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News This Month : September
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  • 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) 
  • Volatility and Dividends :Volatility Modelling with Cash Dividends and simple Credit Risk This article shows how to incorporate cash dividends and credit risk into equity derivatives pricing and risk management. In essence, we show that in an arbitrage-free model the stock price process upon default must have the form St = (F *t - D t )Xt + Dt where X is a (local) martingale with X0 = 1, the curve F * is the “risky” forward and D is the floor imposed on the stock price process in the form of appropriately discounted future dividends. We show that the method presented is the only such method which is consistent with the assumption of cash dividends and simple credit risk. We discuss the implications for implied volatility, no-arbitrage conditions and we derive a version of Dupire’s formula which handles cash dividend and credit risk properly. We discuss pricing and risk management of European options, PDE methods and in quite some detail variance swaps and related derivatives such as gamma swaps, conditional variance swaps and corridor variance swaps. Indeed, to the our best if our knowledge, this is the first article which shows the correct handling of cash dividends when pricing variance swaps. , H.Buelher (2009) 
  • Quanto Skew We assess the effect of an implied volatility skew for an FX rate on quanto forwards and quanto options of an asset that itself is sub ject to an implied volatility skew using a simplistic double displaced diffusion models. , P.Jaeckel (2009) 
  • 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) 
  • Minimal Partial Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks In this paper, we present a generic framework known as the minimal partial proxy simulation scheme. This framework allows stable computation of the Monte-Carlo Greeks for financial products with trigger features via finite difference approximation. The minimal partial proxy simulation scheme can be considered as a special case of the partial proxy simulation scheme (Fries and Joshi, 2008b) as a measure change (weighted Monte Carlo) is performed to prevent path-wise discontinuities. However, our approach differs in term of how the measure change is performed. Specifically, we select the measure change optimally such that it minimises the variance of the Monte-Carlo weight. Our method can be applied to popular classes of trigger products including digital caplets, autocaps and target redemption notes. While the Monte-Carlo Greeks obtained using the partial proxy simulation scheme can blow up in certain cases, these Monte-Carlo Greeks remain stable under the minimal partial proxy simulation scheme. Standard errors for Vega are also significantly lower under the minimal partial proxy simulation scheme. , J.Hong Chan, M.S.Joshi (2009) 
  • Efficient Greek Estimation in Generic Market Models We first develop an efficient algorithm to compute Deltas of interest rate derivatives for a number of standard market models. The computational complexity of the algorithms is shown to be proportional to the number of rates times the number of factors per step. We then show how to extend the method to efficiently compute Vegas in those market models. , M.S.Joshi, C.Yang (2009) 
  • Pricing and Deltas of Discretely-Monitored Barrier Options Using Stratified Sampling on the Hitting-Times to the Barrier We develop new Monte Carlo techniques based on stratifying the stock's hitting-times to the barrier for the pricing and Delta calculations of discretely-monitored barrier options using the Black-Scholes model. We include a new algorithm for sampling an Inverse Gaussian random variable such that the sampling is restricted to a subset of the sample space. We compare our new methods to existing Monte Carlo methods and find that they can substantially improve convergence speeds. , M.S.Joshi, R.Tang (Année) 
  • Fast and Accurate Greeks for the Libor Market Model This paper derives the pathwise adjoint method for the predictor-corrector drift approximation in the displaced-diffusion LIBOR market model. We present a comparison of the Greeks between log-Euler and predictor-corrector, showing both methods have the same computational order but the latter to be much more accurate. , N.Denson, M.S.Joshi (2009) 
  • An arbitrage-free method for smile extrapolation We introduce a method for extrapolating smiles beyond an "observable" region that is consistent with no arbitrage. The extrapolation is not unique, but can be tuned e.g., to different power-law decays. This method has important applications in various areas such as the calculation of CMS rates, inverse FX options etc. , S.Benaim, M.Dodgson, Dherminder Kainth (2009) 
  • A Spot Recovery Rate Extension of the Gaussian Copula The market evolution since the end of 2007 has been characterized by an increase of the systemic risk and a high number of defaults. Realized recovery rates have been very dispersed and different from standard assumptions, while 60%-100% super-senior tranches on standard indices have started to trade with significant spread levels. This has triggered a growing interest for stochastic recovery modelling. This paper presents an extension to the standard Gaussian copula framework that introduces a consistent modelling of stochastic recovery. We choose to model directly the spot recovery, which allows to preserve time consistency, and compare this approach to the standard ones, defined in terms of recovery to maturity. Taking a specific form of the spot recovery function, we show that the model is flexible and tractable, and easy to calibrate to both individual credit spread curves and index tranche markets. Through practical numerical examples, we analyze specific model properties, focusing on default risk. , N.Bennani, J.Maetz (2009) 
  • 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) 
  • 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 prespeciÖed negative power and a deterministic function of time. The empirical work uses a power of 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 F ORD over the period October 2004 to S eptember 2007: , P.Carr (2009) 





















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