Optimal Hedging of Derivatives with Transaction Costs

Optimal Hedging of Derivatives with Transaction Costs

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at ha...

Optimal Hedging of Options with Transaction Costs

One of the most successful approaches to option hedging with transaction costs is the utility based approach, pioneered by Hodges and Neuberger (1989). Judging against the best possible tradeoff between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. However, this approach has one major drawback that prevents the broad application of...

Optimal partial hedging of options with small transaction costs

We use asymptotic analysis to derive the optimal hedging strategy for an option portfolio hedged using an imperfectly correlated hedging asset with small transaction costs, both fixed per trade and proportional to the value traded. In special cases we opbtain explicit formulae. The hedging strategy involves holding a position in the hedging asset whose value lies between two bounds, which are i...

Option Hedging with Transaction Costs

Hedging of American options under transaction costs

We consider a continuous-time model of financial market with proportional transaction costs. Our result is a dual description of the set of initial endowments of self-financing portfolios super-replicating Americantype contingent claim. The latter is a right-continuous adapted vector process describing the number of assets to be delivered at the exercise date. We introduce a specific class of p...