Pricing European options and risk measurement under exponential Lévy models — a practical guide

Salhi, Khaled

doi:10.1142/s2424786317500165

Cited by 3 publications

(3 citation statements)

References 48 publications

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“…where the moment-generating functions (MGF) M (X) t and the cumulant-generating function . It is tempting to find a EMM using the Esscher transform (see Esscher (1932), Gerber and Shiu (1994), Salhi (2017)), as in this case we can set = 0. However, with = 0, the Esscher transform method requires finding a unique solution h * of the equation:…”

Section: Equivalent Martingale Measurementioning

confidence: 99%

Option Pricing with Mixed Lévy Subordinated Price Process and Implied Probability Weighting Function

Shirvani

Rachev

et al. 2020

JOD

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It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this paper, we reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, we employ the method of subordination which has been proposed in the literature by including business (intrinsic, market) time. We define a mixed Lévy subordinated model by adding a single subordinated Lévy process to the well-known log-normal model, resulting in a new log-price process. We apply the proposed models to study the behavioral finance notion of "greed and fear" disposition from the perspective of rational dynamic asset pricing theory. The greedy or fearful disposition of option traders is studied using the shape of the probability weighting function. We then derive the implied probability weighting function for the fear and greed deposition of option traders in comparison to spot traders. Our result shows the diminishing sensitivity of option traders. Diminishing sensitivity results in option traders overweighting the probability of big losses in comparison to spot traders.

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Section: Equivalent Martingale Measurementioning

confidence: 99%

Option Pricing with Mixed Lévy Subordinated Price Process and Implied Probability Weighting Function

Shirvani

Rachev

et al. 2020

JOD

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“…The advantage of using this equivalent martingale measure is that the density process only depends on the current stock price, which permits more explicit computing. See [40] for more details. In terms of Proposition 3.2, the Esscher martingale measure corresponds to the choice p q " .…”

Section: Approximation Of Dual Problemmentioning

confidence: 99%

Approximation of CVaR minimization for hedging under exponential-Lévy models

Deaconu

Lejay

Salhi

2017

Journal of Computational and Applied Mathematics

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In this paper, we study the hedging problem based on the CVaR in incomplete markets. As the superhedging is quite expensive in terms of initial capital, we construct a self-financing strategy that minimizes the CVaR of hedging risk under a budget constraint on the initial capital. In incomplete markets, no explicit solution can be provided. To approximate the problem, we apply the Neyman-Pearson lemma approach with a specific equivalent martingale measure. Afterwards, we explicit the solution for call options hedging under the exponential-Lévy class of price models. This approach leads to an efficient and easy to implement method using the fast Fourier transform. We illustrate numerical results for the Merton model.

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“…Their study shows that option implied intra-horizon risk estimates are much more responsive to market changes compared to the historical measures. Salhi (2017) focusses on European option pricing under exponential Levy models. They provide a survey on new trends in risk measurement and use Fast Fourier transforms to compute the VaR and CVaR for derivatives.…”

Section: Introductionmentioning

confidence: 99%

How Risky Are the Options? A Comparison with the Underlying Stock Using MaxVaR as a Risk Measure

Patra

Bhattacharyya

2020

Risks

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This paper investigates the risk exposure for options and proposes MaxVaR as an alternative risk measure which captures the risk better than Value-at-Risk especially. While VaR is a measure of end-of-horizon risk, MaxVaR captures the interim risk exposure of a position or a portfolio. MaxVaR is a more stringent risk measure as it assesses the risk during the risk horizon. For a 30-day maturity option, we find that MaxVaR can be 40% higher than VaR at a 5% significance level. It highlights the importance of MaxVaR as a risk measure and shows that the risk is vastly underestimated when VaR is used as the measure for risk. The sensitivity of MaxVaR with respect to option characteristics like moneyness, time to maturity and risk horizons at different significance levels are observed. Further, interestingly enough we find that the MaxVar to VaR ratio is higher for stocks than the options and we can surmise that stock returns are more volatile than options. For robustness, the study is carried out under different distributional assumptions on residuals and for different stock index options.

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Pricing European options and risk measurement under exponential Lévy models — a practical guide

Cited by 3 publications

References 48 publications

Option Pricing with Mixed Lévy Subordinated Price Process and Implied Probability Weighting Function

Option Pricing with Mixed Lévy Subordinated Price Process and Implied Probability Weighting Function

Approximation of CVaR minimization for hedging under exponential-Lévy models

How Risky Are the Options? A Comparison with the Underlying Stock Using MaxVaR as a Risk Measure

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