Quadratic Hedging and Optimization of Option Exercise Policies

Optimization methods in portfolio management and option hedging

These lecture notes give an introduction to modern, continuous-time portfolio management and option hedging. We present the stochastic control method to portfolio optimization, which covers Merton’s pioneering work. The alternative martingale approach is also exposed with a nice application on option hedging with value at risk criterion. ∗Lectures for the CIMPA-IMAMIS school on mathematical fin...

Operational risk of option hedging

a r t i c l e i n f o Operational risk is increasingly being recognised as a significant area of risk and regulation, yet there exists relatively little research on it. In this paper we show that operational risk represents a fundamental risk to option hedging and investigate it by proposing a new theoretical model. We derive an exposure indicator for the operational risk of option hedging and ...

Quadratic Hedging of Basis Risk

This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since...

Robust One-Period Option Hedging

The paper considers robust optimization to cope with uncertainty about the stock return process in one period option hedging problems. The robust approach relates portfolio choice to uncertainty, making more cautious hedges when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlying stocks and show that for this set the robust problem is a second ...

Option Hedging with Transaction Costs