On Quadratic Cost Criteria for Option Hedging

Schäl, Manfred

doi:10.1287/moor.19.1.121

Cited by 147 publications

(112 citation statements)

References 7 publications

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“…Clearly, V k (ϕ) is then the theoretical or book value of the portfolio (ϑ k+1 , η k ) with which one leaves date k after trading. While the present notation conforms with the one in Schäl (1994) or Mercurio/Vorst (1997), it is different from the one used in Schweizer (1988Schweizer ( , 1995, and we shall comment on this later on.…”

Section: T Is Adapted Andmentioning

confidence: 68%

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Local Risk-Minimization Under Transaction Costs

1998

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We propose a new approach to the pricing and hedging of contingent claims under transaction costs in a general incomplete market in discrete time. Under the assumptions of a bounded mean-variance tradeoff, substantial risk and a nondegeneracy condition on the conditional variances of asset returns, we prove the existence of a locally risk-minimizing strategy inclusive of transaction costs for every square-integrable contingent claim. Then we show that local risk-minimization is robust under the inclusion of transaction costs: The preceding strategy which is locally risk-minimizing inclusive of transaction costs in a model with bid-ask spreads on the underlying asset is also locally risk-minimizing without transaction costs in a fictitious model which is frictionless and where the fictitious asset price lies between the bid and ask price processes of the original model. In particular, our results apply to any nondegenerate model with a finite state space if the transaction cost parameter is sufficiently small.

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Section: T Is Adapted Andmentioning

confidence: 68%

“…One frequently made assumption on X is that X should have a bounded mean-variance tradeoff process; see for instance Schäl (1994) or Schweizer (1995). The following result provides a sufficient condition to ensure that X γ then also has a bounded mean-variance tradeoff.…”

Section: T and For Every Strategy ϕmentioning

confidence: 99%

Local Risk-Minimization Under Transaction Costs

1998

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“…Using the Itô formula we have 25) where N is a martingale. Therefore applying equalities (4.22),(4.23) and (4.24) we obtain that 26) which implies that µ M -a.e.…”

Section: (419)mentioning

confidence: 99%

Mean-Variance Hedging Under Partial Information

Mania¹,

Tevzadze²,

Toronjadze³

2010

Stochastic Control

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We consider the mean-variance hedging problem under partial Information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that the initial mean variance hedging problem is equivalent to a new mean variance hedging problem with an additional correction term, which is formulated in terms of observable processes. We prove that the value process of the reduced problem is a square trinomial with coefficients satisfying a triangle system of backward stochastic differential equations and the filtered wealth process of the optimal hedging strategy is characterized as a solution of a linear forward equation.2000 Mathematics Subject Classification: 90A09, 60H30, 90C39.

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“…In the case G = F of complete information the mean-variance hedging problem was introduced by Föllmer and Sondermann [8] in the case when S is a martingale and then developed by several authors for price process admitting a trend (see, e.g., [6], [12], [25], [26], [24], [10], [11]). …”

Section: Introductionmentioning

confidence: 99%

L 2-approximating Pricing under Restricted Information

2009

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We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new type and characterize the optimal strategy in terms of the solution of this equation. We give relations between this equation and backward stochastic differential equations for the value process of the problem.

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On Quadratic Cost Criteria for Option Hedging

Cited by 147 publications

References 7 publications

Local Risk-Minimization Under Transaction Costs

Local Risk-Minimization Under Transaction Costs

Mean-Variance Hedging Under Partial Information

L 2-approximating Pricing under Restricted Information

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