🤖 AI Summary
This work addresses the high computational complexity associated with pricing multi-strike options and computing their Greeks under stochastic volatility Bachelier-type models. We propose an efficient numerical method grounded in elementary linear algebra that overcomes the limitations of traditional pointwise evaluation. By performing only a finite number of expectation calculations, the method simultaneously yields option prices and Greeks for infinitely many strikes within a well-defined convergence interval. Specifically, we explicitly characterize this convergence interval for the SABR model and demonstrate the method’s efficacy through numerical experiments on both the SABR and rough Bergomi models. Results show that the approach achieves significant gains in computational efficiency while preserving high accuracy, thereby enabling scalable batch computation across a continuum of strikes.
📝 Abstract
In this paper, we present a numerical method for option pricing and the computation of Greeks under stochastic volatility Bachelier-type models, based on elementary linear algebra. The method allows option prices and Greeks to be computed for infinitely many strikes (within a range of convergence) by evaluating only a finite number of expectations, independent of the number of strikes. For the SABR model, we derive an explicit range of convergence. Numerical examples are provided for both the SABR and the rough Bergomi models.