Intelligent Lattice Search: Efficiency in Option Pricing using Python, C++, Cython and Numba

Intelligent Lattice Search for American Option Pricing 🌟

This video presents a comprehensive exploration of Intelligent Lattice Search (ILS), an advanced computational method designed to optimize option pricing. Benchmarked against the Cantaro implementation (Python) as the baseline, ILS demonstrates remarkable in speed execution and efficiency. Through implementations in Python, Numba, Cython, and C++, this study highlights how ILS reduces computational complexity while maintaining accuracy, making it an invaluable tool in the field of quantitative finance. ⚡

What is intelligent Lattice Search

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### *📊 Performance Benchmarks*

| *Implementation* | *Execution Time* | *Speedup Over Baseline (Cantaro)* |
|-----------------------------------------------------|-----------------------------------|------------------------------------------------------- |
| 🐍 *Cantaro (Python)* | ~20 ms | 1x
| 🔧 *Python-Optimized (ILS)* | ~12 ms | ~1.67x
| ⚡ *Cython (ILS)* | ~7.26 ms | ~2.75x
| 🚀 *Numba (ILS)* | *347 µs (0.347 ms)* | *~57x*
| 🖥️ *C++ (ILS)* | ~1.5 ms | ~13.33x
| 🖥️ *C++ (ILS)* | *351 µs (0.351 ms)* | *~57x* using !g++ -Wall -O3

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### *🔑 Key Highlights*

1️⃣ *Cantaro Baseline*
Cantaro, implemented in Python with NumPy, offers robust functionality and is considered extremely fast relative to standard generic peer pricing.

2️⃣ *Python-Optimized ILS*
By leveraging NumPy's vectorization and dynamic boundary truncation, this version achieves a *1.67x speedup* over Cantaro.

3️⃣ *Cython ILS*
This implementation compiles Python-like code to C, offering *2.75x* faster performance, ideal for production environments.

4️⃣ *Numba ILS*
With Just-In-Time (JIT) compilation, Numba shines as the fastest Python-based solution, achieving a staggering *~57x speedup* over Cantaro! Its integration with NumPy makes it exceptionally efficient.

5️⃣ *C++ (ILS)*
The powerhouse of computational efficiency, delivering *~13.33x speedup* with low-level optimizations. Using !g++ -Wall -O3 estimation speeds up to *~57x*. See how in this video

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### *🔧 Python Libraries in Action*
⚡ Numba: JIT compilation for accelerating Python code.
🔧 Cython: Bridges Python and C, boosting speed with compiled code.

### *🌟 Why Intelligent Lattice Search?*

ILS combines dynamic boundary location with optimized backward recursion, reducing unnecessary computations and driving efficiency. and provides unparalleled speed and precision across platforms.
### *Key Findings*

### *Cantaro as the Baseline*
The Cantaro implementation, written in Python with *NumPy*, provides a robust and functional approach for option pricing. Please see link to extensive coding here:

*Python-Optimize ILS*
By enhancing the Cantaro implementation with dynamic boundary truncation and leveraging = NumPy's vectorization capabilities, this version achieves a *1.67x speedup* over the baseline. It represents a significant improvement in efficiency while maintaining Python’s simplicity and accessibility.

### *Cython Implementation*
With Cython, Python-like code is compiled into C, which eliminates runtime overhead and significantly enhances execution speed. This approach achieves a *2.75x speedup* over Cantaro and is particularly suitable for production environments that require pre-compiled, high-performance code.

### *Numba Implementation*
The *Numba* implementation uses *Just-In-Time (JIT) compilation* to translate Python code into highly optimized machine code during runtime. With a *57x speedup* over Cantaro, Numba offers the fastest execution time among Python-based implementations while retaining flexibility and ease of use for iterative development.

### *C++ Implementation*
The *C++ implementation* achieves *near-native performance* through low-level hardware optimizations, efficient memory management, and minimal abstraction.

### *📂 Resources*

[ranjithramachandran]

Very informative. I was wondering if it is possible to further enhance the execution time for the baseline code using JAX. Can that be implemented ? I do understand that it is ideal for large computations (GPU) and may not perform well (can become slow) in comparison to Numpy. JAX with lax.scan for iterative computations like option pricing. However it is questionable if JAX can beat the Numba execution time.