The valuation of American options and the determination of optimal stopping times remain central challenges in option pricing theory and derivatives valuation. Classical approaches to multidimensional problems rely on the dynamic programming principle, which is notoriously difficult to parallelize. Moreover, the need to store continuation values for all simulated paths in each dynamic programming step imposes severe memory constraints on classical computers, limiting the scale of feasible simulations. Quantum computing offers a promising way to address these limitations. In this paper, the authors introduce a novel algorithm for pricing American options on quantum hardware. To date, only one method has been proposed for this purpose. The authors' approach combines the Quantum Binomial Tree with Quantum Machine Learning to enable direct valuation of American options on a quantum computer. By incorporating quantum amplitude estimation, it could achieve a quadratic speed-up over classical Monte Carlo methods. Furthermore, it exploits the exponential growth of the quantum state vector, overcoming the memory bottlenecks that restrict classical approaches.
Portfolio aggregation further improves convergence towards theoretical VaR values across all generators.
Long before there was rotisserie baseball or fantasy sports or sabermetrics or Strat-O-Matic tabletop sports games, there was Topps '51
Feller conditions are for fairy-believers. Moment explosions? Those actually matter.
The author derives early exercise premium representation formulas for an American put option with bilateral counterparty risk and funding cost. The derivation involves: transforming the American put into an equivalent European instrument that changes characteristics at the exercise boundary, deriving partial differential equation (PDE) based on the hedging strategies and the default Close-out rules, and applying the change-of-variable formula of Peskir (2005b). The vulnerable American put value is the sum of the corresponding vulnerable European put value, the early exercise premium, the value adjustment due to counterparty risk and funding cost, and the option value jump at default. The early exercise premium is the expected cumulative consumption. The formulas are for the values of the vulnerable American and vulnerable European put options with their nonvulnerable counterparts as special cases. Thus, they provide a unified valuation framework for American and European put options whether vulnerable or not. In particular, standard American put can be considered as a vulnerable American put with perfect recovery. Based on the formulas, the author shows that the defaulter never loses but may gain if he is the seller, and the survivor never gains but may lose if he is the buyer. The Risk-Free Close-out, where the Close-out value is the corresponding standard American put value, benefits the buyer but penalizes the seller. If the option value does not jump at default, the buyer's credit quality does not affect the option value. The author derives the condition for the existence of the arbitrage-band, the price interval bounded from below by the buyer's price and above by the seller's price.
Aston Martin's first mid-engine supercar has taken a long time to get here but all good things come to those who wait.
Generating implied volatility surfaces with Gaussian mixtures yields near-arbitrage-free synthetic market data
Jaguar's legendary Lightweight E-Type racer is re-imagined in a stunning recreation for the road.
This study examines the impact of sampling schemes on Monte Carlo=based Value-at-Risk (VaR) estimation at both the risk factor and portfolio levels. The authors compare pseudo-random number generators with low-discrepancy sequences, including Sobol and Halton constructions. At the uncorrelated risk factor level, pseudo-random generators exhibit higher variability and less stable VaR estimates than low-discrepancy sequences. When correlation is introduced, the differences between the generators in how closely the theoretical VaR is achieved are substantially reduced. Moreover, portfolio aggregation further diminishes these differences, while the accuracy with which the theoretical VaR is represented also decreases across all generators. Optimized Sobol sequences (Sobol OPT and Sobol EN) demonstrate superior preservation of correlation structures, particularly in higher-dimensional settings. Overall, the results highlight the role of advanced random number generation techniques in enhancing the efficiency and reliability of VaR estimation in portfolio risk management.
The author derives an explicit analytical formula for the expected return of an equity with a stop-loss. The author shows that under certain conditions on the drift, there can be an optimal level for a stop-loss, and that the expected return can exceed that of the buy-and-hold strategy.
Dariusz Gatarek brings the difference between users and makers into high relief and reminds us of the importance of choosing the right tool for the job.
Would choosing to receive the ball first give a team a winning edge in the NFL's new overtime format?
The growing gap between expectations, investment, and revenue potential, recalls the 1990s.
Espen Haug's latest book Wall Street Short Stories is a collection of fiction grounded in real life concepts. Here we present a selected extract.
Ferrari's hybrid 296 GTB gets a new, race-developed cousin with even more performance, less weight and more exclusivity than ever.
Considering the application of Gaussian Mixture Models, particularly the stochastic sampling algorithm, to yield curve generation.
Dissecting the shark forward, a popular hedging strategy with an alluring sales pitch, revealing hidden risks and true costs.
