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Scientists Alexander Lipton & Artur Sepp Develop Hybrid Methods for Stochastic Volume Options

Scientists Alexander Lipton & Artur Sepp Develop Hybrid Methods for Stochastic Volume Options. Professor Alexander Lipton’s latest paper written with his former colleague and a good friend Artur Sepp. Sepp currently serves as the head of systematic solutions and portfolio construction at Sygnum Bank in Zurich:

In this article, they combine one-dimensional Monte Carlo simulations. And the semianalytical one-dimensional heat potential method.

Moreover, to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. 

Their approach to barrier options valuation utilizes two loops. 

Firstly, they run the outer loop by generating volatility paths via the Monte Carlo method. 
Secondly, they condition the price dynamics on a given volatility path and apply the method of heat potentials to solve the conditional problem in closed-form in the inner loop. 
Next, they illustrate the accuracy and efficacy of their semi analytical approach by comparing it with the 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. 

Lastly, they apply their method to compute state probabilities (Green function), survival probabilities, and the value of call options with barriers. 

As a byproduct of their analysis, they generalize Wiggins’s (1997) conditioning formula for valuation of path-independent options to path-dependent options. Additionally, they derive a novel expression for the joint probability density for the value of drifted 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 the existing methods. The methodology is general and can equally efficiently manage all known stochastic volatility models. Besides, relatively simple extensions (will be described elsewhere) can also handle rough volatility models. 

In conclusion, with minimal changes, one can use the method to price popular double-no-touch options and other similar instruments.

Scientists Alexander Lipton & Artur Sepp Develop Hybrid Methods for Stochastic Volume Options

Alex is Global Head of Research and Development at the Abu Dhabi Investment Authority, Connection Science Fellow at MIT and a Visiting Professor and Dean’s Fellow at HUJI. His background is in Investment Banking, OTC tradings, electronic markets, and Risk Management.
Alex is a strong thought leader with a proven track-record of managing large quantitative organisations in challenging environments, building teams from scratch. Lastly, merging existing teams, and re-aligning teams to fulfill new mandates.

His current interests include FinTech, including distributed ledger and other applications of cryptography in banking. And furthermore, payment systems, and holistic risk management. His scientific interests are centered on quantitative development of modern Monetary Circuit Theory. In addition, mechanisms of money creation, interlinked banking networks, etc.
Artur Sepp is head systematic solutions and portfolio construction at Sygnum Bank’s Asset Management in Zurich, specializing in crypto assets and decentralized finance.
Artur Sepp – Risk.net › static › artur-sepp
Books: Affine models in mathematical finance: an analytical approachResearch interests: Systematic Investing, Machine Learning, Asset Allocation, Quantitative Finance, Option Pricing
Scientists Alexander Lipton & Artur Sepp Develop Hybrid Methods for Stochastic Volume Options