Numerical solution of a stochastic control problem of option pricing for a liquidity switching market

Abstract

We consider the problem of European option pricing in a market which experiences instances of liquidity and illiquidity. Our model of market liquidity takes the form of a regime-switching continuous Markov process. We study the investor's problem of maximising both terminal wealth and option payo whose solution is characterised by a semilinear coupled HJB equation. We present several numerical studies based on our model.