Scientists Alexander Lipton and Artur Sepp develop hybrid methods for stochastic volume options. Professor Alexander Lipton’s latest article written with his former colleague and good friend Artur Sepp. Sepp is currently Head of Systematic Solutions and Portfolio Construction at Sygnum Bank in Zurich: https://lnkd.in/etB9ff3Y.
In this article, they combine one-dimensional Monte Carlo simulations. And the semi-analytical one-dimensional thermal potential method.
Additionally, devise an efficient technique to price barrier options on assets with correlated stochastic volatility.
Their approach to pricing barrier options uses two loops.
First, they run the outer loop by generating volatility trajectories via the Monte Carlo method.
Second, they condition the price dynamics on a given volatility trajectory and apply the heat potentials method to solve the closed-form conditional problem in the inner loop.
Next, they illustrate the accuracy and efficiency of their semi-analytical approach by comparing it to two-dimensional Monte Carlo simulation and a hybrid method. Which combines the finite difference technique for the inner loop and the Monte Carlo simulation for the outer loop.
Finally, they apply their method to calculate state probabilities (Green’s function), survival probabilities and the value of call options with barriers.
As a by-product of their analysis, they generalize Wiggins’ (1997) conditioning formula for the valuation of path-independent options to path-dependent options. Additionally, they derive a new expression for the joint probability density for the value of the derived Brownian motion and its running minimum or maximum in the case of time-dependent drift.
Their approach provides better accuracy and is orders of magnitude faster than existing methods. The methodology is general and can also effectively handle all known stochastic volatility models. Additionally, relatively simple extensions (will be described elsewhere) can also handle approximate volatility patterns.
In conclusion, with minimal changes, one can use the method to price popular non-contact options and other similar instruments.