Analysis, Geometry, and Modeling in Finance

Henry-Labordère, Pierre

doi:10.1201/9781420087000

Cited by 133 publications

(121 citation statements)

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“…, as observed by Henry-Labordère (Remark 5.2 in [26]). Generic time-inhomogeneous local volatility models dS t = σ(S t , t)S t dW t could be treated very similarly, using the heat kernel expansion in Section 3 of [22], itself taken from Yosida [38].…”

Section: Generic Local Volatility Modelssupporting

confidence: 67%

Option Pricing in the Moderate Deviations Regime

2016

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We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options. First and higher order small-time moderate deviation estimates of call prices and implied volatility are obtained. The expansions involve only simple expressions of the model parameters, and we show in detail how to calculate them for generic local and stochastic volatility models. Some numerical examples for the Heston model illustrate the accuracy of our results.

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Section: Generic Local Volatility Modelssupporting

confidence: 67%

Option Pricing in the Moderate Deviations Regime

2016

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“…For example, in the log-normal SABR model, if the asset price process is positively correlated with the stochastic volatility process, then it follows strict local martingale dynamics; see Example 6.1 in Henry-Labordère [17].…”

Section: Related Literaturementioning

confidence: 99%

On the hedging of options on exploding exchange rates

Carr

Fisher²,

Ruf

2013

Finance Stoch

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We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of numéraire (change of currency) technique when the underlying is only a local martingale modelling for example an exchange rate. The new pricing operator assigns prices to contingent claims according to the minimal cost for superreplication strategies that succeed with probability one for both currencies as numéraire. Within this context, we interpret the lack of the martingale property of an exchange-rate as a reflection of the possibility that the numéraire currency may devalue completely against the asset currency (hyperinflation).

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“…In recent years there has been an explosion of literature on small-time asymptotics for stochastic volatility models (see Berestycki et al [5], [6], Forde & Jacquier [21,22], Hagan et al [29], Henry-Labordère [30], Laurence [38] and Robertson [44]). …”

Section: Introductionmentioning

confidence: 99%

The Large Maturity Smile for the Heston Model

Forde

Jacquier

2009

SSRN Journal

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Abstract. Using the Gärtner-Ellis theorem from large deviations theory, we characterize the leadingorder behaviour of call option prices under the Heston model, in a new regime where the maturity is large and the log-moneyness is also proportional to the maturity. Using this result, we then derive the implied volatility in the large-time limit in the new regime, and we find that the large-time smile mimics the large-time smile for the Barndorff-Nielsen Normal Inverse Gaussian model. This makes precise the sense in which the Heston model tends to an exponential Lévy process for large times. We find that the implied volatility smile does not flatten out as the maturity increases, but rather it spreads out, and the large-time, large-moneyness regime is needed to capture this effect. As a special case, we provide a rigorous proof of the well known result by Lewis [40] for the implied volatility in the usual large-time, fixed-strike regime, at leading order. We find that there are two critical strike values where there is a qualitative change of behaviour for the call option price, and we use a limiting argument to compute the asymptotic implied volatility in these two cases.

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Analysis, Geometry, and Modeling in Finance

Cited by 133 publications

References 0 publications

Option Pricing in the Moderate Deviations Regime

Option Pricing in the Moderate Deviations Regime

On the hedging of options on exploding exchange rates

The Large Maturity Smile for the Heston Model

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