×

Portfolio sensitivity to changes in the maximum and the maximum drawdown. (English) Zbl 1192.91184

Summary: We define new “Greeks” for financial derivatives: sensitivities to the running maximum and the running maximum drawdown of an underlying asset. Some types of portfolios, such as the net asset value of a hedge fund or performance fees, are sensitive to these parameters. In order to illustrate the concept of the new “Greeks”, we derive probabilistic representations of sensitivities for two classes of financial contracts: forwards on the maximum drawdown and lookback options. These results allow us to interpret the delta-hedge of the contracts in a novel way.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
Full Text: DOI

References:

[1] DOI: 10.1016/j.spa.2004.07.003 · Zbl 1114.91049 · doi:10.1016/j.spa.2004.07.003
[2] DOI: 10.2307/2327238 · doi:10.2307/2327238
[3] DOI: 10.1007/s007800050044 · Zbl 0907.90023 · doi:10.1007/s007800050044
[4] DOI: 10.1239/jap/1077134674 · Zbl 1051.60083 · doi:10.1239/jap/1077134674
[5] Pospisil L, J. Comput. Finance 12 pp 1– (2008)
[6] Shreve S, Stochastic Calculus for Finance II (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.