OPTION PRICING AND HEDGING WITH EXECUTION COSTS AND MARKET IMPACT

Option Hedging with Smooth Market Impact

We consider a large investor hedging a long or short options position, whose trades generate adverse market impact. Unlike the complete-market or proportional transaction cases, the agent no longer finds it tenable to be perfectly hedged or even within a fixed distance of being hedged. Instead, he may find himself arbitrarily mishedged and optimally trades towards the classical Black-Scholes de...

Pricing and hedging contingent claims with liquidity costs and market impact

We study the influence of taking liquidity costs and market impact into account when hedging a contingent claim, first in the discrete time setting, then in continuous time. In the latter case and in a complete market, we derive a fully non-linear pricing partial differential equation, and characterizes its parabolic nature according to the value of a numerical parameter naturally interpreted a...

Option Pricing and Hedging with Temporal Correlations

We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic–risk minimisation scheme, we obtain a general formula, valid for weakly correlated non–Gaussian processes. We show that for Gaussian price increments, the correlations are irrelevant, and the Black–Scholes formula holds with the volatility of the price increments on the scale of t...

Option Hedging with Transaction Costs

On option pricing in binomial market with transaction costs

Option replication is studied in a discrete-time framework with proportional transaction costs. The model represents an extension of the Cox-RossRubinstein binomial option-pricing model to cover the case of proportional transaction costs for one risky asset with different interest rates on bank credit and deposit. Contingent claims are supposed to be 2-dimensional random variables. Explicit for...