A subdiffusive stochastic volatility jump model

Jean-Loup Dupret and Donatien Hainaut
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Jean-Loup Dupret: Université catholique de Louvain, LIDAM/ISBA, Belgium
Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2022001, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Subdiffusions appear as good candidates for modeling illiquidity in financial markets. Existing subdiffusive models of asset prices are indeed able to capture the motionless periods in the quotes of thinly-traded assets. However, they fail at reproducing the jumps and the time-varying volatility observed in the price of these assets. The aim of this work is hence to propose a new model of subdiffusive asset prices reproducing the main characteristics exhibited in illiquid markets. This is done by considering a stochastic volatility jump model, time-changed by an inverse subordinator. We derive the forward fractional partial differential equations (PDE) governing the probability density function of the introduced model and we prove that it leads to an arbitrage-free and incomplete market. By proposing a new procedure for estimating the model parameters and using a series expansion for solving numerically the obtained fractional PDE, we are able to price various financial derivatives on illiquid assets and to propose a corresponding hedging strategy. This way, we show that the introduced subdiffusive stochastic volatility jump model yields consistent and more reliable results in illiquid markets.

Keywords: Illiquidity modeling; subdiffusion; fractional Fokker-Planck equations; stochastic volatility jump model; option pricing (search for similar items in EconPapers)
Pages: 35
Date: 2022-01-01
New Economics Papers: this item is included in nep-ore and nep-rmg
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