Numerical analysis for spread option pricing model of markets with finite liquidity: first-order feedback model. (English) Zbl 1311.91195
Summary: We discuss the numerical analysis and the pricing and hedging of European Spread options on correlated assets when, in contrast to the standard framework and consistent with a market with imperfect liquidity, the option trader’s trading in the stock market has a direct impact on one of the stocks price. We consider a first-order feedback model which leads to a linear partial differential equation. The Peaceman-Rachford scheme is applied as an alternating direction implicit method to solve the equation numerically. We also discuss the stability and convergence of this numerical scheme. Finally, we provide a numerical analysis of the effect of the illiquidity in the underlying asset market on the replication of an European Spread option; compared to the Black-Scholes case, a trader generally buys less stock to replicate a call option.
MSC:
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
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