Constant Proportion Portfolio Insurance in Presence of Jumps in Asset Prices

Cont, Rama; Tankov, Peter

doi:10.2139/ssrn.1021084

Cited by 33 publications

(11 citation statements)

References 20 publications

(6 reference statements)

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“…The properties of CPPI strategies have been extensively studied in the literature (see 6 Black and Perold, 1992) 4 . The literature also deals with the effects of jump processes, stochastic volatility models and extreme value approaches on the CPPI method with an unconditional multiple (Prigent, 2001;Prigent, 2002 andCont and Tankov, 2009). The management of a cushioned portfolio follows a dynamic strategic portfolio allocation.…”

Section: On Proportion Portfolio Insurance Principlesmentioning

confidence: 99%

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A Dynamic Autoregressive Expectile for Time-Invariant Portfolio Protection Strategies

2009

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Abstract"Constant proportion portfolio insurance" (CPPI) is nowadays one of the most popular techniques for portfolio insurance strategies. It simply consists of reallocating the risky part of a portfolio with respect to market conditions, via a leverage parameter -called the multiple -guaranteeing a predetermined floor. We propose to introduce a conditional time-varying multiple as an alternative to the standard unconditional CPPI method, directly linked to actual risk management problematics. This ex ante approach for the conditional multiple aims to diversify the risk model associated, for example, with the expected shortfall (ES) or extreme risk measure estimations. First, we recall the portfolio insurance principles, and main properties of the CPPI strategy, including the time-invariant portfolio protection (TIPP) strategy, as introduced by Estep and Kritzman (1988). We emphasize the existence of an upper bound on the multiple, for example to hedge against sudden drops in the market. Then, we provide the main properties of the conditional multiples for well-known financial models including the discrete-time portfolio rebalancing case and Lévy processes to describe the risky asset dynamics. For this purpose, we precisely define and evaluate different gap risks, in both conditional and unconditional frameworks. As a by-product, the introduction of discrete or random time portfolio rebalancing allows us to determine and/or estimate the density of durations between rebalancements. Finally, from a more practical and statistical point of view due to trading restrictions, we present the class of Dynamic AutoRegressive Expectile (DARE) models for estimating the conditional multiple. This latter approach provides useful complementary information about the risk and performance associated with probabilistic approaches to the conditional multiple. Abstract"Constant proportion portfolio insurance" (CPPI) is nowadays one of the most popular techniques for portfolio insurance strategies. It simply consists of reallocating the risky part of a portfolio with respect to market conditions, via a leverage parameter -called the multiple -guaranteeing a predetermined floor. We propose to introduce a conditional time-varying multiple as an alternative to the standard unconditional CPPI method, directly linked to actual risk management problematics. This ex ante approach for the conditional multiple aims to diversify the risk model associated, for example, with the expected shortfall (ES) or extreme risk measure estimations. First, we recall the portfolio insurance principles, and main properties of the CPPI strategy, including the time-invariant portfolio protection (TIPP) strategy, as introduced by Estep and Kritzman (1988). We emphasize the existence of an upper bound on the multiple, for example to hedge against sudden drops in the market. Then, we provide the main properties of the conditional multiples for well-known financial models including the discrete-time portfolio rebalancing case and Lévy processes to describe the r...

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Section: On Proportion Portfolio Insurance Principlesmentioning

confidence: 99%

“…Cont and Tankov (2009) examine CPPI strategies for exponential Lévy processes. However, these traditional methods do not sufficiently take account of the underlying asset risk changes, according for instance to market conditions exposure.…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Autoregressive Expectile for Time-Invariant Portfolio Protection Strategies

2009

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“…In this case, there is an option included in the product, which must be priced and hedged. For a very simple CPPI strategy with continuous rebalancing, the gap risk comes only from instantaneous jumps and can be quantified analytically [CT07]. With a discrete rebalancing scheme, there is a closed formula for the embedded option price if the underlying follows a Black-Scholes diffusion [BBM05].…”

Section: Introductionmentioning

confidence: 99%

One-Dimensional Pricing of CPPI

Paulot¹,

Lacroze²

2011

Applied Mathematical Finance

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Constant Proportion Portfolio Insurance (CPPI) is an investment strategy designed to give participation in the performance of a risky asset while protecting the invested capital. This protection is however not perfect and the gap risk must be quantified. CPPI strategies are path-dependent and may have American exercise which makes their valuation complex. A naive description of the state of the portfolio would involve three or even four variables. In this paper we prove that the system can be described as a discrete-time Markov process in one single variable if the underlying asset follows a homogeneous process. This yields an efficient pricing scheme using transition probabilities. Our framework is flexible enough to handle most features of traded CPPIs including profit lock-in and other kinds of strategies with discrete-time reallocation.

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“…due to price jumps or trading restrictions. An analysis of gap risk is, for example, provided in Cont and Tankov (2007) and Balder et al (2009). 6 A comparison of hedging is also impeded by model risk and market frictions.…”

Section: Introductionmentioning

confidence: 99%