Optimal static quadratic hedging

Leung, Tim; Lorig, Matthew

doi:10.1080/14697688.2016.1161229

Cited by 17 publications

(9 citation statements)

References 28 publications

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“…Notice that we work directly with contingent claims, and disregard the details on how to construct replicating portfolios composed by vanilla and derivatives. For such details, in discrete setting, see (Leung and Loring 2016).…”

Section: The Hedging Modelmentioning

confidence: 99%

Static hedging of weather and price risks in electricity markets

Robayo

Vera

2020

Optim Eng

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We present the closed-form solution to the problem of hedging price and quantity risks for energy retailers (ER), using financial instruments based on electricity price and weather indexes. Our model considers an ER who is intermediary in a regulated electricity market. ERs buy a fixed quantity of electricity at a variable cost and must serve a variable demand at a fixed cost. Thus ERs are subject to both price and quantity risks. To hedge such risks, an ER could construct a portfolio of financial instruments based on price and weather indexes. We construct the closed form solution for the optimal portfolio for the mean-VaR model in the discrete setting. Our model does not make any distributional assumption.

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Section: The Hedging Modelmentioning

confidence: 99%

Static hedging of weather and price risks in electricity markets

Robayo

Vera

2020

Optim Eng

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“…13 In our static replicating portfolios, we have chosen to include futures only for comparison to VXX. Alternatively, one can also construct a static portfolio of options and optimize to minimize tracking errors with respect to an index or its leveraged exposure (see Leung and Lorig (2016)). It would be interesting to compare the tracking performance of portfolios with different derivatives.…”

Section: Discussionmentioning

confidence: 99%

Tracking VIX with VIX Futures: Portfolio Construction and Performance

Leung

Ward

2019

SSRN Journal

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We study a series of static and dynamic portfolios of VIX futures and their effectiveness to track the VIX index. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. Among our results, we show that static portfolios of different VIX futures fail to track VIX closely. VIX futures simply do not react quickly enough to movements in the spot VIX. In a discrete-time model, we design and implement a dynamic trading strategy that adjusts daily to optimally track VIX. The model is calibrated to historical data and a simulation study is performed to understand the properties exhibited by the strategy. In addition, comparing to the volatility ETN, VXX, we find that our dynamic strategy has a superior tracking performance.

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“…While in reality calls and puts trade at only finitely many strikes, this can be addressed following techniques described in Leung and Lorig (2015), who show how to optimally adjust static hedges when calls and puts are traded at only discrete strikes in a finite interval.…”

Section: Introductionmentioning

confidence: 99%

Robust Replication of Volatility and Hybrid Derivatives on Jump Diffusions

Carr¹,

Lee²,

Lorig³

2021

Preprint

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We price and replicate a variety of claims written on the log price X and quadratic variation [X] of a risky asset, modeled as a positive semimartingale, subject to stochastic volatility and jumps. The pricing and hedging formulas do not depend on the dynamics of volatility process, aside from integrability and independence assumptions; in particular, the volatility process may be non-Markovian and exhibit jumps of unknown distribution. The jump risk may be driven by any finite activity Poisson random measure with bounded jump sizes. As hedging instruments, we use the underlying risky asset, a zero-coupon bond, and European calls and puts with the same maturity as the claim to be hedged. Examples of contracts that we price include variance swaps, volatility swaps, a claim that pays the realized Sharpe ratio, and a call on a leveraged exchange traded fund.

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Optimal static quadratic hedging

Cited by 17 publications

References 28 publications

Static hedging of weather and price risks in electricity markets

Static hedging of weather and price risks in electricity markets

Tracking VIX with VIX Futures: Portfolio Construction and Performance

Robust Replication of Volatility and Hybrid Derivatives on Jump Diffusions

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