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  • Valuing Convertible Bonds with Stock Price, Volatility, Interest Rate, and Default Risk , P. Kovalov, V. Linetsky (2008)
    Nb Clicks : 3835
  • 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 : 3814
  • 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 : 3120
  • No-Dynamic-Arbitrage and Market Impact , J. Gatheral (2008)
    Nb Clicks : 3051
  • High order discretization schemes for the CIR process: application to Affine Term Structure and Heston models , A.Alfonsi (2008)
    Nb Clicks : 2938
  • 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 : 2845
  • A Comparative Analysis of Basket Default Swaps Pricing Using the Stein Method , E.Benhamou, D.Bastide, M.Ciuca (2007)
    Nb Clicks : 2485
  • An Improved Implied Copula Model and its Application to the Valuation of Bespoke CDO Tranches , J.Hull, A.White (2008)
    Nb Clicks : 2429
  • The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing , A.Kalemanova, B.Schmid, R.Werner (2007)
    Nb Clicks : 2412
  • Target Redemption Note , Y.Kuen Kwok, C.Chiu Chu (2006)
    Nb Clicks : 2344
  • 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 : 2332
  • 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 : 2321
  • 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 : 2262
  • 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 : 2224
  • 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 : 2175
  • Improved Long-Period Generators Based on Linear Recurrences Modulo 2 , F. Panneton, P. L Ecuyer, and M. Matsumoto (2006)
    Nb Clicks : 2105
  • 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 : 2072
  • Introduction to Weather Derivative Pricing , S.Jewson (2004)
    Nb Clicks : 2054
  • A jump to default extended CEV model: an application of Bessel processes , P. Carr, V. Linetsky (2006)
    Nb Clicks : 2031
  • Not-so-complex logarithms in the Heston model , C.Kahl, P.Jackel (2006)
    Nb Clicks : 1992
  • Efficient Simulation of the Heston Stochastic Volatility Model , L.Andersen (2006)
    Nb Clicks : 1946
  • 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 : 1896
  • 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 : 1861
  • Local Volatility Enhanced by a Jump to Default A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may simultaneously recover from the prices of credit default swap contracts and equity option prices both the deterministic component of the hazard rate function and revised local volatility. The procedure is implemented on prices of credit default swaps and equity options for GM and FORD over the period October 2004 to September 2007. , P.Carr, D.P.Madan (2010)
    Nb Clicks : 1852
  • Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator , M. Matsumoto and T. Nishimura (1998)
    Nb Clicks : 1826
  • 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 : 1822
  • Quasi-monte carlo methods and pseudo-random numbers , H. Niederreiter (1978)
    Nb Clicks : 1781
  • On Models of Stochastic Recovery for Base Correlation This paper discusses various ways to add correlated stochastic recovery to the Gaussian Copula base correlation framework for pricing CDOs. Several recent models are extended to more general framework. It is shown that, conditional on the Gaussian systematic factor, negative forward recovery rate may appear in these models. This suggests that current static copula models of correlated default and recovery processes are inherently inconsistent. , Li, Hui (2009)
    Nb Clicks : 1750
  • Fast strong approximation Monte-Carlo schemes for stochastic volatility models , C.Kahl, P.Jaeckel (2006)
    Nb Clicks : 1726
  • 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 : 1722
  • Numerical Methods and Volatility Models for Valuing Cliquet Options , H.A.Windcliff, P.A.Forsyth, K.R.vetzal (2005)
    Nb Clicks : 1711
  • Complex Logarithms in Heston-Like Models , R. Lord, C. Kahl (2008)
    Nb Clicks : 1705
  • 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 : 1700
  • Models with time-dependent parameters using transform methods: application to Heston s model , A.Elices (2007)
    Nb Clicks : 1686
  • Analytical Formulas for Local Volatility Model with Stochastic Rates This paper presents new approximation formulae of European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1275872 for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurate approximations with tight estimates of the error terms. This approach can also be used in the case of stochastic dividends or stochastic convenience yields. We finally provide numerical results to illustrate the accuracy with real market data. , E.Benhamou, E.Gobet, M.Miri (2009)
    Nb Clicks : 1686
  • No-Dynamic-Arbitrage and Market Impact , J.Gatheral (2009)
    Nb Clicks : 1670
  • Calibration Of the Heston Model with Application in Derivative Pricing and Hedging , C.Bin (2007)
    Nb Clicks : 1667
  • Option Valuation Using Fast Fourier Transforms , P.Carr, D.Madan (1999)
    Nb Clicks : 1663
  • Closed Forms for European Options in a Local Volatility Model Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms. , E. Benhamou, E. Gobet, M. Miri (2008)
    Nb Clicks : 1663
  • Two-Dimensional Markovian Model for Dynamics of Aggregate Credit Loss , A.V.Lopatin, T.Misirpashaev (2007)
    Nb Clicks : 1653
  • 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 : 1652
  • Liquidity Risk and Option Pricing Theory , R. A. Jarrow, P. Protter (2005)
    Nb Clicks : 1652
  • A Penalty Method for American Options with Jump Diffusion Processes , Y. d Halluin, P.A. Forsyth, G. Labahn (2003)
    Nb Clicks : 1650
  • Implied Volatility: Statics, Dynamics, and Probabilistic Interpretation Given the price of a call or put option, the Black-Scholes implied volatility is the unique volatility parameter for which the Bulack-Scholes formula recovers the option price. This article surveys research activity relating to three theoretical questions: First, does implied volatility ad- mit a probabilistic interpretation? Second, how does implied volatility behave as a function of strike and expiry? Here one seeks to characterize the shapes of the implied volatility skew (or smile) and term structure, which together constitute what can be termed the statics of the implied volatility surface. Third, how does implied volatility evolve as time rolls forward? Here one seeks to characterize the dynamics of implied volatility. , R. Lee (2002)
    Nb Clicks : 1649
  • Hedging under the Heston Model with Jump-to-Default , P.Carr, W.Schoutens (2007)
    Nb Clicks : 1635
  • Convexity of option prices in the Heston model , J.Wang (2007)
    Nb Clicks : 1634
  • Modern Logarithms for the Heston Model , I.Fahrner (2007)
    Nb Clicks : 1633
  • ADI finite difference schemes for option pricing in the Heston model with correlation , K.J.Hout, S.Foulon (2007)
    Nb Clicks : 1631
  • Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model , A.V.Haastrecht, A.Pelsser (2008)
    Nb Clicks : 1630
  • Pricing and Hedging Options in Incomplete Markets : Idiosyncratic Risk, Systematic Risk and Stochastic Volatility , T. Chauveau, H. Gatfaoui (2004)
    Nb Clicks : 1629





















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