Estimation the risk-neutral processes in jump–diffusion models of gold coin future contracts in Iran Mercantile Exchange

Subject Areas : Journal of Investment Knowledge

Nahid Malekiniya ¹ , hosein asgari alouj ²

1 - Ph.D. of financial-Industrial management, Accounting & Management Department, Bilesavar branch, Islamic Azad University, Bilesavar, Iran.
2 - Assistant Professor, Accounting & Management Department, Bilesavar branch, Islamic Azad University, Bilesavar, Iran

Received: 2018-02-01 Accepted : 2018-10-16 Published : 2021-06-22

Keywords: Jump–diffusion stochastic processes, Nadaraya–Watson nonparametric estimation, Gold Coin Future Contracts, Risk-neutral measure, Numerical differentiation,

Abstract :

Estimation the risk market prices and the functions of the stochastic processes of the model are necessary in commodity derivatives pricing. When a closed-form solution is unclear, estimating of the risk market price is a main question in the jump–diffusion models. This paper along with Gomez's, Habibilashgari's and Rodriguez's review (2016) is suggested to estimate the functions of the risk-neutral processes directly from market data of Iran. In this approach, there is no need to estimate the physical drift and the risk market prices of coin future contracts pricing. This research estimates the risk-neutral drifts, volatilities and parameters of the jump range distributions with Iran Mercantile Exchange data of the coin future contract , from 2010 to 2017. The findings show that JDM and DM under price the futures prices and the prices obtained with the JDM are closer to the observed prices than those obtained with the DM. For the longest maturities the JDM provides smaller errors than the DM. The higher the maturity, the higher the differences between the two models.

References:

• Andreas Kaeck, Paulo Rodrigues, Norman J. Seeger. (2017). Equity index variance: Evidence from flexible parametric jump–diffusion models, Journal of Banking & Finance, Volume 83, October 2017, Pages 85-103.


• Bandi, F.M. Nguyen, T.H. (2003). On the functional estimation of jump- diffusion models. J. Econometrics 116: 293–328.


• Baum C.F., Zerilli, P. (2014).Jumps and stochastic volatility in crude oil futures prices using conditional moments of integrated volatility. Boston College Working Papers in Economics


• Chenxi Fan, Xingguo Luo, Qingbiao Wu. (2017). Stochastic volatility vs. jump diffusions: Evidence from the Chinese convertible bond market, International Review of Economics & Finance ,Volume 49, May 2017, Pages 1-16


• Cont, R. Tankov, P. (2004).Financial modeling with Jump Processes, Chapman and Hall/CRC. Boca Raton, Florida


• Deng, S. (2000).stochastic models of energy commodity prices and their applications: mean-reversion with jumps and spikes. Working Paper, University of California Energy Institute, University of California.


• Diana, R., Ribeiroy, S., Hodgesz, D. (2004), A Two-Factor Model for Commodity Prices and Futures Valuation. Working paper.


• Gibson, R.Schwartz, E.S. (1990).Stochastic convenience yield and the pricing of oil contingent claims.J. Finance, 45 (3): 959–973.


• Gomez-Valle, L. Martnez-Rodriguez, J. (2013).Advances in pricing commodity futures: Multifactor models.Math.Comput.Modelling 57: 1722–1731.


• Gomez-Valle,L.Martnez-Rodriguez,J. (2015).The role of the risk-neutral jump size distribution in single-factor interest rate models.Abstr. Appl. Anal. 2015: 1–8.


• Gomez-Valle,L.Martnez-Rodriguez,J. (2016).Estimation of risk-neutral processes in single-factor jump-diffusion interest rate models.J. Comput. Appl. Math.291: 48–57.


• Gomez-Valle,L.,Habibilashkary,Z.,Martinez-Rodriguez,J. (2016).A new technique to estimate the risk-neutral processes in jump–diffusion commodity futures models. Journal of Computational and Applied Mathematics,


• Hardle, W. (1999). Applied Nonparametric Regression, in: Econometric Society Monographs. vol. 19, Cambridge University Press, New York


• Hilliard, J.E. Hilliard, J. (2015). Estimating early exercise premiums on gold and copper options using a multifactor model and density matched lattice. Financ.Rev. 50: 27–56.


• Hilliard, J. E. Reis, J.(1998). Valuation of commodity futures and options under stochastic convenience yields, interest rates, and jump diffusion in the spot.J. Financ. Quant. Anal. 33 (1) 61–86.


• Kyriakou, I., Nomikos, N.K., Papastolou, N., Poliasis, P.K. (2015).Affine structure models and the pricing of energy commodity derivatives.Cass Business School.Working Paper Series. N 24


• Miltersen, R. Schwartz,E.S. (1998).Pricing of options on commodity futures with stochastic term structures of convenience yields and interest rates.J. Financ.Quant. Anal., 33 (1) 33–59.


• Namhyoung Kim, Younhee Lee. (2018). Estimation and prediction under local volatility jump–diffusion model, Physica A: Statistical Mechanics and its Applications, Volume 491, 1 February 2018, Pages 729-740.


• Nawalkha, S.K. Beliaeva, N., Soto, G. (2007). Dynamic Term Structure Modeling: The Fixed Income Valuation Course. John Wiley & Sons, Inc.,


• Oksendal, B. Sulem, A. (2007).Applied Stochastic Control of Jump Diffusions.Springer-Verlag, Berlin,Heidelberg.


• Runggaldier,W.J. (2003). Jump-diffusion models, in: S.T. Rachev (Ed.), Handbook of Heavy Tayled Distributions in Finance. North Holland, UniversitatKarisruhe, Karisruhe, Germany, pp. 169–209.


• Schmitz, A. Wang, Z. Kim, J.H. (2014).A jump diffusion model for agricultural commodities with Bayesian analysis .J. Futures Mark. 34 (3) 235–260.


• Schwartz, E.S. (1997).The stochastic behavior of commodity prices: implications for a valuation and hedging. J. Finance, 52 (3) 923–973.


• Stanton, R. (1997). A nonparametric model of term structure dynamics and the market price of interest rate risk. J. Finance 52: 1973–2002.


• Xiao, Y. Colwell, D.B. Bhar, R. (2015). Risk premium in electricity prices: evidence from the PJM market. J. Futures Mark. 35 (8): 776–793.


• Yan, X. (2002). Valuation of commodity derivatives in a new multi-factor model. Rev. Deriv. Res. 5 251–271.


• Yu-hong Liu, I-Ming Jiang, Wei-tze Hsu,(2018), Compound option pricing under a double exponential Jump-diffusion model, The North American Journal of Economics and Finance,Volume 43, January 2018, Pages 30-53