Auto-static for the people: risk-minimizing hedges of barrier options

Siven, Johannes Vitalis; Poulsen, Rolf

doi:10.1007/s11147-009-9040-7

Cited by 8 publications

(9 citation statements)

References 40 publications

(44 reference statements)

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“…For comparison, the last column shows the hedging performance under the original BS model, which are the results reported in Table . We use the four risk measures in Siven and Poulsen () to evaluate the hedging performance based on the demeaned hedging error

H E^{*} = HE - E [HE]

. BS: Black–Scholes; SSHP: semistatic hedging portfolio; SV: stochastic volatility.…”

Section: Discussion Of Model Riskmentioning

confidence: 99%

“…To further assess the hedging effectiveness concisely, we employ four risk measures used in Siven and Poulsen () to estimate the hedging performance of the SSHP and the DHP approaches. In addition, to reduce the sampling error from using only 2,000 simulated paths, we calculate four risk measures based on the demeaned hedging error (

H E^{*}

), where

H E^{*} = HE - E [HE]

.…”

Section: Hedging Performance Of Sshp and Dhpmentioning

confidence: 99%

“…We simulate 2,000 stock price paths, with 1,000 time steps per day. We calculate four risk measures used in Siven and Poulsen () with the demeaned hedging error (

H E^{*}

) to assess the hedging performance, where

H E^{*} = HE - E [HE]

. The first risk measure, 5% value‐at‐risk, is defined as

{V a R}_{0.05}^{*} = inf {MJX-TeXAtom-ORD z ϵ frakturR; Pr ({MJX-TeXAtom-ORD H E}^{MJX-TeXAtom-ORD *} \geq z) \leq 0.05}

.…”

Section: Hedging Performance Of Sshp and Dhpmentioning

confidence: 99%

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Semistatic hedging and pricing American floating strike lookback options

Chung

Huang

Shih

et al. 2018

Journal of Futures Markets

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We price an American floating strike lookback option under the Black–Scholes model with a hypothetic static hedging portfolio (HSHP) composed of nontradable European options. Our approach is more efficient than the tree methods because recalculating the option prices is much quicker. Applying put–call duality to an HSHP yields a tradable semistatic hedging portfolio (SSHP). Numerical results indicate that an SSHP has better hedging performance than a delta‐hedged portfolio. Finally, we investigate the model risk for SSHP under a stochastic volatility assumption and find that the model risk is related to the correlation between asset price and volatility.

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H E^{*} = HE - E [HE]

. BS: Black–Scholes; SSHP: semistatic hedging portfolio; SV: stochastic volatility.…”

Section: Discussion Of Model Riskmentioning

confidence: 99%

H E^{*}

), where

H E^{*} = HE - E [HE]

.…”

Section: Hedging Performance Of Sshp and Dhpmentioning

confidence: 99%

“…We simulate 2,000 stock price paths, with 1,000 time steps per day. We calculate four risk measures used in Siven and Poulsen () with the demeaned hedging error (

H E^{*}

) to assess the hedging performance, where

H E^{*} = HE - E [HE]

. The first risk measure, 5% value‐at‐risk, is defined as

{V a R}_{0.05}^{*} = inf {MJX-TeXAtom-ORD z ϵ frakturR; Pr ({MJX-TeXAtom-ORD H E}^{MJX-TeXAtom-ORD *} \geq z) \leq 0.05}

.…”

Section: Hedging Performance Of Sshp and Dhpmentioning

confidence: 99%

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Semistatic hedging and pricing American floating strike lookback options

Chung

Huang

Shih

et al. 2018

Journal of Futures Markets

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“…For our price analysis, this is not a restriction; if we were to study construction and performance of hedge portfolios both the risk-neutral pricing measure and the real-world measure would matter -though possibly less so in practice than in theory, see Poulsen, Schenk-Hoppé & Ewald (2009) and Siven & Poulsen (2009 , Table 4). …”

Section: The Black-scholes Modelmentioning

confidence: 99%

Empirical performance of models for barrier option valuation

Jessen

Poulsen

2013

Quantitative Finance

Self Cite

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In this paper the empirical performance of five different models for barrier option valuation is investigated: the Black-Scholes model, the constant elasticity of variance model, the Heston stochastic volatility model, the Merton jump-diffusion model, and the infinite activity Variance Gamma model. We use time-series data from the USD/EUR exchange rate market: standard put and call (plain vanilla) option prices and a unique set of observed market values of barrier options. The models are calibrated to plain vanilla option prices, and prediction errors at different horizons for plain vanilla and barrier option values are investigated. For plain vanilla options, the Heston and Merton models have similar and superior performance for prediction horizons up to one week. For barrier options, the continuous-path models (Black-Scholes, constant elasticity of variance, and Heston) do almost equally well, while both models with jumps (Merton and Variance Gamma) perform markedly worse.JEL classification: G13 Keywords: Barrier option valuation, empirical performance. * We are deeply indebted to Morten Nalholm for his help cleaning and organizing the barrier option data, and to Fiodar Kilin for his help calibrating the Bates and VG-CIR models. We also thank three referees for valuable comments.

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“…Several researchers also consider optimization approaches to barrier option pricing and hedging . Siven and Poulsen () investigate risk‐minimizing hedges of barrier options based on four risk measures (i.e., the quadratic, the positive part, value‐at‐risk, and expected shortfall). Maruhn, Nalholm, and Fengler () study model‐dependent super‐replicating hedges for reverse barrier options.…”

Section: Introductionmentioning

confidence: 99%

Valuation Bounds on Barrier Options Under Model Uncertainty

Hong

2012

Journal of Futures Markets

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This article investigates valuation bounds on barrier options under model uncertainty. This investigation enriches the literature on the model-free valuation of these exotic options. It is found that with weak assumptions on underlying price processes, tight valuation bounds on barrier options can be sought from a set of European options. As a result, the numerical routine developed in this article can be reviewed as a new method for the evaluation of barrier options, which is independent of model assumptions.

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Auto-static for the people: risk-minimizing hedges of barrier options

Abstract: Risk-minimization, Static hedge, Barrier option, Bates model, NIG model, Model risk, G13, C61,

Cited by 8 publications

References 40 publications

Semistatic hedging and pricing American floating strike lookback options

Semistatic hedging and pricing American floating strike lookback options

Empirical performance of models for barrier option valuation

Valuation Bounds on Barrier Options Under Model Uncertainty

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