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Weak Convergence of Path-Dependent SDEs and Functionals in Pricing Basket CDS with Counterparty Risk and Contagion Risk  [PDF]
Yao Tung Huang,Qingshuo Song,Harry Zheng
Quantitative Finance , 2015,
Abstract: We investigate the computational aspects of the basket CDS pricing with counterparty risk under a credit contagion model of multinames. This model enables us to capture the systematic volatility increases in the market triggered by a particular bankruptcy. The drawback of this problem is its analytical complication due to its path-dependent functional, which bears a potential failure in its convergence of numerical approximation under standing assumptions. In this paper we find sufficient conditions for the desired convergence by means of the weak convergence method to a class of path-dependent stochastic differential equations.
Pricing of basket options II  [PDF]
Alexander Kushpel
Statistics , 2014,
Abstract: We consider the problem of approximation of density functions which is important in the theory of pricing of basket options. Our method is well adopted to the multidimensional case. Observe that implementations of polynomial and spline approximation in this situation are connected with difficulties of fundamental nature. A simple approximation formula for European call options is presented. It is shown that this approximation formula has exponential rate of convergence.
Pricing of basket options I  [PDF]
Alexander Kushpel
Quantitative Finance , 2014,
Abstract: Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a transparent and intuitively easily acceptable concept. In our case this is a linear system of stochastic equations. Our market model is based on the principle of inheritance, i.e. for the particular choice of parameters it coincides with known models. Also, the model proposed is effectively numerically realizable. For the class of models under cosideration, we give an explicit representations of characteristic functions. This allows us us to construct a sequence of approximation formulas to price basket options. We show that our approximation formulas have almost optimal rate of convergence in the sense of respective n-widths.
Pricing and Hedging Basket Options with Exact Moment Matching  [PDF]
Tommaso Paletta,Arturo Leccadito,Radu Tunaru
Quantitative Finance , 2013,
Abstract: Theoretical models applied to option pricing should take into account the empirical characteristics of the underlying financial time series. In this paper, we show how to price basket options when assets follow a shifted log-normal process with jumps capable of accommodating negative skewness. Our technique is based on the Hermite polynomial expansion that can match exactly the first m moments of the model implied-probability distribution. This method is shown to provide superior results for basket options not only with respect to pricing but also for hedging.
Valuation of a Basket Loan Credit Default Swap  [cached]
Jin Liang,Yujing Zhou
International Journal of Financial Research , 2010, DOI: 10.5430/ijfr.v1n1p21
Abstract: This paper provides a methodology for valuing a basket Loan CDS (LCDS) by considering both default and prepayment risks. Under “top down” and intensity framework, using a single-factor model, correlated default and prepayment risks are considered, where the stochastic interest rate is used to be their common factor. All stochastic processes in the model are assumed to follow CIR processes. Through Feynman-Kac formula, we obtain a PDE problem and its closed-form solution. Numerical examples are provided.
On Pricing Basket Credit Default Swaps  [PDF]
Jia-Wen Gu,Wai-Ki Ching,Tak-Kuen Siu,Harry Zheng
Quantitative Finance , 2012,
Abstract: In this paper we propose a simple and efficient method to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. We give the analytical expressions for the ordered default time distributions with recursive formulas for the coefficients, which makes the calculation fast and efficient in finding rates of basket CDSs. In the homogeneous case, we explore the ordered default time in limiting case and further include the exponential decay and the multistate stochastic intensity process. The numerical study indicates that, in the valuation of the swap rates and their sensitivities with respect to underlying parameters, our proposed model outperforms the Monte Carlo method.
Adaptive numerical integration and control variates for pricing Basket Options  [PDF]
Christophe De Luigi,Jér?me Lelong,Sylvain Maire
Mathematics , 2012,
Abstract: We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting strategy based on a geometrical criterion. In higher dimensions, this new algorithm is used as a control variate after a dimension reduction based on principal component analysis. Numerical tests are performed on the pricing of basket, put on minimum and digital options in dimensions up to ten.
Pricing of European Basket Call Option under Exponential Ornstein-Uhlenbeck Process  [PDF]
Jingwei Liu,Jiwen Luo,Xing Chen
Quantitative Finance , 2014,
Abstract: Pricing of European basket call option with n-assets and a bond is discussed in this paper, where all prices of n-assets and the bond are driven by Exponential Ornstein-Uhlenbeck processes. The close-form of European basket option pricing formula is derived. Utilizing with 1-order differential approximate numerical solution of stochastic differential equation (Milstein method), a simulation example of European basket option pricing with 3 assets is also given.
Pricing of Basket Options Using Polynomial Approximations  [PDF]
Pablo Olivares
Quantitative Finance , 2014,
Abstract: In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning on the remaining underlying assets and calculating the mixed exponential-power moments of a Gaussian distribution that arise as a consequence of such approximation. Our numerical implementation on spread contracts shows the method is as accurate as a standard Monte Carlo approach at considerable lesser computational effort.
A General Closed Form Approximation Pricing Formula for Basket and Multi-Asset Spread Options  [PDF]
Tommaso Pellegrino
Journal of Mathematical Finance (JMF) , 2016, DOI: 10.4236/jmf.2016.65063
Abstract: The aims of this paper are twofold. Firstly, we present an approximating formula for pricing basket and multi-asset spread options, which genuinely extends Caldana and Fusai’s (2013) two-asset spread options formula. Secondly, under the lognormal setting, we show that our formula becomes a Black and Scholes type formula, extending Bjerksund and Stensland’s (2011). Numerical experiments and comparison with Monte Carlo simulations and other methods available in the literature are discussed. The main contribution of this paper is to provide practitioners with a pricing formula, which can be used for pricing basket and multi-asset spread options, even under a non-Gaussian framework.
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