International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

On Modelling and Pricing Weather Derivatives Driven by Nonlinear Brownian Motion

  • Javed Hussain1*
  • Pervez Ali2
  1. Sukkur IBA University Pakistan; University of York UK
  2. Sukkur IBA University

* Corresponding author

Abstract

In this paper, our focus is to derive the estimates satisfied by the risk-neutral prices of a class of weather derivatives, contingent upon temperature which satisfies G-stochastic differential equation driven by nonlinear G-Brownian motion.

How to Cite

J. Hussain, P. Ali, On Modelling and Pricing Weather Derivatives Driven by Nonlinear Brownian Motion, Int. J. Anal. Appl. 19 (2021), 29–46. https://doi.org/10.28924/2291-8639-19-2021-29

BibTeX
@article{Hussain2021,
  author  = {Hussain, Javed and Ali, Pervez},
  title   = {On Modelling and Pricing Weather Derivatives Driven by Nonlinear Brownian Motion},
  journal = {Int. J. Anal. Appl.},
  volume  = {19},
  year    = {2021},
  pages   = {29--46},
  doi     = {10.28924/2291-8639-19-2021-29}
}

References

  • [1] P. Alaton, B. Djehiche, D. Stillberger, On modelling and pricing weather derivatives, Appl. Math. Finance. 9 (2002), 1-20.
  • [2] P. Artzner, F. Delbaen, J.-M. Eber, D. Heath, Coherent Measures of Risk, Math. Finance. 9 (1999), 203-228.
  • [3] M. Avellaneda, A. Levy, A. ParAS, Pricing and hedging derivative securities in markets with uncertain volatilities, Appl. ´ Math. Finance. 2 (1995), 73-88.
  • [4] A. Alexandridis, A.D. Zapranis, Weather derivatives: modeling and pricing weather-related risk. Springer Science & Business Media, New York, (2012).
  • [5] T.G. Bali, S.J. Brown, Y. Tang, Is economic uncertainty priced in the cross-section of stock returns?, J. Financ. Econ. 126 (2017), 471-489.
  • [6] Z. Chen, L. Epstein, Ambiguity, Risk, and Asset Returns in Continuous Time, Econometrica. 70 (2002), 1403-1443.
  • [7] P. Glasserman, X. Xu, Robust risk measurement and model risk, Quant. Finance. 14 (2014), 29-58.
  • [8] M.A. Soomro, J. Hussain, On Study of Generalized Novikov Equation by Reduced Differential Transform Method, Indian J. Sci. Technol. 12 (2019), 1-6.
  • [9] J. Hussain, B. Khan, On Cox-Ross-Rubinstein Pricing Formula for Pricing Compound Option, Int. J. Anal. Appl. 18 (1) (2020), 129-148.
  • [10] J. Hussain, M.S. Khan, On the Pricing of Call-Put Parities of Asian Options by Reduced Differential Transform Algorithm, Int. J. Anal. Appl. 18 (3) (2020), 513-530.
  • [11] J. Hussain, Valuation of European Style Compound Option Written on European Style Currency and Power Options, Int. J. Anal. Appl. 18 (6) (2020), 1015-1028.
  • [12] J. Hussain, On Existence and invariance of sphere, of solutions of constrained evolution equation, Int. J. Math. Comput. Sci. 15 (2020), 325-345.
  • [13] M.-U. Rehman, J. Alzabut, J.H. Brohi, A. Hyder, On Spectral Properties of Doubly Stochastic Matrices, Symmetry. 12 (2020), 369.
  • [14] M.-U. Rehman, J. Alzabut, J. Hussain Brohi, Computing µ-values for LTI Systems, AIMS Math. 6 (2021), 304-313.
  • [15] J. Holzermann, Pricing Interest Rate Derivatives under Volatility Uncertainty, ArXiv:2003.04606 [q-Fin]. (2020).
  • [16] K. Ito, Differential equations determining a markoff process. Kiyosi Itˆo Selected Papers (DW Stroock and SRS Varadhan, eds.), Springer-Verlag, pp. 42-75. 1987.
  • [17] L. Jiang, Convexity, translation invariance and subadditivity for G-expectations and related risk measures, Ann. Appl. Probab. 18 (2008), 245-258.
  • [18] G. Leobacher, P. Ngare, On Modelling and Pricing Rainfall Derivatives with Seasonality, Appl. Math. Finance. 18 (2011), 71-91.
  • [19] T.J. Lyons, Uncertain volatility and the risk-free synthesis of derivatives, Appl. Math. Finance. 2 (1995), 117-133.
  • [20] S. Marginson M. Considine. The Enterprise University: Power, Governance and Reinvention in Australia Cambridge University Press Cambridge. (2000).
  • [21] J. Mollmann, M. Buchholz, O. Musshoff, Comparing the hedging effectiveness of weather derivatives based on remotely sensed vegetation health indices and meteorological indices. Weather Climate Soc. 11 (2019), 33-48.
  • [22] F. P ´erez-Gonzalez, H. Yun, Risk Management and Firm Value: Evidence from Weather Derivatives: Risk Management and Firm Value, J. Finance. 68 (2013), 2143-2176.
  • [23] M. Ritter, O. Mußhoff, M. Odening, Minimizing Geographical Basis Risk of Weather Derivatives Using A Multi-Site Rainfall Model, Comput. Econ. 44 (2014), 67-86.
  • [24] S. Peng, G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty, ArXiv:0711.2834 [Math]. (2007).
  • [25] S. Peng, Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation, Stoch. Proc. Appl. 118 (2008), 2223-2253.
  • [26] S. Peng, Backward stochastic differential equation, nonlinear expectation and their applications, Proceedings of the International Congress of Mathematicians 2010, pp. 393-432, (2010).
  • [27] S. Peng, Nonlinear Expectations and Stochastic Calculus under Uncertainty: with Robust CLT and G-Brownian Motion, Springer Berlin Heidelberg, 2019.
  • [28] A. Salgueiro, M. T. Rodon, Approaching rainfall-based weather derivatives pricing and operational challenges, Rev. Deriv. Res. 23 (2020), 163-190.
  • [29] I. Stulec, Effectiveness of Weather Derivatives as a Risk Management Tool in Food Retail: The Case of Croatia, Int. J. ˇ Financ. Stud. 5 (2017), 2.
  • [30] K. E. Trenberth. The definition of el nino. Amer. Meteorol. Soc. 78 (12) (1997), 2771-2778.
  • [31] J. Xu, M.P. Xu, European Call Option Price under G-Framework. Math. Practice Theory, 4 (2010), 41-45.
  • [32] J. Xu, H. Shang, B. Zhang, A Girsanov Type Theorem Under G-Framework, Stoch. Anal. Appl. 29 (2011), 386-406.
  • [33] J. Yang, W. Zhao, Numerical simulations for G-Brownian motion, Front. Math. China. 11 (2016), 1625-1643.