FPGA-based Reconfigurable Computing for Pricing Multi-asset Barrier Options Rahul Sridharan*, Gregg Cooke † , Kenneth Hill*, Herman Lam*, Alan George* * NSF Center for High-Performance Reconfigurable Computing Dept. of ECE, University of Florida Gainesville FL, USA e-mail: {sridharan, hill, hlam, george}@chrec.org † UBS AG Global CTO Applied Innovation Team Chicago, IL e-mail: gregg.cooke@ubs.com Abstract—Multi-asset barrier contracts are path-dependent exotic options consisting of two or more underlying assets. As the dimensions of an option increase, so does the mathematical complexity of a closed form solution. Monte Carlo (MC) methods offer an attractive solution under such conditions. MC methods have an O(n -1/2 ) convergence rate irrespective of the dimension of the integral. However, such methods using conventional computing with CPUs are not scalable enough to enable banks to realize the potential that these exotic options promise. This paper presents an FPGA-based accelerated system architecture to price multi-asset barrier contracts. The architecture consists of a parallel set of Monte Carlo cores, each capable of simulating multiple Monte Carlo paths. Each MC core is designed to be customizable so that the core for the model (i.e., “model” core) can be easily replaced. In our current design, a Heston core based on the full truncation Euler discretization method is used as the model core. Similarly, we can use different payoff calculator kernels to compute various payoffs such as vanilla portfolios, barriers, look-backs, etc. The design leverages an early termination condition of “out” barrier options to efficiently schedule MC paths across multiple cores in a single FPGA and across multiple FPGAs. The target platform for our design is Novo-G, a reconfigurable supercomputer housed at the NSF Center for High-Performance Reconfigurable Computing (CHREC), University of Florida. Our design is validated for the single- asset configuration by comparing our output to option prices calculated analytically and achieves an average speedup of ranging from 123 to 350 on one FPGA as we vary the number of underlying assets from 32 down to 4. For a configuration with 16 underlying assets, the speedup achieved is 7134 when scaled to 48 FPGAs as compared to a single-threaded version of an SSE2-optimized C program running on a single Intel Sandy Bridge E5-2687 core at 3.1 GHz with hyper-threading turned on. Finally, the techniques described in this paper can be applied to other exotic multi-asset option classes, such as lookbacks, rainbows, and Asian-style options. Keywords-FPGA-based reconfigurable computing; option- pricing; multi-asset Heston model; Monte Carlo simulation I. INTRODUCTION Financial institutions are increasingly exploring high performance computing (HPC) solutions to meet computational demands on various fronts. At the heart of any banking operation are increasingly complex mathematical models and the simulation of such models that aims to accurately model market conditions. One important area is the simulation of options pricing models that predict the future price (and hence potential risk) of every asset that a bank trades. Accelerating complex pricing models enables banks to explore a vast array of underlying assets (stocks, bonds, etc.), resulting in valuations that are most beneficial to their clients. Most important in determining the price (and its risk) is the range over which an asset's value is expected to change (i.e., volatility). Measuring current volatilities, predicting future volatilities, and balancing volatilities against one another are all activities that banks perform constantly. Interestingly, the often-used Black-Scholes model for calculating the price of a simple “vanilla” option treats volatility as a constant parameter. By doing so, it may expose the trader to arbitrage by other traders as long as he/she owns the option contract. Heston [10] proposed a solution to this problem by modeling the volatility in the Black-Scholes model with a random (or stochastic) variable. The use of a stochastic volatility model becomes even more important for a variation on the vanilla option contract called a barrier option, a contract whose value is much cheaper than its vanilla counterpart because the trader is only paying for a small range of benefit. A barrier option is very sensitive to volatility. The slightest variation in the value of the underlying asset can cause the price of the option to tip over the barrier, rendering the option worthless. It is therefore important to model the volatility of the asset as accurately as possible. For this reason, the Heston model is often used with barrier options pricing. Finally, investors in recent years have found multi-asset barrier options to be particularly attractive because they give the investor a single relatively cheap contract that captures the relationship among related sets of assets and offers some protection against the complicated volatility relationships that make the risk of the contract uncertain. Their complex covariance structure makes the Heston stochastic volatility model particularly suitable as a means to model multi-asset barrier options. Note that the Heston layered with a barrier option contract has a closed-form solution. However, the additional mathematical complexity is enough to justify the use a Monte Carlo method with the Heston model instead. Furthermore, no closed-form solution has been found when multiple underlying assets are used to construct the barrier option contract. In this case, the mathematics change from using single variables to represent the asset value and volatility, to using matrices of parameters for a set of assets,