By Louis Paulot, Head of Quantitative Research at Misys
Traders and risk managers are increasingly facing challenges to acquire accurate valuation and hedging figures. The SABR model is vital in assisting firms to achieve this by fitting implied volatility across all strikes, as well as capturing dynamics of the volatility smile.
The quantitative research division at Misys proposes a correction to the well-known first order expansion in time of implied volatility, in addition to an extension to the second order, to provide more precision and a better fit to prices of stochastic volatility models. It is then applied to the SABR model to compare it with the standard formula and numerical solution of the PDE.
In this paper I explain how these significant achievements are obtained using mathematical physics methodology: differential geometry – Riemannian manifolds – and heat kernel expansion.
The intention of this paper is to provide faster, more consistent and more accurate computations of prices and Greeks to assist traders and risk managers.
Register for your free copy of Precision flying on the wings of SABR by clicking here.
Lastly, don’t miss my presentation “Fast American Monte Carlo” on day 2 of the main conference in the Innovations in Computational Efficiency stream at Global Derivatives USA, where I will introduce a new algorithm from Misys that delivers fully parallel computation and reduced memory usage with the flexibility to price new types of products.
During my presentation I will discuss the benefits of this new approach, namely:
- Full parallelization: All phases of the computation can be parallelized.
- No path storage: Monte Carlo paths are only used once
- Forward computation: Exercise decisions and payoff computation can be performed forwards to facilitate all kinds of path dependence
- Boosting: Improve the precision of estimates of the exercise boundaries
- More general regression: Least squares regression can be performed for sets of dates
I look forward to seeing you in Chicago!