Quantum Computing Applications in Stochastic Modeling

Happy to announce a new #quantumcomputing work produced jointly by the Global Technology #appliedresearch and #quantitativeresearch teams at JPMorgan Chase & Co. in collaboration with QC Ware Corp. In this work, we propose two #quantum algorithms for pricing discretely monitored Asian options over T monitoring points where the underlying asset is modeled by an exponentiated Gaussian process. Compared to standard methods based on #montecarlo sampling, which have complexity linear in T, our algorithms have complexity that is at most poly-logarithmic in T. Our first algorithm is built upon a new semi-digital quantum encoding for stochastic processes that combines the advantages of the analog encoding and the digital encoding, allowing speedups in T without restricting the type of operations applicable onto the stochastic process. The other algorithm utilizes a time-domain sub-sampling technique, also proposed in this work, which is inspired by the semi-digital encoding approach. Our algorithms generalize to pricing options where the underlying asset price is modeled by a smooth function of a sub-Gaussian process and the payoff is dependent on the weighted time-average of the underlying asset price. Link to paper: https://lnkd.in/gcAmTpeY Coauthors: QC Ware Corp.: Anupam Prakash, Aditi Dandapani, Iordanis Kerenidis JPMorgan Chase & Co. Quantitative Research: Charlie Che, Ben Wood, JPMorgan Chase & Co. Global Technology Applied Research: Yue Sun, Shouvanik Chakrabarti, Dylan Herman, Niraj Kumar, Shree Hari Sureshbabu, and Marco Pistoia

A More General Quantum Credit Risk Analysis Framework   "..Monte Carlo simulations are computationally expensive due to the rare-event simulation problems inherent in credit risk evaluation. Additionally, Monte Carlo simulations can only generate pseudo-random variables, and the quality of the simulation can be compromised by the appearance of patterns." "To overcome these limitations, researchers have explored new methods, such as those based on quantum computing, which can naturally generate true random samples due to the probabilistic nature of qubits. Moreover, quantum amplitude estimation (QAE) has shown promise in estimating the value at risk and offers a quadratic speedup over classical Monte Carlo methods."   By Emanuele Dri , Antonello Aita , Edoardo Giusto , Davide Ricossa , Davide Corbelletto , Bartolomeo Montrucchio  and Roberto Ugoccioni IBM Italy Intesa Sanpaolo Politecnico di Torino Link https://lnkd.in/dspnyG9v  

In finance, Monte Carlo simulations help us to measure risks like VaR or price derivatives, but they’re often painfully slow because you need to generate millions of scenarios. Matsakos and Nield suggest something different: they build everything directly into a quantum circuit. Instead of precomputing probability distributions classically, they simulate the future evolution of equity, interest rate, and credit variables inside the quantum computer, including binomial trees for stock prices, models for rates, and credit migration or default models. All that is done within the circuit, and then quantum amplitude estimation is used to extract risk metrics without any offline preprocessing. This means you keep the quadratic speedup of quantum MC while also removing the bottleneck of classical distribution generation. If you want to explore the topic further, here is the paper: https://lnkd.in/dMHeAGnS #physics #markets #physicsinfinance #derivativespricing #quant #montecarlo #simulation #finance #quantitativefinance #financialengineering #modeling #quantum