Optimal hedging in discrete time

Rémillard, Bruno; Rubenthaler, Sylvain

doi:10.1080/14697688.2012.745012

“…Furthermore, we state the regime-switching specialization of the optimal hedging algorithm [18] which generates optimal discrete-time (in our case, daily)…”

Section: Discussionmentioning

confidence: 99%

“…Note that 0 V is chosen such that the expected hedging error G is zero. [18] also showed that t C (defined by…”

Section: T T T T T a E Pmentioning

confidence: 99%

Option Pricing and Hedging for Discrete Time Regime-Switching Models

Rémillard¹,

Hocquard²,

Lamarre³

et al. 2017

Self Cite

View full text Add to dashboard Cite

We propose optimal mean-variance dynamic hedging strategies in discrete time under a multivariate Gaussian regime-switching model. The methodology, which also performs pricing, is robust to time-varying and clustering risk observed in financial time series. As such, it overcomes the main theoretical drawbacks of the Black-Scholes model. To support our approach, we provide goodness-of-fit tests to validate the model and for choosing the appropriate number of regimes, and we illustrate the methodology using monthly S & P 500 vanilla options prices. Then, we present the associated out-of-sample hedging results in the context of harvesting the implied versus realized volatility premium. Using the proposed methodology, the Sharpe ratio derived from the strategy doubles over the Black-Scholes delta-hedging methodology.

show abstract

“…Since we fitted a Gaussian HMM to the daily returns, an obvious solution of the hedging problem would be to use the results of [23] for optimal hedging in discrete time; see also [11]. However, implementing this methodology requires interpolating functions on a (d + 1)-dimensional grid.…”

Section: Discrete Time Hedgingmentioning

confidence: 99%

Replication Methods for Financial Indexes

Rémillard

¹

,

Nasri

²

,

Ben-Abdellatif

³

2018

Innovations in Insurance, Risk- And Asset Management

Self Cite

0

View full text Add to dashboard Cite

In this paper, we first present a review of statistical tools that can be used in asset management either to track financial indexes or to create synthetic ones. More precisely, we look at two important replication methods: the strong replication, where a portfolio of very liquid assets is created and the goal is to track an actual index with the portfolio, and weak replication, where a portfolio of very liquid assets is created and used to either replicate the statistical properties of an existing index, or to replicate the statistical properties of a custom asset. In addition, for weak replication, the target is not an index but a payoff, and the replication amounts to hedge the portfolio so it is as close as possible to the payoff at the end of each month. For strong replication, the main tools are predictive tools, so filtering techniques and regression play an important role. For weak replication, which is the main topic of this paper, in order to determine the target payoff, the investor has to find or choose the distribution function of the target index or custom index, as well as its dependence with other assets, and use a hedging technique. Therefore, the main tools for weak replication are modeling (estimation and goodness-of-fit) and optimal hedging. For example, an investor could wish to obtain Gaussian returns that are independent of some ETFs replicating the Nasdaq and S&P 500 indexes. In order to determine the dependence of the target and a given number of indexes, we introduce a new class of easily constructed models of conditional distributions called B-vines. We also propose to use a flexible model to fit the distribution of the assets composing the portfolio and then hedge the portfolio in an optimal way. Examples are given to illustrate all the important steps required for the implementation of this new asset management methodology.

show abstract

“…Since we fitted a Gaussian HMM to the daily returns, an obvious solution of the hedging problem would be to use the results of Rémillard and Rubenthaler (2013) for optimal hedging in discrete time; see also Rémillard (2013). However, implementing this methodology requires interpolating functions on a (d + 1)-dimensional grid.…”

Section: Discrete Time Hedgingmentioning

confidence: 99%

Replication Methods for Financial Indexes

Rémillard

¹

,

Nasri

²

,

Ben-Abdellatif

³

2017

SSRN Journal

1

0

View full text Add to dashboard Cite

In this paper, we first present a review of statistical tools that can be used in asset management either to track financial indexes or to create synthetic ones. More precisely, we look at two important replication methods: the strong replication, where a portfolio of very liquid assets is created and the goal is to track an actual index with the portfolio, and weak replication, where a portfolio of very liquid assets is created and used to either replicate the statistical properties of an existing index, or to replicate the statistical properties of a custom asset. In addition, for weak replication, the target is not an index but a payoff, and the replication amounts to hedge the portfolio so it is as close as possible to the payoff at the end of each month. For strong replication, the main tools are predictive tools, so filtering techniques and regression play an important role. For weak replication, which is the main topic of this paper, in order to determine the target payoff, the investor has to find or choose the distribution function of the target index or custom index, as well as its dependence with other assets, and use a hedging technique. Therefore, the main tools for weak replication are modeling (estimation and goodness-of-fit) and optimal hedging. For example, an investor could wish to obtain Gaussian returns that are independent of some ETFs replicating the Nasdaq and S&P 500 indexes. In order to determine the dependence of the target and a given number of indexes, we introduce a new class of easily constructed models of conditional distributions called B-vines. We also propose to use a flexible model to fit the distribution of the assets composing the portfolio and then hedge the portfolio in an optimal way. Examples are given to illustrate all the important steps required for the implementation of this new asset management methodology.

show abstract

Optimal hedging in discrete time

Cited by 25 publications

References 15 publications

Option Pricing and Hedging for Discrete Time Regime-Switching Models

Option Pricing and Hedging for Discrete Time Regime-Switching Models

Replication Methods for Financial Indexes

Replication Methods for Financial Indexes

Contact Info

Product

Resources

About