feat: SABR model volatility and fitting

avhz · Nov 24, 2024 · 0851a88 · 0851a88
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diff --git a/book/src/Modules/autodiff.md b/book/src/Modules/autodiff.md
@@ -0,0 +1,29 @@
+# `autodiff`
+
+The `autodiff` module can be used to differentiate scalar output functions of the form:
+
+\\[f : \mathbb{R}^n \rightarrow \mathbb{R} \\]
+
+
+Simple expressions are differentiated as follows:
+
+```rust,noplayground
+{{#include ../../../examples/examples/autodiff.rs:simple_expressions}}
+```
+
+Block expressions are also supported:
+
+```rust,noplayground
+{{#include ../../../examples/examples/autodiff.rs:block_expressions}}
+```
+
+Closures and functions are also supported:
+
+```rust,noplayground
+{{#include ../../../examples/examples/autodiff.rs:closures}}
+```
+
+```rust,noplayground
+{{#include ../../../examples/examples/autodiff.rs:functions}}
+```
+
diff --git a/book/src/Modules/autodiff/autodiff.md b/book/src/Modules/autodiff/autodiff.md
diff --git a/book/src/Modules/cashflows/cashflows.md b/book/src/Modules/cashflows/cashflows.md
diff --git a/book/src/Modules/data/data.md → book/src/Modules/data.md b/book/src/Modules/data/data.md → book/src/Modules/data.md
@@ -6,3 +6,12 @@ That is, anything that can be observed, either in markets or derived from market
 
 Another form of data is contextual (or reference) data. These are things such as calendars and date conventions. While there are facilities to handle these data inside the `data` module, the underlying implementations are in other modules, such as the `time` module.
 
+## Curves
+
+Curves can be fit to market data. Here we include an example of a spot curve being fitted.
+
+![`Spot curve`](../assets/spotcurve.png)
+
+```rust
+{{#include ../../../examples/examples/curves_spot.rs}}
+```
diff --git a/book/src/Modules/data/curves.md b/book/src/Modules/data/curves.md
diff --git a/book/src/Modules/error.md b/book/src/Modules/error.md
diff --git a/book/src/Modules/instruments.md b/book/src/Modules/instruments.md
@@ -0,0 +1,29 @@
+# `instruments`
+
+
+## European Vanilla Options
+
+To price a vanilla European option, we begin by defining the option itself:
+
+```rust,noplayground
+{{#include ../../../examples/examples/option_pricing_vanilla.rs:option_definition}}
+```
+
+Then we need to define a model to price the option with:
+
+```rust,noplayground
+{{#include ../../../examples/examples/option_pricing_vanilla.rs:model_definitions}}
+```
+
+Lastly, we construct an `AnalyticOptionPricer`, from which we can generate a report.
+The report simply prints the option, model, price, and Greeks.
+
+```rust,noplayground
+{{#include ../../../examples/examples/option_pricing_vanilla.rs:option_pricing}}
+```
+
+The output will look something like this:
+
+```rust,noplayground
+{{#include ../../../examples/examples/option_pricing_vanilla.rs:output}}
+```
diff --git a/book/src/Modules/instruments/instruments.md b/book/src/Modules/instruments/instruments.md
diff --git a/book/src/Modules/instruments/options.md b/book/src/Modules/instruments/options.md
diff --git a/book/src/Modules/iso/iso.md b/book/src/Modules/iso/iso.md
diff --git a/book/src/Modules/macros.md b/book/src/Modules/macros.md
diff --git a/book/src/Modules/math.md b/book/src/Modules/math.md
@@ -0,0 +1,13 @@
+# `math`
+
+## Numerical Integration
+
+Here we integrate the Gaussian density, which integrates to 1:
+
+\\[
+\int_{\mathbb{R}} \frac{1}{\sqrt{2  \pi}} e^{\left( -\frac{x^2}{2} \right)} dx = 1    
+\\]
+
+```rust,noplayground
+{{#include ../../../examples/examples/numerical_integration.rs:numerical_integration}}
+```
diff --git a/book/src/Modules/math/math.md b/book/src/Modules/math/math.md
diff --git a/book/src/Modules/ml/ml.md b/book/src/Modules/ml/ml.md
diff --git a/book/src/Modules/models/models.md b/book/src/Modules/models/models.md
diff --git a/book/src/Modules/portfolio/portfolio.md b/book/src/Modules/portfolio/portfolio.md
diff --git a/book/src/Modules/stochastics.md b/book/src/Modules/stochastics.md
@@ -0,0 +1,11 @@
+# `stochastics`
+
+Many stochastic processes can be generated:
+
+```rust,noplayground
+{{#include ../../../examples/examples/stochastic_processes.rs:stochastic_processes}}
+```
+
+Paths can be plotted via the `plot_vector!` macro or `plotly`:
+
+![Geometric Brownian Motion](../assets/gbm.png)
diff --git a/book/src/Modules/stochastics/stochastics.md b/book/src/Modules/stochastics/stochastics.md
diff --git a/book/src/Modules/time/time.md b/book/src/Modules/time/time.md
diff --git a/book/src/Modules/trading/trading.md b/book/src/Modules/trading/trading.md
diff --git a/book/src/SUMMARY.md b/book/src/SUMMARY.md
@@ -8,21 +8,19 @@
 
 # Modules
 
-<!-- - [`autodiff`](./Modules/autodiff/autodiff.md)
-- [`cashflows`](./Modules/cashflows/cashflows.md) -->
-
-- [`data`](./Modules/data/data.md)
-    - [Curves](./Modules/data/curves.md)
+- [`autodiff`](./Modules/autodiff.md)
+- [`data`](./Modules/data.md)
+- [`instruments`](./Modules/instruments.md)
+- [`math`](./Modules/math.md)
+- [`stochastics`](./Modules/stochastics.md)
 
+<!-- - [`cashflows`](./Modules/cashflows/cashflows.md) -->
 <!-- - [`error`](./Modules/error.md) -->
-- [`instruments`](./Modules/instruments/instruments.md)
-    - [Options](./Modules/instruments/options.md)
 <!-- - [`iso`](./Modules/iso/iso.md)
 - [`macros`](./Modules/macros.md)
 - [`math`](./Modules/math/math.md)
 - [`ml`](./Modules/ml/ml.md)
 - [`portfolio`](./Modules/portfolio/portfolio.md)
-- [`stochastics`](./Modules/stochastics/stochastics.md)
 - [`time`](./Modules/time/time.md)
 - [`trading`](./Modules/trading/trading.md) -->
 

diff --git a/crates/RustQuant_instruments/Cargo.toml b/crates/RustQuant_instruments/Cargo.toml
@@ -26,6 +26,7 @@ RustQuant_stochastics = { workspace = true }
 RustQuant_iso = { workspace = true }
 
 ## External dependencies
+argmin = { workspace = true }
 time = { workspace = true }
 derive_builder = { workspace = true }
 errorfunctions = { workspace = true }