedia.org/wiki/Kernel_smoother) is a 95 | non-parametric approach to volatility surface construction. The kernel 96 | function determines the weight assigned to each option data point based 97 | on its distance from the point being estimated. Kernel smoothing does 98 | not assume a specific functional form for the volatility surface, making 99 | it adaptable to various shapes and market conditions. This approach 100 | ensures that the estimate at each point is primarily influenced by 101 | nearby data, capturing local market behaviors. 102 | 103 | At each grid point $j$ on the volatility surface, the smoothed 104 | volatility $\hat{\sigma}_j$ is calculated as a weighted sum where $i$ is 105 | the index over all the options on the given underlying. 106 | """ 107 | ) 108 | st.latex( 109 | r""" 110 | \hat{\sigma}_j = \frac{ 111 | \sum_{i=1}^n \sigma^\text{mark}_i w_i \phi(x_{ij},y_{ij}) 112 | }{ 113 | \sum_{i=1}^n w_i \phi(x_{ij},y_{ij}) 114 | } 115 | """ 116 | ) 117 | st.markdown( 118 | r""" 119 | Our choice of kernel function $\phi$ is Gaussian-like and inspired by 120 | the industry standard "TradFi" data vendor 121 | [OptionMetrics](https://optionmetrics.com/). 122 | """ 123 | ) 124 | st.latex( 125 | r""" 126 | \phi(x,y) = \frac{1}{\sqrt{2 \pi}} 127 | \exp \left(-\frac{x^2}{2h_x} -\frac{y^2}{2h_y} \right) 128 | """ 129 | ) 130 | 131 | with cols[1]: 132 | st.markdown( 133 | r""" 134 | The bandwidth hyperparameters $h_x$ and $h_y$ control the smoothness of 135 | the surface and the parameters to the kernel function $x_{ij}$ and 136 | $y_{ij}$ are measures of distance between the option data point and the 137 | target grid point. 138 | """ 139 | ) 140 | st.latex(r"x_{ij} = k_i - k_j \quad\quad y_{ij} = \log(\tau_i / \tau_j)") 141 | h_x = st.slider( 142 | label="Moneyness Smoothing $h_x$", 143 | min_value=0.005, 144 | max_value=0.05, 145 | value=0.01, 146 | step=0.005, 147 | format="%f", 148 | ) 149 | h_y = st.slider( 150 | label="Horizon Smoothing $h_y$", 151 | min_value=0.05, 152 | max_value=0.2, 153 | value=0.10, 154 | step=0.01, 155 | ) 156 | 157 | with st.spinner("Constructing kernel smoothed surface..."): 158 | figs = generate_figures(df, kernel_smoothing, h_x, h_y) 159 | cols = st.columns(len(figs), gap="large") 160 | for col, fig in zip(cols, figs): 161 | with col: 162 | st.plotly_chart(fig, use_container_width=True) 163 | 164 | st.divider() # ---------------------------------------------------------------- 165 | 166 | st.header("Stochastic Volatility Inspired (SVI) Parameterization") 167 | cols = st.columns(2, gap="large") 168 | with cols[0]: 169 | st.markdown( 170 | r""" 171 | The [Stochastic Volatility Inspired (SVI)](https://api.semanticscholar.org/CorpusID:156076635) 172 | parameterization of the volatility surface was introduced by Merill 173 | Lynch in 1999 and popularized by Jim Gatheral. It is designed for 174 | calibration of a time-specific slice of the implied volatility surface, 175 | capturing the dynamics of the skew/smile across strikes, which can be 176 | challenging to model using other traditional approaches. SVI aligns with 177 | the behavior of the [Heston model](https://en.wikipedia.org/wiki/Heston_model), 178 | a widely-used stochastic volatility model, in the long-term maturity 179 | limit. 180 | 181 | For a given parameter set $\chi = \{a, b, \rho, m, s\}$, the raw SVI 182 | parameterization of total implied variance is 183 | """ 184 | ) 185 | st.latex( 186 | r""" 187 | f(k; \chi) = a + b \left( \rho (k+m) + \sqrt{(k-m)^2 + s^2}\right) 188 | """ 189 | ) 190 | st.markdown(r"with implied volatility for a grid point $j$ given by") 191 | st.latex(r"\hat{\sigma}_j = \sqrt{\frac{f(k_j; \chi_{\tau_j})}{\tau_j}}") 192 | 193 | 194 | with cols[1]: 195 | st.markdown( 196 | r""" 197 | For each time slice $\tau$, where $i$ is the index over all options on 198 | the given underlying with $\tau$ days to expiry, we solve the following 199 | non-linear weighted least squares problem: 200 | """ 201 | ) 202 | st.latex( 203 | r""" 204 | \begin{align*} 205 | \min_{\chi_{\tau}} \quad& \sum_{i=1}^n 206 | w_i \left(\hat{\sigma}_i - \sigma^{\text{mark}}_i \right)^2 \\ 207 | \text{s.t.} \quad& b \geq 0 \\ 208 | &|\rho| \leq 1 \\ 209 | &s \geq 0 210 | \end{align*} 211 | """ 212 | ) 213 | st.markdown( 214 | r""" 215 | Note that our calibration of the SVI surface does not guarantee the 216 | absence of static (calendar and butterfly) arbitrage. Interpolation over 217 | various time slices is performed with quadratic bivariate spline 218 | approximations. 219 | """ 220 | ) 221 | 222 | with st.spinner("Constructing SVI surface..."): 223 | figs = generate_figures(df, svi) 224 | cols = st.columns(len(figs), gap="large") 225 | for col, fig in zip(cols, figs): 226 | with col: 227 | st.plotly_chart(fig, use_container_width=True) 228 | 229 | st.divider() # ---------------------------------------------------------------- 230 | 231 | st.markdown( 232 | "[![GitHub](https://img.shields.io/badge/github-%23121011.svg?style=for-the-badge&logo=github&logoColor=white&color=rgba(0%2C0%2C0%2C0))](https://github.com/joshuapjacob/crypto-volatility-surface)" 233 | ) 234 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /uv.lock: -------------------------------------------------------------------------------- 1 | version = 1 2 | requires-python = ">=3.12" 3 | 4 | [[package]] 5 | name = "altair" 6 | version = "5.5.0" 7 | source = { registry = "https://pypi.org/simple" } 8 | dependencies = [ 9 | { name = "jinja2" }, 10 | { name = "jsonschema" }, 11 | { name = "narwhals" }, 12 | { name = "packaging" }, 13 | { name = "typing-extensions", marker = "python_full_version < '3.14'" }, 14 | ] 15 | sdist = { url = "https://files.pythonhosted.org/packages/16/b1/f2969c7bdb8ad8bbdda031687defdce2c19afba2aa2c8e1d2a17f78376d8/altair-5.5.0.tar.gz", hash = "sha256:d960ebe6178c56de3855a68c47b516be38640b73fb3b5111c2a9ca90546dd73d", size = 705305 } 16 | wheels = [ 17 | { url = 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