Optimal hedging when the underlying asset follows a regime-switching Markov process

François, Pascal; Gauthier, Geneviève; Godin, Frédéric

doi:10.1016/j.ejor.2014.01.034

Cited by 32 publications

(12 citation statements)

References 34 publications

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Section: Valuation With General Loss Functionsmentioning

confidence: 99%

“…As an insurer, the major concern is to avoid a shortfall, namely situations where S > θ • Y. Various authors (for instance Leukert, 2000 andFrançois et al, 2014) proposed alternative penalty functions that only penalise losses or penalise losses and gains asymmetrically. • The total level of assets that the insurer has to hold with respect to their liabilities is typically given by a risk measure, for example in the case of Solvency II, VaR 0.995 .…”

Section: Valuation With General Loss Functionsmentioning

confidence: 99%

“…Furthermore, quadratic hedging, leading to residuals with zero expectation, is divorced from the preferences encoded in regulation, which requires neutralisation of a risk measure such as Value-at-Risk (VaR). Föllmer and Leukert (2000) and François et al (2014) proposed to use general expected penalties that only penalise losses. Föllmer and Leukert (1999) defined the quantile hedging scheme, which maximises the probability that the hedging loss does not exceed a certain threshold at maturity, given an initial capital.…”

Section: Introductionmentioning

confidence: 99%

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Insurance Valuation: A Two-Step Generalised Regression Approach

Barigou¹,

Bignozzi²,

Tsanakas³

2021

ASTIN Bull.

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Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.

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Section: Valuation With General Loss Functionsmentioning

confidence: 99%

Section: Valuation With General Loss Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Insurance Valuation: A Two-Step Generalised Regression Approach

Barigou¹,

Bignozzi²,

Tsanakas³

2021

ASTIN Bull.

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“…Zhipang and Shenghong (2017) suggested the use of the Markov Regime Switching Diagonal BEKK-GARCH model for estimating hedge ratios. François et al (2014) believed that the regime-switching behaviour of the underlying market is to be considered while calculating the optimal hedge ratio. Bai et al (2019) agree that the hedging performance can be improved by incorporating conditional heteroskedasticity into the estimation.…”

Section: [ ∆ ∆ mentioning

confidence: 99%

Tackling Investment Risks Using Equity Options During Extreme Economic Upheavals: Indian Evidence

Jose

Varghese

2021

Colombo Bus. J

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The study is an empirical scrutiny on the Indian equity options market to examine whether it facilitates the reduction of investment risks, focusing on an economic sphere with financial upheavals. The risk mitigation ability is examined with respect to the integration of nearmonth call and put options markets having different levels of exercisability with the equity market in the National Stock Exchange of India. The optimal size of options contracts required for establishing a hedge portfolio that minimises the risk exposure to a maximum possible magnitude and the level of gains resulting from such hedges are identified following the minimum variance approach, using Diagonal BEKK GARCH. The results indicate that ATM, ITM, and DITM call options and ATM, OTM, DOTM, and DITM put options provide effective risk reduction that can be efficiently utilised by the existing as well as prospective investors in the equity market.

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“…n+1 (V 0 ) are to be understood as the optimal time-t n hedges for the long and short position when time-0 capital investment is V 0 , and I n is a F n -measurable random vector containing a set of additional state variables summarizing all necessary information to make the optimal portfolio rebalancing decision. For instance, I n can contain underlying asset volatilities if the latter asset has a GARCH dynamics (see Augustyniak et al, 2017), current probabilities of being in the various respective regimes when in a regime-switching setup (see François et al, 2014), implied volatilities when options are used as hedging instruments (see Carbonneau and Godin, 2021a), current assets positions when in the presence of transaction costs (see Breton and Godin, 2017), and so on.…”

Section: Neural Network Approximation Of the Optimal Solutionmentioning

confidence: 99%

Deep equal risk pricing of financial derivatives with non-translation invariant risk measures

Carbonneau¹,

Godin²

2021

Preprint

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The use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives is investigated. The ability to move beyond the class of convex risk measures considered in several prior studies provides more flexibility within the pricing scheme. In particular, suitable choices for the risk measure embedded in the ERP framework such as the semi-mean-square-error (SMSE) are shown herein to alleviate the price inflation phenomenon observed under Tail Value-at-Risk based ERP as documented for instance in Carbonneau and Godin (2021b). The numerical implementation of non-translation invariant ERP is performed through deep reinforcement learning, where a slight modification is applied to the conventional deep hedging training algorithm (see Buehler et al., 2019) so as to enable obtaining a price through a single training run for the two neural networks associated with the respective long and short hedging strategies. The accuracy of the neural network training procedure is shown in simulation experiments not to be materially impacted by such modification of the training algorithm.

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Optimal hedging when the underlying asset follows a regime-switching Markov process

Cited by 32 publications

References 34 publications

Insurance Valuation: A Two-Step Generalised Regression Approach

Insurance Valuation: A Two-Step Generalised Regression Approach

Tackling Investment Risks Using Equity Options During Extreme Economic Upheavals: Indian Evidence

Deep equal risk pricing of financial derivatives with non-translation invariant risk measures

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