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The price of liquidity in constant leverage strategies

  • Marcos Escobar
  • Andreas Kiechle
  • Luis Seco
  • Rudi Zagst
Article
  • 43 Downloads

Abstract

In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS). These financial products are path dependent options where the underlying typically is a hedge fund portfolio. We describe and explain the functionality of CLSs, showing a closed form expression for the price of a CLS on a hedge fund assuming a Geometric Brownian Motion, discrete rebalancing for the hedge fund investment as well as stochastic interest rates. The risk of default before the next rebalancing date leads to a liquidity premium for the CLS which increases with the volatility of the underlying hedge fund portfolio and the leverage of the strategy. An increasing rebalancing period first leads to a higher liquidity premium, however, as the rebalancing period is extended further the liquidity premium begins to shrink again.

Keywords

CPPI hedge fund liquidity premium constant leverage strategy 

Mathematics Subject Classifications

91B30 47N30 

El precio de liquidez en estrategias con apalancamiento constante

Resumen

La funcionalidad de las estrategias de apalancamiento constante (CLS) es investigada en este artículo. Estos productos financieros son opciones depedendientes del camino, donde los típicos subyacentes son Hedge Funds. En particular se encuentra una fórmula cerrada para el precio de liquidez de este derivado en el contexto de procesos brownianos geométricos con reajuste discreto de la cartera y tasa de interés estocástica. El riesgo de bancarrota antes de un reajuste conlleva a un precio de liquidez para el CLS, el cual es proporcional a la volatilidad del activo subyacente y al apalancamiento de la estrategia. Un incremento en el periodo entre reajustes implica un incremento inicial en el precio, sin embargo, el precio disminuye para largos periodos de reajuste.

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Copyright information

© Springer 2009

Authors and Affiliations

  • Marcos Escobar
    • 1
  • Andreas Kiechle
    • 2
  • Luis Seco
    • 3
  • Rudi Zagst
    • 4
  1. 1.Department for MathematicsRyerson UniversityMunich
  2. 2.Munich University of TechnologyMunich
  3. 3.Risklab Toronto Sigma Analysis & ManagementToronto
  4. 4.HVB-Institute for Mathematical FinanceMunich University of TechnologyMunich

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