On Modelling and Pricing Weather Derivatives Driven by Nonlinear Brownian Motion

Main Article Content

Javed Hussain
Pervez Ali

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.

Article Details

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.