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50
Static Hedging under TimeHomogeneous Diffusions
 SIAM J. FINANCIAL MATH
, 2011
"... We consider the problem of semistatic hedging of a single barrier option in a model where the underlying is a timehomogeneous diffusion, possibly running on an independent stochastic clock. The main result of the paper is an analytic expression for the payoff of a Europeantype contingent claim, w ..."
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We consider the problem of semistatic hedging of a single barrier option in a model where the underlying is a timehomogeneous diffusion, possibly running on an independent stochastic clock. The main result of the paper is an analytic expression for the payoff of a Europeantype contingent claim, which has the same price as the barrier option up to hitting the barrier. We then consider some examples, such as the Black–Scholes, constant elasticity of variance, and zerocorrelation SABR models. Finally, we investigate an approximation of the static hedge with options of at most two different strikes.
Coupling index and stocks
 n o 392, ENPC/CERMICS
, 2008
"... In this paper, we are interested in continuous time models in which the index level induces some feedback on the dynamics of its composing stocks. More precisely, we propose a model in which the logreturns of each stock may be decomposed into a systemic part proportional to the logreturns of the i ..."
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In this paper, we are interested in continuous time models in which the index level induces some feedback on the dynamics of its composing stocks. More precisely, we propose a model in which the logreturns of each stock may be decomposed into a systemic part proportional to the logreturns of the index plus an idiosyncratic part. We show that, when the number of stocks in the index is large, this model may be approximated by a local volatility model for the index and a stochastic volatility model for each stock with volatility driven by the index. We address calibration of both the limit and the original models. hal00350652, version 1 7 Jan 2009
A Bayesian Approach to Financial Model Calibration, Uncertainty Measures and Optimal Hedging
"... Michaelmas 2009This thesis is dedicated to the late ..."
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Michaelmas 2009This thesis is dedicated to the late
Shorttime asymptotics for marginal distributions of semimartingales
, 2012
"... We study the shorttime aymptotics of conditional expectations of smooth and nonsmooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior of ca ..."
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We study the shorttime aymptotics of conditional expectations of smooth and nonsmooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior of call options with short maturity in a semimartingale model: whereas the behavior of outofthemoney options is found to be linear in time, the short time asymptotics of atthemoney options is
Calibration of local volatility using the local and implied instantaneous variance
 The Journal of Computational Finance
, 2009
"... We document the calibration of the local volatility in terms of local and implied instantaneous variances; we first explore the theoretical properties of the method for a particular class of volatilities. We confirm the theoretical results through a numerical procedure which uses a GaussNewton styl ..."
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We document the calibration of the local volatility in terms of local and implied instantaneous variances; we first explore the theoretical properties of the method for a particular class of volatilities. We confirm the theoretical results through a numerical procedure which uses a GaussNewton style approximation of the Hessian in the framework of a sequential quadratic programming (SQP) approach. The procedure performs well on benchmarks from the literature and on FOREX data.
Robust Calibration of Financial Models Using Bayesian Estimators
, 2012
"... We consider a general calibration problem for derivative pricing models, which we reformulate into a Bayesian framework to attain posterior distributions for model parameters. It is then shown how the posterior distribution can be used to estimate prices for exotic options. We apply the procedure to ..."
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We consider a general calibration problem for derivative pricing models, which we reformulate into a Bayesian framework to attain posterior distributions for model parameters. It is then shown how the posterior distribution can be used to estimate prices for exotic options. We apply the procedure to a discrete local volatility model and work in great detail through numerical examples to clarify the construction of Bayesian estimators and their robustness to the model specification, number of calibration products, noisy data and misspecification of the prior. 1
Model uncertainty and its impact on derivative pricing
 Rethinking Risk Management and Reporting: Uncertainty, Bayesian Analysis and Expert Judgement. Risk Books
, 2010
"... Financial derivatives written on an underlying can normally be priced and hedged accurately only after a suitable mathematical model for the underlying has been determined. This chapter explains the difficulties in finding a (unique) realistic model — model uncertainty. If the wrong model is chosen ..."
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Financial derivatives written on an underlying can normally be priced and hedged accurately only after a suitable mathematical model for the underlying has been determined. This chapter explains the difficulties in finding a (unique) realistic model — model uncertainty. If the wrong model is chosen
Deltahedging vega risk
 Journal Of Quantitative Finance
"... In this article we compare the Profit and Loss arising from the deltaneutral dynamic hedging of options, using two possible values for the delta of the option. The first one is the Black– Scholes implied delta, while the second one is the local delta, namely the delta of the option in a generalized ..."
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In this article we compare the Profit and Loss arising from the deltaneutral dynamic hedging of options, using two possible values for the delta of the option. The first one is the Black– Scholes implied delta, while the second one is the local delta, namely the delta of the option in a generalized Black–Scholes model with a local volatility, recalibrated to the market smile every day. We explain why in negatively skewed markets the local delta should provide a better hedge than the implied delta during slow rallies or fast selloffs, and a worse hedge, though to a lesser extent, during fast rallies or slow selloffs. Since slow rallies and fast selloffs are more likely to occur than fast rallies or slow selloffs in negatively skewed markets (provided we have physical as well as implied negative skewness), we conclude that on average the local delta provides a better hedge than the implied delta in negatively skewed markets. We obtain the same conclusion in the case of positively skewed markets. We illustrate these results by using both simulated and real timeseries of equityindex data, that have had a large negative implied skew since the stock market crash of October 1987. Moreover we check numerically that the conclusions we draw are true when transaction costs are taken into account. In the last section we discuss the case of barrier options.
Small time central limit theorems for semimartingales with applications
, 2012
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