D. Y. Tangman

Publications (8)2.03 Total impact

• Article: A New Fourth-Order Numerical Scheme for Option Pricing under the CEV Model

  N. Thakoor, D. Y. Tangman, M. Bhuruth
  [show abstract] [hide abstract]
  ABSTRACT: The empirically observed negative relationship between a stock price and its return volatility can be captured by the constant elasticity of variance option pricing model. For European options, closed form expressions involve the non-central chi-square distribution whose computation can be slow when the elasticity factor is close to one, volatility is low or time to maturity is small. We present a fast numerical scheme based on a high-order compact discretisation which accurately computes the option price. Various numerical examples indicate that for comparable computational times, the option price computed with the scheme has higher accuracy than the Crank-Nicolson numerical solution. The scheme accurately computes the hedging parameters and is stable for strongly negative values of the elasticity factor.
  Applied Mathematics Letters 08/2012; · 1.37 Impact Factor
• Article: Fast approximations of bond option prices under CKLS models

  D.Y. Tangman, N. Thakoor, K. Dookhitram, M. Bhuruth
  [show abstract] [hide abstract]
  ABSTRACT: A new computational method for approximating prices of zerocoupon bonds and bond option prices under general Chan–Karolyi– Longstaff–Schwartz models is proposed. The pricing partial differential equations are discretized using second-order finite difference approximations and an exponential time integration scheme combined with best rational approximations based on the Carathéodory–Fejér procedure is employed for solving the resulting semi-discrete equations. The algorithm has a linear computational complexity and provides accurate bond and European bond option prices. We give several numerical results which illustrate the computational efficiency of the algorithm and uniform second-order convergence rates for the computed bond and bond option prices.
  Finance Research Letters 01/2011; 8:206 - 212. · 0.33 Impact Factor
• Article: Fast approximations of bond option prices under CKLS models

  D. Y. Tangman, N. Thakoor, K. Dookhitram, M. Bhuruth
  [show abstract] [hide abstract]
  ABSTRACT: (Top 25 Download in Science-Direct) http://top25.sciencedirect.com/subject/economics-econometrics-and-finance/10/journal/finance-research-letters/15446123/archive/33 A new computational method for approximating prices of zero-coupon bonds and bond option prices under general Chan–Karolyi–Longstaff–Schwartz models is proposed. The pricing partial differential equations are discretized using second-order finite difference approximations and an exponential time integration scheme combined with best rational approximations based on the Carathéodory–Fejér procedure is employed for solving the resulting semi-discrete equations. The algorithm has a linear computational complexity and provides accurate bond and European bond option prices. We give several numerical results which illustrate the computational efficiency of the algorithm and uniform second-order convergence rates for the computed bond and bond option prices.
  Finance Research Letters 01/2011; · 0.33 Impact Factor
• Article: Fast simplified approaches to Asian option pricing

  D. Y. Tangman, A. Peer, N. Rambeerich, M. Bhuruth
  Journal of Computational Finance. 07/2009;
• Article: Exponential time integration for fast finite element solutions of some financial engineering problems

  N. Rambeerich, D. Y. Tangman, Gopaul. A, M. Bhuruth
  [show abstract] [hide abstract]
  ABSTRACT: We consider exponential time integration schemes for fast numerical pricing of European, American, barrier and butterfly options when the stock price follows a dynamics described by a jump-diffusion process. The resulting pricing equation which is in the form of a partial integro-differential equation is approximated in space using finite elements. Our methods require the computation of a single matrix exponential and we demonstrate using a wide range of numerical tests that the combination of exponential integrators and finite element discretisations with quadratic basis functions leads to highly accurate algorithms for cases when the jump magnitude is Gaussian. Comparison with other time-stepping methods are also carried out to illustrate the effectiveness of our methods
  Journal of Computational and Applied Mathematics. 03/2009; 224:668-678.
• Article: Numerical pricing of options using high-order compact finite difference schemes

  D.Y. Tangman, A. Gopaul, M. Bhuruth
  [show abstract] [hide abstract]
  ABSTRACT: We consider high-order compact (HOC) schemes for quasilinear parabolic partial differential equations to discretise the Black–Scholes PDE for the numerical pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC schemes attain clear fourth-order convergence but fail if non-smooth payoff conditions are used. To restore the fourth-order convergence, we use a grid stretching that concentrates grid nodes at the strike price for European options. For an American option, an efficient procedure is also described to compute the option price, Greeks and the optimal exercise curve. Comparisons with a fourth-order non-compact scheme are also done. However, fourth-order convergence is not experienced with this strategy. To improve the convergence rate for American options, we discuss the use of a front-fixing transformation with the HOC scheme. We also show that the HOC scheme with grid stretching along the asset price dimension gives accurate numerical solutions for European options under stochastic volatility.
  Journal of Computational and Applied Mathematics.
• Article: Exponential time integration and Chebychev discretisation schemes for fast pricing of options

  D.Y. Tangman, A. Gopaul, M. Bhuruth
  [show abstract] [hide abstract]
  ABSTRACT: We consider exponential time differencing (ETD) schemes for the numerical pricing of options. Special treatments for the implementation of the boundary conditions that arise in finance are described. We show that only one explicit time step computation gives unconditional second order accuracy for European, Barrier and Butterfly spread options under both Black–Scholes geometric Brownian motion model and Merton's jump diffusion model with constant coefficients. In comparison, the commonly used Crank–Nicolson scheme is shown to be only conditionally stable due to lack of L0-stability. Finally, we describe how the use of spectral spatial discretisation based on a Chebychev grid point concentration strategy gives fourth order accurate option prices for both the Black–Scholes and Merton's jump–diffusion model.
  Applied Numerical Mathematics.
• Article: A fast high-order finite difference algorithm for pricing American options

  D.Y. Tangman, A. Gopaul, M. Bhuruth
  [show abstract] [hide abstract]
  ABSTRACT: We describe an improvement of Han and Wu’s algorithm [H. Han, X.Wu, A fast numerical method for the Black–Scholes equation of American options, SIAM J. Numer. Anal. 41 (6) (2003) 2081–2095] for American options. A high-order optimal compact scheme is used to discretise the transformed Black–Scholes PDE under a singularity separating framework. A more accurate free boundary location based on the smooth pasting condition and the use of a non-uniform grid with a modified tridiagonal solver lead to an efficient implementation of the free boundary value problem. Extensive numerical experiments show that the new finite difference algorithm converges rapidly and numerical solutions with good accuracy are obtained. Comparisons with some recently proposed methods for the American options problem are carried out to show the advantage of our numerical method.
  Journal of Computational and Applied Mathematics.