Options pricing for several maturities in a jump-diffusion model. (English) Zbl 1270.91094
Plaskota, Leszek (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2010. Selected papers based on the presentations at the 9th international conference on Monte Carlo and quasi Monte Carlo in scientific computing (MCQMC 2010), Warsaw, Poland, August 15–20, 2010. Berlin: Springer (ISBN 978-3-642-27439-8/hbk; 978-3-642-27440-4/ebook). Springer Proceedings in Mathematics & Statistics 23, 385-398 (2012).
Summary: Estimators for options prices with different maturities are constructed on the same trajectories of the underlying asset price process. The weighted sum of their variances (the weighted variance) is chosen as a criterion of minimization. Optimal estimators with minimal weighted variance are pointed out in the case of a jump-diffusion model. The efficiency of the constructed estimators is discussed and illustrated on particular examples.
For the entire collection see [Zbl 1252.65004].
For the entire collection see [Zbl 1252.65004].
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91G80 | Financial applications of other theories |
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
References:
| [1] | Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Chapman & Hall/CRC, Boca Raton (2004) · Zbl 1052.91043 |
| [2] | Dimitroff, G., Lorenz, S., Szimayer, A.: A parsimonious milti-asset heston model: Calibration and derivative pricing. http://ssrn.com/abstract=1435199 (19 April, 2010) · Zbl 1233.91263 |
| [3] | Fouque, J. P.; Han, C. H., Variance reduction for Monte Carlo methods to evaluate option prices under multi-factor stochastic volatility models, Quantitative Finance, 4, 5, 597-606 (2004) · Zbl 1405.91692 |
| [4] | Fouque, J. P.; Tullie, T., Variance reduction for Monte Carlo simulation in a stochastic volatiltiy environment, Quantitative Finance, 2, 24-30 (2002) · Zbl 1405.91693 |
| [5] | Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York (2004) · Zbl 1038.91045 |
| [6] | Gormin, A.A.: Importance sampling and control variates in the weighted variance minimization. Proceedings of the 6th St.Petersburg Workshop on Simulation, 109-113 (2009) |
| [7] | Gormin, A. A.; Kashtanov, Y. N., The weighted variance minimization for options pricing, Monte Carlo Methods and Applications, 13, 5-6, 333-351 (2007) · Zbl 1133.91419 |
| [8] | Gormin, A. A.; Kashtanov, Y. N., Variance reduction for multiple option parameters, Journal of Numerical and Applied Mathematics, 1, 96, 96-104 (2008) · Zbl 1164.60049 |
| [9] | Gormin, A.A., Kashtanov, Y.N.: The weighted variance minimization in jump-diffusion stochastic volatility models. Monte Carlo and Quasi-Monte Carlo Methods 2008, 383-395 (2009) · Zbl 1182.91198 |
| [10] | Lyuu, Y.-D.,Teng, H.-W.: Unbiased and efficient greeks of financial options. Finance and Stochastic, Online First^TM (3 September, 2010) |
| [11] | Newton, N. J., Variance reduction for simulated diffusions, SIAM Journal on Applied Mathematics, 54, 6, 1780-1805 (1994) · Zbl 0811.60046 |
| [12] | Schoenmakers, J. G. M.; Heemink, A. W., Fast valuation of financial derivatives, The Journal of Computational Finance, 1, 1, 47-62 (1997) |
| [13] | Situ, R.: Theory of Stochastic Differential Equations with Jumps and Applications. Springer-Verlag, New York (2005) · Zbl 1070.60002 |
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