Results 1  10
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16
Risk neutral compatibility with option prices
, 2006
"... Abstract A common problem is to choose a “risk neutral ” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure ” by completing the market with option prices. We do this by model ..."
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Cited by 13 (2 self)
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Abstract A common problem is to choose a “risk neutral ” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure ” by completing the market with option prices. We do this by modeling the behavior of the stock price X, together with the behavior of the option prices for a relevant family of options which are (or can theoretically be) effectively traded. In doing so, we need to ensure a kind of ’‘compatibility ” between X and the prices of our options, and this poses some significant mathematical difficulties.
Recovering a timehomogeneous stock price process from perpetual option prices
 Ann. Appl. Probab
"... Abstract. It is wellknown how to determine the price of perpetual American options if the underlying stock price is a timehomogeneous diffusion. In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a ti ..."
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Cited by 10 (3 self)
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Abstract. It is wellknown how to determine the price of perpetual American options if the underlying stock price is a timehomogeneous diffusion. In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a timehomogeneous model for the stock price which reproduces the given option prices. 1.
R.: Symmetric martingales and symmetric smiles
 Stochastic Processes and Their Applications 119(10), 3785  3797
, 2009
"... Abstract. A local martingale X is called arithmetically symmetric if the conditional distribution of XT −Xt is symmetric given Ft, for all 0 ≤ t ≤ T. Letting FTt = Ft ∨ σ(〈X〉T), the main result of this note is that for a continuous local martingale X the following are equivalent (1) X is arithmetic ..."
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Cited by 7 (0 self)
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Abstract. A local martingale X is called arithmetically symmetric if the conditional distribution of XT −Xt is symmetric given Ft, for all 0 ≤ t ≤ T. Letting FTt = Ft ∨ σ(〈X〉T), the main result of this note is that for a continuous local martingale X the following are equivalent (1) X is arithmetically symmetric. (2) The conditional distribution of XT given FTt is N(Xt, 〈X〉T − 〈X〉t) for all 0 ≤ t ≤ T. (3) X is a local martingale for the enlarged filtration (FTt)t≥0 for each T ≥ 0. The notion of a geometrically symmetric martingale is also defined and characterized as the DoléansDade exponential of an arithmetically symmetric local martingale. As an application of these results, we show that a market model of the implied volatility surface that is initially flat and that remains symmetric for all future times must be the Black–Scholes model. 1.
An infinite dimensional stochastic analysis approach to local volatility dynamic models
 COMMUNICATIONS ON STOCHASTIC ANALYSIS
, 2008
"... The difficult problem of the characterization of arbitrage free dynamic stochastic models for the equity markets was recently given a new life by the introduction of market models based on the dynamics of the local volatility. Typically, market models are based on Itô stochastic differential equatio ..."
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Cited by 5 (2 self)
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The difficult problem of the characterization of arbitrage free dynamic stochastic models for the equity markets was recently given a new life by the introduction of market models based on the dynamics of the local volatility. Typically, market models are based on Itô stochastic differential equations modeling the dynamics of a set of basic instruments including, but not limited to, the option underliers. These market models are usually recast in the framework of the HJM philosophy originally articulated for Treasury bond markets. In this paper we streamline some of the recent results on the local volatility dynamics by employing an infinite dimensional stochastic analysis approach as advocated by the pioneering work of L. Gross and his students.
Tangent Lévy Market Models
"... In this paper, we introduce a new class of models for the time evolution of the prices of call options of all strikes and maturities. We capture the information contained in the option prices in the density of some timeinhomogeneous Lévy measure (an alternative to the implied volatility surface), ..."
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In this paper, we introduce a new class of models for the time evolution of the prices of call options of all strikes and maturities. We capture the information contained in the option prices in the density of some timeinhomogeneous Lévy measure (an alternative to the implied volatility surface), and we set this static codebook in motion by means of stochastic dynamics of Itôs type in a function space, creating what we call a tangent Lévy model. We then provide the consistency conditions, namely, we show that the call prices produced by a given dynamic codebook (dynamic Lévy density) coincide with the conditional expectations of the respective payoffs if and only if certain restrictions on the dynamics of the codebook are satisfied (including a drift condition à la HJM). We then provide an existence result, which allows us to construct a large class of tangent Lévy models, and describe a specific example for the sake of illustration.
TANGENT MODELS AS A MATHEMATICAL FRAMEWORK FOR DYNAMIC CALIBRATION
"... ABSTRACT. Motivated by the desire to integrate repeated calibration procedures into a single dynamic market model, we introduce the notion of tangent market model in an abstract set up, and we show that this new mathematical paradigm accommodates all the recent attempts to study consistency and abse ..."
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ABSTRACT. Motivated by the desire to integrate repeated calibration procedures into a single dynamic market model, we introduce the notion of tangent market model in an abstract set up, and we show that this new mathematical paradigm accommodates all the recent attempts to study consistency and absence of arbitrage in market models. For the sake of illustration, we concentrate on equity models and we assume that market quotes provide the prices of European call options for a specific set of strikes and maturities. While reviewing our recent results on dynamic local volatility and tangent L’evy models, we provide new results on the short timetomaturity asymptotics which shed new light on the dichotomy between these two disjoint classes of models, with and without jumps, helping choose in practice, which class of models is most appropriate to the market characteristics at hand. 1.
Optimal investment and price dependence in a semistatic market, Finance Stoch., forthcoming
, 2013
"... ar ..."
ArbitrageFree Models for VIX and Equity Derivatives
, 2015
"... This thesis must be used in accordance with the provisions of the Copyright Act 1968. Reproduction of material protected by copyright may be an infringement of copyright and copyright owners may be entitled to take legal action against persons who infringe their copyright. Section 51 (2) of the Copy ..."
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This thesis must be used in accordance with the provisions of the Copyright Act 1968. Reproduction of material protected by copyright may be an infringement of copyright and copyright owners may be entitled to take legal action against persons who infringe their copyright. Section 51 (2) of the Copyright Act permits an authorized officer of a university library or archives to provide a copy (by communication or otherwise) of an unpublished thesis kept in the library or archives, to a person who satisfies the authorized officer that he or she requires the reproduction for the purposes of research or study. The Copyright Act grants the creator of a work a number of moral rights, specifically the right of attribution, the right against false attribution and the right of integrity. You may infringe the author’s moral rights if you: fail to acknowledge the author of this thesis if you quote sections from the work attribute this thesis to another author subject this thesis to derogatory treatment which may prejudice the author’s reputation
Implied Volatility Surface Simulation with Tangent Lévy Models
, 2014
"... With the recent developments of a liquid derivative market, as well as the demands for an improved risk management framework post the financial crisis, it is becoming increasingly important to consistently model the implied volatility dynamics of an asset. Many attempts have been made on this front, ..."
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With the recent developments of a liquid derivative market, as well as the demands for an improved risk management framework post the financial crisis, it is becoming increasingly important to consistently model the implied volatility dynamics of an asset. Many attempts have been made on this front, but few manage to exclude arbitrage opportunities with reasonable tractability. In this thesis, we present two approaches based on tangent Lévy models to achieve the task. One of the biggest advantages of tangent Lévy models is that, by using the tangent process ’ jump density as the codebook to describe the option price dynamics, it enables an explicit expression of the noarbitrage conditions, hence allows for tractable implementation. Our first approach is based on the tangent Lévy model with tangent processes being derived from the double exponential process. This approach is easy to implement given the small number of parameters and the availability of an analytical pricing formula. In the second approach, the tangent process takes only finitely many jump sizes. With
MPRA Munich Personal RePEc Archive
, 2007
"... Noname manuscript No. (will be inserted by the editor) An Hilbert space approach for a class of arbitrage free implied volatilities models ..."
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Noname manuscript No. (will be inserted by the editor) An Hilbert space approach for a class of arbitrage free implied volatilities models