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  • Robust Replication of Volatility Derivatives In this paper we investigate the behaviour and hedging of discretely observed volatility derivatives. We begin by comparing the effects of variations in the contract design, such as the differences between specifying log returns or actual returns, taking into consideration the impact of possible jumps in the underlying asset. We then focus on the difficulties associated with hedging these products. Naive delta-hedging strategies are ineffective for hedging volatility derivatives since they require very frequent rebalancing and have limited ability to protect the writer against possible jumps in the underlying asset. We investigate the performance of a hedging strategy for volatility swaps that establishes small, fixed positions in straddles and out-of-the-money strangles at each volatility observation. , P.Carr, R.Lee (2003)
    Nb Clicks : 2419
  • Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lending We present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), DVA Hedging, Closeout conventions, Netting clauses, Collateral modeling, Gap Risk, Re-hypothecation, Wrong Way Risk, Basel III, inclusion of Funding costs, First to Default risk, Contingent Credit Default Swaps (CCDS) and CVA restructuring possibilities through margin lending. The dialogue is in the form of a Q&A between a CVA expert and a newly hired colleague , Damiano Brigo (2011)
    Nb Clicks : 2410
  • Advanced Monte Carlo methods for barrier and related exotic options In this work, we present advanced Monte Carlo techniques applied to the pricing of barrier options and other related exotic contracts. It covers in particular the Brown- ian bridge approaches, the barrier shifting techniques (BAST) and their extensions as well. We leverage the link between discrete and continuous monitoring to de- sign efficient schemes, which can be applied to the Black-Scholes model but also to stochastic volatility or Merton?s jump models. This is supported by theoretical results and numerical experiments. , E. Gobet (2008)
    Nb Clicks : 1906
  • A Comparative Analysis of Basket Default Swaps Pricing Using the Stein Method , E.Benhamou, D.Bastide, M.Ciuca (2007)
    Nb Clicks : 1698
  • A jump to default extended CEV model: an application of Bessel processes , P. Carr, V. Linetsky (2006)
    Nb Clicks : 1657
  • Is Multi-Factor Really Necessary to Price European Options in Commodity? The main result of this article is the presentation of the Distribution Match Method. This method applies to a general multi-factor pricing model under assumption of normal law drift. The idea is to find an equivalent one-factor model for European options. The equivalent model admits a weak solution, which has the same one-dimensional marginal probability distribution. Moreover, the one-dimensional distribution can be explicitly calculated under certain condition. This result can consequently induct closed formula for the future price and European option price. We apply these results to two well known commodity models, the Gabillon and the Gibson Schwartz model, to provide the price for the future price and a closed formula for the European options. , E. Benhamou, Z. Wang, A.G. Galli (2009)
    Nb Clicks : 1579
  • An Improved Implied Copula Model and its Application to the Valuation of Bespoke CDO Tranches , J.Hull, A.White (2008)
    Nb Clicks : 1579
  • Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. The model is quite accurate. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large position gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio high profitable, especially for a large movement in the underlying stock price. , Tim Xiao (2013)
    Nb Clicks : 1530
  • Dynamic Factor Copula Model an factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. We introduce a multi-period factor copula model to overcome the calibration deficiency of factor copula models by allowing the factor loadings to be time-dependent. Usually, multi-period factor copula models require multi-dimensional integration, typically computed by Monte Carlo simulation, which makes calibration extremely time consuming. In our model, the portfolio loss of a completely homogeneous pool possesses the Markov property, thus we can compute the portfolio loss distribution analytically without multi-dimensional integration. Numerical results demonstrate the efficiency and flexibility of our model to match market quotes. , K.Jackson, A.Kreinin, W.Zhang (2009)
    Nb Clicks : 1513
  • Dynamics of implied volatility surfaces The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to reproduce. However, the implied volatility surface also changes dynamically over time in a way that is not taken into account by current modelling approaches, giving rise to ?Vega? risk in option portfolios. Using time series of option prices on the SP500 and FTSE indices, we study the deformation of this surface and show that it may be represented as a randomly fluctuating surface driven by a small number of orthogonal random factors. We identify and interpret the shape of each of these factors, study their dynamics and their correlation with the underlying index. Our approach is based on a Karhunen?Lo`eve decomposition of the daily variations of implied volatilities obtained from market data. A simple factor model compatible with the empirical observations is proposed. We illustrate how this approach models and improves the well known ?sticky moneyness? rule used by option traders for updating implied volatilities. Our approach gives a justification for use of ?Vega?s for measuring volatility risk and provides a decomposition of volatility risk as a sum of contributions from empirically identifiable factors. , R. Cont, J. da Fonseca (2009)
    Nb Clicks : 1497
  • A Class of Levy Process Models with almost exact calibration of both barrier and vanilla FX options Vanilla (standard European) options are actively traded on many underlying asset classes, such as equities, commodities and foreign exchange. The market quotes for these options are typically used by exotic options traders to calibrate the parameters of the (risk-neutral) stochastic process for the underlying asset. Barrier options, of many different types, are also widely traded in all these markets but one important of the FX Options market is that barrier options, especially Double-no-touch (DNT) options, are now so activley traded that they are o longer considered, in ay way, exotic options. Instead, traders would, in principle, like ot use them as instruments to which they can calibrate their model. The desirability of doing this has been highlighted by talks at practitioner conferences but, to our best knowledge (at least within the realm of the published literature), there have been no models which are specifically designed to cater for this. In this paper, we indtoruce such a model. It allows for calibration in a two-stage process. The first stage fits to DNT options (or other types of double barrier options). The seocnd stage fits to vanilla options. The model allows for jumps (ether finite activity or infinite activity) and also for stochastic volatility. Hence, not only can it give a good fit to the market prices of options, it can also allow for realistic dynamics of the underlying FX rate and realistic future volatility smiles and skews. En route, we significantly extend existing results in the literature by providing closed form (up to Laplace inversion) expressions for the prices of several types of barrier options as well as results related to the distribution of first passage times and of the ``overshoot'. , P.Carr, J.Crosby (2009)
    Nb Clicks : 1441
  • Introduction to Weather Derivative Pricing , S.Jewson (2004)
    Nb Clicks : 1379
  • Flaming Logs This paper extends the pathwise adjoint method for Greeks to the displaced-diffusion LIBOR market model and also presents a simple way to improve the speed of the method. The speed improvements of approximately 20% are achieved without using any additional approximations to those of Giles and Glasserman. , N.Denson, M.S.Joshi (2009)
    Nb Clicks : 1320
  • Calibrating the SABR Model to Noisy FX Data We consider the problem of fitting the SABR model to an FX volatility smile. It is demonstrated that the model parameter β cannot be determined from a log-log plot of σATM against F. It is also shown that, in an FX setting, the SABR model has a single state variable. A new method is proposed for fitting the SABR model to observed quotes. In contrast to the fitting techniques proposed in the literature, the new method allows all the SABR parameters to be retrieved and does not require prior beliefs about the market. The effect of noise on the new fitting technique is also investigated. , Hilary (2018)  
    Nb Clicks : 1261
  • A Fourier transform method for spread option pricing Spread options are a fundamental class of derivative contract written on multiple assets,and are widely used in a range of financial markets. There is a long history of approximationmethods for computing such products, but as yet there is no preferred approach thatis accurate, efficient and flexible enough to apply in general models. The present paperintroduces a new formula for general spread option pricing based on Fourier analysis of thespread option payoff function. Our detailed investigation proves the effectiveness of a fastFourier transform implementation of this formula for the computation of prices. It is foundto be easy to implement, stable, efficient and applicable in a wide variety of asset pricingmodels. , T.R.Hurd, Z.Zhou (2009)
    Nb Clicks : 1248
  • CDS with Counterparty Risk in a Markov Chain Copula Model with Joint Defaults In this paper we study the counterparty risk on a payer CDS in a Markov chain model of two reference credits, the firm underlying the CDS and the protection seller in the CDS. We first state few preliminary results about pricing and CVA of a CDS with counterparty risk in a general set-up. We then introduce a Markov chain copula model in which wrong way risk is represented by the possibility of joint defaults between the counterpart and the firm underlying the CDS. In the set-up thus specified we have semi-explicit formulas for most quantities of interest with regard to CDS counterparty risk like price, CVA, EPE or hedging strategies. Model calibration is made simple by the copula property of the model. Numerical results show adequation of the behavior of EPE and CVA in the model with stylized features. , S.Crepey, M.Jeanblanc, B.Zargari (2009)
    Nb Clicks : 1193
  • When are Swing options bang-bang and how to use it? In this paper we investigate a class of swing options with firm constraints in view of the modeling of supply agreements. We show, for a fully general payoff process, that the premium, solution to a stochastic control problem, is concave and piecewise affine as a function of the global constraints of the contract. The existence of bang-bang optimal controls is established for a set of constraints which generates by affinity the whole premium function. When the payoff process is driven by an underlying Markov process, we propose a quantization based recursive backward procedure to price these contracts. A priori error bounds are established, uniformly with respect to the global constraints. , O. Bardou, S. Bouthemy, G. Pages (2007)
    Nb Clicks : 1134
  • On the Valuation of Fader and Discrete Barrier Options in Heston s Stochastic Volatility Model We focus on closed-form option pricing in Heston s stochastic volatility model, where closed-form formulas exist only for a few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this closed-form approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times. , U.Wystup, S.Griebsch (2008)
    Nb Clicks : 1130
  • Robust Numerical Methods for PDE Models of Asian Options , R. Zvan, P.A. Forsyth, K.R. Vetzal (2000)
    Nb Clicks : 1109
  • A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks , E.Benhamou (2001)
    Nb Clicks : 1103
  • Fast strong approximation Monte-Carlo schemes for stochastic volatility models , C.Kahl, P.Jaeckel (2006)
    Nb Clicks : 1092
  • Time Dependent Heston Model The use of the Heston model is still challenging because it has a closed formula only when the parameters are constant [Hes93] or piecewise constant [MN03]. Hence, using a small volatility of volatility expansion and Malliavin calculus techniques, we derive an accurate analytical formula for the price of vanilla options for any time dependent Heston model (the accuracy is less than a few bps for various strikes and maturities). In addition, we establish tight error estimates. The advantage of this approach over Fourier based methods is its rapidity (gain by a factor 100 or more), while maintaining a competitive accuracy. From the approximative formula, we also derive some corollaries related first to equivalentHestonmodels (extending some work of Piterbarg on stochastic volatility models [Pit05b]) and second, to the calibration procedure in terms of ill-posed problems. , E. Benhamou, E. Gobet, M. Miri (2009)
    Nb Clicks : 1091
  • Models with time-dependent parameters using transform methods: application to Heston s model , A.Elices (2007)
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  • Efficient Simulation of the Heston Stochastic Volatility Model , L.Andersen (2006)
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  • Securitization of catastrophe mortality risks , Y. Lin, S. H. Cox (2006)
    Nb Clicks : 1077
  • Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator , M. Matsumoto and T. Nishimura (1998)
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  • Liquidity Risk and Option Pricing Theory , R. A. Jarrow, P. Protter (2005)
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  • Fast Delta Computations in the Swap-Rate Market Model We develop an efficient algorithm to implement the adjoint method that computes sensitivities of an interest rate derivative (IRD) with respect to different underlying rates in the co-terminal swap-rate market model. The order of computation per step of the new method is shown to be proportional to the number of rates times the number of factors, which is the same as the order in the LIBOR market model. , M.S.Joshi, C.Yang (2009)
    Nb Clicks : 1066
  • Convexity of option prices in the Heston model , J.Wang (2007)
    Nb Clicks : 1064
  • No-Dynamic-Arbitrage and Market Impact , J.Gatheral (2009)
    Nb Clicks : 1063
  • Convergence Heston to SVI By an appropriate change of variables, we prove here that the SVI implied volatility parameterisation proposed in [2] and the large-time asymptotic of the Heston implied volatility derived in [1] do agree algebraically, thus confirming a conjecture proposed by J. Gatheral in [2] as well as proposing a simpler expression for the asymptotic implied volatility under the Heston model. , J.Gatheral, A.Jacquier (2010)
    Nb Clicks : 1055
  • Efficient Option Pricing with Multi-Factor Equity-Interest Rate Hybrid Models In this article we discuss multi-factor equity-interest rate hybrid models with a full matrix of correlations. We assume the equity part to be modeled by the Heston model [Heston-1993] with as a short rate process either a Gaussian two-factor model [Brigo,Mercurio-2007] or a stochastic volatility short rate process of Heston type [Heidari, et al.-2007]. We develop an approximation for the discounted characteristic function. Our approximation scheme is based on the observation that sqrt{sigma_t}, with sigma_t a stochastic quantity of CIR type [Cox, et al.-1985], can be well approximated by a normal distribution. Our approximate hybrid fits almost perfectly to the original model in terms of implied Black-Scholes [Black,Scholes-1973] volatilities for European options. Since fast integration techniques allow us to get European style option prices for a whole strip of strikes in a split second, the hybrid approximation can be directly used for model calibration. , L.A.Grzelak, K.Oosterlee, S.Van Weeren (2009)
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  • ADI finite difference schemes for option pricing in the Heston model with correlation , K.J.Hout, S.Foulon (2007)
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  • High order discretization schemes for the CIR process: application to Affine Term Structure and Heston models , A.Alfonsi (2008)
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  • Liquidity Risk and Risk Measure Computation , R. Jarrow, P. Protter (2005)
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  • Markovian Projection Onto a Heston Model , V. Piterbarg, A.Antonov, T.Misirpashaev (2007)
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  • Calibration Of the Heston Model with Application in Derivative Pricing and Hedging , C.Bin (2007)
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  • Not-so-complex logarithms in the Heston model , C.Kahl, P.Jackel (2006)
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  • Calibrating Option Pricing Models with Heuristics Calibrating option pricing models to market prices often leads to optimisation problems to which standard methods (like such based on gradients) cannot be applied. We investigate two models: Heston?s stochastic volatility model, and Bates?s model which also includes jumps. We discuss how to price options under these models, and how to calibrate the parameters of the models with heuristic techniques. Sample Matlab code is provided. , M.Gilli, E.Schumann (2010)
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  • Pricing and Hedging Options in Incomplete Markets : Idiosyncratic Risk, Systematic Risk and Stochastic Volatility , T. Chauveau, H. Gatfaoui (2004)
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  • Option Valuation Using Fast Fourier Transforms , P.Carr, D.Madan (1999)
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  • Liquidity Risk , R.Protter (2005)
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  • The Little Heston Trap , H.Albrecher, P.Mayer, W.Schoutens, J.Tistaert (2006)
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  • The Heston Model: A Practical Approach , N.Moodley (2005)
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  • Introduction to Variance Swaps The purpose of this article is to introduce the properties of variance swaps, and give insights into the hedging and valuation of these instruments from the particular lens of an option trader. Section 1 gives general details about variance swaps and their applications. Section 2 explains in intuitive financial mathematics terms how variance swaps are hedged and priced. , Sebastien Bossu (2006)
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  • American Options in the Heston Model With Stochastic Interest Rate , S.Boyarchenko, S.Levendorski (2007)
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  • Hedging Exotic Options in Stochastic Volatility and Jump Diffusion Models , K. Detlefsen (2005)
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  • Pricing death : Frameworks for the valuation and securitization of mortality risk , A. J. Cairns, D. Blake & K. Dowd (2006)
    Nb Clicks : 1033
  • Probability distribution of returns in the Heston model with stochastic volatility We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the variance, find an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula is in excellent agreement with the Dow Jones index for time lags from 1 to 250 trading days. For large returns, the distribution is exponential in log-returns with a time-dependent exponent, whereas for small returns it is Gaussian. For time lags longer than the relaxation time of variance, the probability distribution can be expressed in a scaling form using a Bessel function. The Dow Jones data for 1982-2001 follow the scaling function for seven orders of magnitude. , A. Dragulescu, V.M. Yakovenko (2002)
    Nb Clicks : 1032
  • Hedging under the Heston Model with Jump-to-Default , P.Carr, W.Schoutens (2007)
    Nb Clicks : 1030

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