A Revolutionary, Straight-Forward Way to Accelerate Derivative Pricing and Risk Models in Finance 


Published 26/06/2024 By Jason Charlesworth

Transform risk, pricing, Monte Carlo, PDE, CVA models, and more to deliver calculations up to 15x quicker without needing a large team, rewriting libraries, or changing hardware.

nZetta Derivatives Pricing Toolkit is a finance-specific, comprehensive library of mathematical components that can be seamlessly and gradually dropped into existing derivative pricing systems and hardware.

Up to 15x faster calculations, with no need to change hardware, no need to rewrite anything, no need for a large team, and no need to worry about future hardware changes.

nZetta is unique in the finance industry. It delivers performance and portability with components that can be added seamlessly to existing infrastructure to maximise the productivity of your hardware, whether it is on cloud, CPU or GPU.

Modernizing your existing pricing or risk models, or even building new ones, can now be accomplished much faster and at a lower cost. Our toolkit is designed for phased adoption, enabling you to test and transition without the risks associated with comprehensive system changes.

With these advantages, nZetta doesn’t just accelerate your calculations, it opens up a world of new business opportunities. From intraday risk and real-time CVA to e-trading of exotics, you’ll have the power to make strategic moves in seconds, giving you a competitive edge in the market.

What Are the nZetta Financial Components? 

Calculation Engines:

  • Monte Carlo
  • Multi-factor PDE 

Pseudo/Quasi Random Variates: ​

  • Mersenne, L’Ecuyer, Sobol​  
  • Correlation and Repair (Cholesky, ​  
    PCA, Rectangular)​  
  • Brownian Bridge​  
  • Antithetic​  

Interpolation: ​ 

  • Uniform/Non-Uniform/Multidimensional​  
  • Range of extrapolations & interpolations​  

Tensor shaping:   

  • Concatenate, Broadcast, ​ 
  • Repeat, Extract, Insert, Append, Transpose…​  

Reductions:  

  • Sum, Mean, Var, Min, Max, Prod​  

Regression:   

  • Linear, Quadratic 
  • Windowed Reductions e.g., vol targets​  

Processes:  

  • (Quanto) (shifted) Log-Normal, CIR …​  

Finance Functions:  

  • SABR, BS Options, BS Implied vol, ​  
    ND2, ND3 and much more… 
nZetta Benefits:

nZetta Toolkit reduces compute time and cost by using key acceleration technologies, AAD and SIMD, whilst hiding hardware dependence. By dramatically accelerating pricing and risk management calculations up to 15x using the quant team’s models, nZetta creates new business opportunities such as: 

  • Real-time hedging  
  • Heavily moving markets  
  • Real-time CVA  
  • E-Trading  
  • Exotic derivatives  
nZetta Functionality: 
  • nZetta has an easy-to-use interface so you can begin to use and benefit from it immediately.    
  • Functionality is available to use​ through C-API as part of the migration step​.  
  • Extensible adaptor support for container libraries, i.e.,​ nZetta will work with whatever matrix and vector objects you already use.  
  • Hides hardware dependence – using the tensor framework, the same quant code works for x86, thread-distributed calc and GPU  
  • Can incorporate Automatic Differentiation (AD) for rapid calculation of sensitivities.  
How the nZetta Tensor Framework Works:   

nZetta Basic Unit – Tensor<Type> (0D-4D) 


double g,c,cap, floor;
Tensor<double> rate;
//...
Tensor<double> coupon = max(min(g * rate - c, cap), floor);

This basic unit delivers maximum benefit from parallelism of bulk operations​. 

nZetta – Full support for conditionals, including Tensor<bool>


double strike;
Tensor<double> cap_count, coupon, autocap;
int M = 10;
//...
IF((coupon > strike) && (cap_count < M))
{
  autocap += max(coupon - strike, 0.0);
  cap_count += 1.0;
}
ELSE
{
  // ...
}

This tensor condition determines which tensor elements to evaluate and update.

Let’s Talk Performance:
4-CCY Monte Carlo Basket Option

Implementing the pricing using the nZetta toolkit we see a 15x speed-up on x86 and over 100x speed-up when moving from CPU to GPU. 

PDE Methods and Sizes

For calibration and one-asset trades, the ability to quickly price (backward induction) or construct the distribution (Kolmogorov forward PDE) is essential.

The nZetta toolkit provides a wide range of 2D PDE capabilities so you can choose the ideal method for your trade. All the algorithms have been designed for modern hardware and memory to provide the very best performance.

The nZetta Toolkit 2D-PDE is over 10 times faster than the reference implementation. Choosing the best method and abcissæ for your problem can give a further 50% speed-up for a given accuracy goal.

Thanks for taking the time to read our blog! If you would like to learn more about nZetta, or talk to us, visit the link below.

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