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  • 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 : 404
  • A Comparative Analysis of Basket Default Swaps Pricing Using the Stein Method , E.Benhamou, D.Bastide, M.Ciuca (2007)
    Nb Clicks : 397
  • An Improved Implied Copula Model and its Application to the Valuation of Bespoke CDO Tranches , J.Hull, A.White (2008)
    Nb Clicks : 372
  • 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 : 355
  • 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 : 352
  • 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 : 342
  • Introduction to Weather Derivative Pricing , S.Jewson (2004)
    Nb Clicks : 338
  • 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 : 337
  • 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)  
    Nb Clicks : 332
  • Collateral and Credit Issues in Derivatives Pricing Regulatory changes are increasing the importance of collateral agreements and credit issues in over-the-counter derivatives transactions. This paper considers the nature of derivatives collateral agreements and examines the impact of collateral agreements, two-sided credit risk, funding costs, liquidity, and bid-offer spreads on the valuation of derivatives portfolios. , John Hull and Alan White (2014)  
    Nb Clicks : 317
  • Recent Issues in the Pricing of Collateralized Derivatives Contracts presentation , Jean-Paul Laurent (2014)  
    Nb Clicks : 311
  • 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 : 300
  • Optimal Posting of Sticky Collateral We study optimal strategies for posting collateral for OTC derivatives under Credit Support Annexes (CSAs) where "substitution rights'' either do not exist or are hard to enforce. We present a simplified model which we are able to solve approximately in an efficient manner. Additionally we show that the optimal posting strategy is defined by the relation between suitably-defined term, rather than instantaneous, collateral rates, as would be the case in "full substitution'' situations that have been studied in the literature so far. , Vladimir Piterbarg (2013)
    Nb Clicks : 291
  • Collateral,Funding and Discounting presentation , Vladimir V. Piterbarg (2012)
    Nb Clicks : 271
  • Coco Bonds Valuation with Equity- and Credit-Calibrated First Passage Structural Models After the beginning of the credit and liquidity crisis, financial institutions have been considering creating a convertible-bond type contract focusing on Capital. Under the terms of this contract, a bond is converted into equity if the authorities deem the institution to be under-capitalized. This paper discusses this Contingent Capital (or Coco) bond instrument and presents a pricing methodology based on firm value models. The model is calibrated to readily available market data. A stress test of model parameters is illustrated to account for potential model risk. Finally, a brief overview of how the instrument performs is presented. , Damiano Brigo, Joao Garcia, Nicola Pede (2013)  
    Nb Clicks : 267
  • CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives valuation and risk analysis has moved from exotic derivatives managed on simple single asset classes to simple derivatives embedding the new or previously neglected types of complex and interconnected nonlinear risks we address here. This dialogue is the continuation of the "Counterparty Risk, Collateral and Funding FAQ" by Brigo (2011). In this dialogue we focus more on funding costs for the hedging strategy of a portfolio of trades, on the non-linearities emerging from assuming borrowing and lending rates to be different, on the resulting aggregation-dependent valuation process and its operational challenges, on the implications of the onset of central clearing, on the macro and micro effects on valuation and risk of the onset of CCPs, on initial and variation margins impact on valuation, and on multiple discount curves. Through questions and answers (Q&A) between a senior expert and a junior colleague, and by referring to the growing body of literature on the subject, we present a unified view of valuation (and risk) that takes all such aspects into account. , Damiano Brigo, Andrea Pallavicini (2013)  
    Nb Clicks : 265
  • 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 : 265
  • 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 : 245
  • An overview of the valuation of collateralized derivative contracts We consider the valuation of collateralized derivative contracts such as interest rate swaps, forward FX contracts or term repos. First, we provide a precise framework regarding collateralization, under which computations are made easy. We allow for posting securities or cash in different currencies. In the latter case, we focus on using overnight index rates on the interbank market, in line with LCH.Clearnet framework. We provide an intuitive way to derive the basic discounting results, keeping in line with the most standard theoretical and market views. Under perfect collateralization, pricing rules for collateralized trades remain linear, thus the use of (multiple) discount curves. We then show how to deal with partial collateralization, involving haircuts, asymmetric CSA, counterparty risk and funding costs as an extension of the perfect collateralization case. We therefore intend to provide a unified view. Mathematical or legal details are not dealt with and we privilege financial intuition and easy to grasp concepts and tools. , Jean-Paul LAURENT , Philippe AMZELEK and Joe BONNAUD (2012)
    Nb Clicks : 240
  • Monte-Carlo Methods: ENSAI , N.Baud (2004)
    Nb Clicks : 238
  • Convexity of option prices in the Heston model , J.Wang (2007)
    Nb Clicks : 227
  • 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 : 227
  • Efficient Simulation of the Heston Stochastic Volatility Model , L.Andersen (2006)
    Nb Clicks : 226
  • 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)
    Nb Clicks : 226
  • Exact Simulation of Stochastic Volatility and other Affine Jump Diffusion Processes , M.Broadie, O.Kaya (2004)
    Nb Clicks : 224
  • Monte-Carlo for the Newbies , S.Leger (2006)
    Nb Clicks : 223
  • High order discretization schemes for the CIR process: application to Affine Term Structure and Heston models , A.Alfonsi (2008)
    Nb Clicks : 223
  • Liquidity Risk and Option Pricing Theory , R. A. Jarrow, P. Protter (2005)
    Nb Clicks : 222
  • 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)
    Nb Clicks : 222
  • An N-Dimensional Markov-Functional Interest Rate Model This paper develops an n-dimensional Markov-functional interest rate model, i.e. a model driven by an n-dimensional state process and constructed using Markov-functional techniques. It is shown that this model is very similar to an n-factor LIBOR market model hence allowing intuition from the LIBOR market model to be transferred to the Markov-functional model. This generalizes the results of Bennett & Kennedy from one-dimensional to n-dimensional driving state processes. The model is suitable for pricing certain type of exotic interest rate derivative products whose payoffs depend on the LIBORs at their setting dates. Specifically we investigate the pricing of TARNs and find that the n-dimensional Markov-functional model is faster and can be calibrated more easily to a target correlation structure than an n-factor LIBOR market model. , L.Kaisajuntti, J.Kennedy (2008)
    Nb Clicks : 221
  • A Hybrid Markov-Functional Model with Simultaneous Calibration to Interest Rate and FX Smile In this paper we present a Markov functional hybrid interest rate/fx model which allows the calibration of a given market volatility surface in both dimension simultaneously. We extend the approach introduced in [FriesRott] by introducing a functional for the FX which allows a fast, yet accurate calibration to a given market fx volatility surface. This calibration procedure comes as an additional step to the known calibration of the LIBOR functional. , C.P.Fries, F.Eckstaedt (2006)
    Nb Clicks : 221
  • A Comparison of Markov-Functional and Market Models: The One-Dimensional Case The LIBOR Markov-functional model is an efficient arbitrage-free pricing model suitable for callable interest rate derivatives. We demonstrate that the one-dimensional LIBOR Markov-functional model and the separable onefactor LIBOR market model are very similar. Consequently, the intuition behind the familiar SDE formulation of the LIBOR market model may be applied to the LIBOR Markov-functional model. The application of a drift approximation to a separable one-factor LIBOR market model results in an approximating model driven by a one-dimensional Markov process, permitting efficient implementation. For a given parameterisation of the driving process, we find the distributional structure of this model and the corresponding Markov-functional model are numerically virtually indistinguishable for short maturity tenor structures over a wide variety of market conditions, and both are very similar to the market model. A theoretical uniqueness result shows that any accurate approximation to a separable market model that reduces to a function of the driving process is effectively an approximation to the analogous Markov-functional model. Therefore, our conclusions are not restricted to our particular choice of driving process. Minor differences are observed for longer maturities, nevertheless the models remain qualitatively similar. These differences do not have a large impact on Bermudan swaption prices. Under stress-testing, the LIBOR Markov-functional and separable LIBOR market models continue to exhibit similar behaviour and Bermudan prices under these models remain comparable. However, the drift approximation model now appears to admit arbitrage that is practically significant. In this situation, we argue the Markov-functional model is a more appropriate choice for pricing. , M.N.Bennett, J.E.Kennedy (2005)
    Nb Clicks : 220
  • Securitization of life insurance assets and liabilities , J. D. Cummins (2004)
    Nb Clicks : 220
  • Hedging under the Heston Model with Jump-to-Default , P.Carr, W.Schoutens (2007)
    Nb Clicks : 220
  • Fast strong approximation Monte-Carlo schemes for stochastic volatility models , C.Kahl, P.Jaeckel (2006)
    Nb Clicks : 219
  • SIMD-oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator , M. Matsumoto, Nishimura T. (2008)
    Nb Clicks : 219
  • Markov Functional Modeling of Equity, Commodity and other Assets In this short note we show how to setup a one dimensional single asset model, e.g. equity model, which calibrates to a full (two dimensional) implied volatility surface. We show that the efficient calibration procedure used in LIBOR Markov functional models may be applied here too. In a addition to the calibration to a full volatility surface the model allows the calibration of the joint asset-interest rate movement (i.e. local interest rates) and forward volatility. The latter allows the calibration of compound or Bermudan options. The Markov functional modeling approach consists of a Markovian driver process x and a mapping functional representing the asset states S(t) as a function of x(t). It was originally developed in the context of interest rate models, see [Hunt Kennedy Pelsser 2000]. Our approach however is similar to the setup of the hybrid Markov functional model in spot measure, as considered in [Fries Rott 2004]. For equity models it is common to use a deterministic Num?raire, e.g. the bank account with deterministic interest rates. In our approach we will choose the asset itself as Num?raire. This is a subtle, but crucial difference to other approaches considering Markov functional modeling. Choosing the asset itself as Num?raire will allow for a very efficient numerically calibration procedure. As a consequence interest rates have to be allowed to be stochastic, namely as a functional of x too. The Black-Scholes model with deterministic interest rates is a special case of such a Markov functional model. The most general form of this modeling approach will allow for a simultaneous calibration to a full two dimensional volatility smile, a prescribed joint movement of interest rates and a given forward volatility structure. , C.P.Fries (2009)
    Nb Clicks : 218
  • Fast Greeks for Markov-Functional Models Using Adjoint Pde Methods This paper demonstrates how the adjoint PDE method can be used to compute Greeks in Markov-functional models. This is an accurate and efficient way to compute Greeks, where most of the model sensitivities can be computed in approximately the same time as a single sensitivity using finite difference. We demonstrate the speed and accuracy of the method using a Markov-functional interest rate model, also demonstrating how the model Greeks can be converted into market Greeks. , N.Denson, M.J.Joshi (2010)
    Nb Clicks : 218
  • The law of the Euler scheme for stochastic differential equations: I. Convergence rate of the distribution function , V. Bally, D. Talay (1996)
    Nb Clicks : 218
  • American Options in the Heston Model With Stochastic Interest Rate , S.Boyarchenko, S.Levendorski (2007)
    Nb Clicks : 218
  • Calibration Of the Heston Model with Application in Derivative Pricing and Hedging , C.Bin (2007)
    Nb Clicks : 218
  • An Objected-Oriented Random-Number Package with Many Long Streams and Substreams , P. L Ecuyer, R. Simard, E. J. Chen, and W. D. Kelton (2002)
    Nb Clicks : 217
  • Gamma Expansion of the Heston Stochastic Volatility Model , P.Glasserman, K-K.Kim (2008)
    Nb Clicks : 217
  • Modern Logarithms for the Heston Model , I.Fahrner (2007)
    Nb Clicks : 217
  • The Little Heston Trap , H.Albrecher, P.Mayer, W.Schoutens, J.Tistaert (2006)
    Nb Clicks : 217
  • The Heston Model: A Practical Approach , N.Moodley (2005)
    Nb Clicks : 217
  • A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , S. L. Heston (1993)
    Nb Clicks : 217
  • Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model , A.V.Haastrecht, A.Pelsser (2008)
    Nb Clicks : 216
  • Models with time-dependent parameters using transform methods: application to Heston s model , A.Elices (2007)
    Nb Clicks : 216
  • Finite Difference Based Calibration and Simulation In the context of a stochastic local volatility model, we present a numerical solution scheme that achieves full (discrete) consistency between calibration, finite difference solution and Monte-Carlo simulation. The method is based on an ADI finite difference discretisation of the model. , J.Andreasen, B.N.Huge (2010)
    Nb Clicks : 216

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