Option Hedging with Stochastic Volatility

Kurpiel, Adam; Roncalli, Thierry

doi:10.2139/ssrn.1031927

Cited by 4 publications

(7 citation statements)

References 15 publications

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“…Amongst the stochastic volatility model, the SV model as the simplest model, does not underperform and sometimes even is the best-performing model. For the choice of a SV hedge model, the ∆ SV − V SV hedge is a replicating strategy (Kurpiel and Roncalli, 1999) and performs often better than other models under the same or different strategies. As calibrated jump intensities λ SV J and λ SV CJ are low, the SVJ or SVCJ are often similar to the SV leading to comparable hedge results.…”

Section: Hedge Resultsmentioning

confidence: 99%

Hedging Cryptocurrency Options

2021

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The cryptocurrency (CC) market is volatile, non-stationary and non-continuous. This poses unique challenges for pricing and hedging CC options. We study the hedge behaviour and effectiveness for a wide range of models. First, we calibrate market data to SVI-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate price paths using two types of Monte Carlo simulations. In the first approach, price paths follow an SVCJ model (stochastic volatility with correlated jumps). The second approach simulates paths from a GARCH-filtered kernel density estimation. In these two markets, options are hedged with models from the class of affine jump diffusions and infinite activity Lévy processes. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. Dynamic Delta, Delta-Gamma, Delta-Vega and minimum variance hedge strategies are applied.The calibration results reveal a strong indication for stochastic volatility, low jump intensity and evidence of infinite activity. With the exception of short-dated options, a consistently good performance is achieved with Delta-Vega hedging in stochastic volatility models. Judging on the calibration and hedging results, the study provides evidence that stochastic volatility is the driving force in CC markets.

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Section: Hedge Resultsmentioning

confidence: 99%

Hedging Cryptocurrency Options

2021

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“…Equation (28) details the calculation of the expectation of the hedging strategy. This expression is obtained applying the tower law (or iterated expectations) to equation (14) (see that the cash amount H t N t N cancels the cash value of the position α t N on underlying and β t N on vanilla call). The expectation on the right hand side is equal to zero, because H is composed of two traded assets: the underlying S t B f t and the vanilla call option C t .…”

Section: Rigorous Derivation Of Hedging Strategymentioning

confidence: 99%

“…Considering hedging strategies to contrast valuation models is not new (see for instance [14], [4] and [3]). In this context, the main goal of this paper is to estimate relative model risk in a way which could be consistent and robust, general purpose and applicable to a portfolio of deals.…”

Section: Introductionmentioning

confidence: 99%

“…See that the hedging position is sold at the beginning of the second period with the positive income H t 0 t 1 of the hedging position of the previous instant t 0 (valued at t 1 ) and the negative outcome, H t 1 t 1 , to buy the new hedging position (α 1 , β 1 ). Finally, equation(14) shows the hedging portfolio5 In practice, the hedging portfolio is not sold and bought again, but just rebalanced 6. A Discrete dividend payment would not have impact as the income to the cash account would be compensated by a down jump move in the underlying spot.…”

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Applying hedging strategies to estimate model risk and provision calculation

Elices¹,

Giménez

2013

Quantitative Finance

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This paper introduces a relative model risk measure of a product priced with a given model, with respect to another reference model for which the market is assumed to be driven. This measure allows comparing products valued with different models (pricing hypothesis) under a homogeneous framework which allows concluding which model is the closest to the reference. The relative model risk measure is defined as the expected shortfall of the hedging strategy at a given time horizon for a chosen significance level. The reference model has been chosen to be Heston calibrated to market for a given time horizon (this reference model should be chosen to be a market proxy). The method is applied to estimate and compare this relative model risk measure under volga-vanna and Black-Scholes models for double-notouch options and a portfolio of forward fader options.

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“…Researchers also use higher order Greeks to quantify different aspects of risk in option portfolios and attempt to make the portfolio immune to big changes in the underlying asset price. Kurpiel and Roncalli [1998] implemented both a pure delta hedge and a delta-gamma hedge the under the framework of Black-Scholes. Under a delta-gamma hedging scheme, both the delta and gamma of the portfolio remain neutral at each rebalancing step.…”

Section: Introductionmentioning

confidence: 99%

Hedging Barrier Options through a Log-Normal Local Stochastic Volatility model

2017

Syme, G., Hatton MacDonald, D., Fulton, B. And Piantadosi, J. (Eds) MODSIM2017, 22nd International Congress on Modelling and Si

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In the equity and foreign exchange (FX) markets, there has been a shift towards using nonaffine pricing models as these have been shown to produce more realistic volatility distributions and more accurately capture market dynamics. One such non-affine model is the Inverse Gamma model, which we have incorporated into a Local-Stochastic Volatility (LSV) model termed the Log-normal-LSV (LN-LSV) that can, once calibrated, accurately reproduce market prices of exotic options Langrene and Zhu [2016]. The LN-LSV model is a non-parametric combination of local volatility and stochastic volatility models, in which both the spot price and stochastic volatility follow log-normal processes. The LN-LSV model is calibrated using both the market-traded implied volatility surface and market exotic option prices. However, while the accurate pricing of exotic options is necessary for good pricing model performance, it is also necessary for models to perform in risk management applications, where hedges are entered into to minimise risk. Therefore, the accurate calculation of the derivatives of the option price with respect to the asset or volatility (the Greeks) is also necessary for good model performance. This paper aims to characterise the hedging performance of the Log-normal Local-Stochastic Volatility model for a variety of hedging instruments using an historical dataset consisting of daily spots and volatility surfaces for the EUR/USD market over a five-year time period. We use delta-gamma hedging for different barrier options under the LN-LSV model and compare the hedging performance with that of the Black-Scholes (BS) model. Then we use the numerical results to demonstrate that the LN-LSV model is more effective than the BS model. We use five types of reverse knockout options as test cases over a time period of five years. On each trading day from 2007 to 2011, the five options are firstly priced using the LN-LSV model. After pricing, each option is hedged daily until the expiry date of the option using a delta-gamma neutral scheme under both the LN-LSV and BS models. To measure the hedging performance, each profit-loss outcome forms one point of the P&L distribution. During Jan 2007 to Dec 2011, the profit and loss of a total of 1100 traded options for each option type forms the P&L distribution. Compared to the Black-Scholes model, the P&L distribution of the numerical results from LN-LSV model is more symmetric and is less likely to have extreme profit-loss outliers. Thus it produces more superior hedging performance.

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Option Hedging with Stochastic Volatility

Cited by 4 publications

References 15 publications

Hedging Cryptocurrency Options

Hedging Cryptocurrency Options

Applying hedging strategies to estimate model risk and provision calculation

Hedging Barrier Options through a Log-Normal Local Stochastic Volatility model

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