A Comparison of Prices Generated by The Derivative Commodity Model (Ornstein-Uhlenbeck Process) With Those Obtained by The Conventional Arbitrage-Free Method of Pricing Forward Derivatives with Respect to Tea in Nduti Tea Factory Kenya.

Authors

  • Patrick MUMU Nairobi University

Keywords:

price derivatives, Ornstein Uhlenbeck process, commodity derivative, forwards, futures, options or swaps.

Abstract

Purpose: The purpose of this study was to compare the prices generated by the derivative commodity model with those obtained by the conventional arbitrage-free method of pricing forward derivatives with respect to tea.

Methodology: The study used descriptive survey research design. The study used descriptive survey research design. This study used secondary data which was collected from Nduti Tea Factory website. The target population of the study were 318 auction days auction days on the stock exchange spread over from 18/12/2007 to 2/12/2014. Purposive sampling was used to select 6 working days excluding Sundays and holidays starting from 18/12/2014 to 2/12/2014.Data from the websites was analysed   using the Ornstein Uhlenbeck process, to derive descriptive results.

Results: The findings implied that   there was variations in forward prices calculated by derivative commodity model as compared to those calculated   conventional arbitrage-free.

Unique contribution to theory, practice and policy: The study provides need to insuring farmers from uncertainty by ensuring they get value for the input and costs of production. On the other hand, consumers are protected from the volatile food commodity prices. An incentive for the farmer is established and hence increased and more efficient productivity is witnessed. The study will lead to designing a simple commodity derivative with different times to expiry for tea in Kenya and elsewhere based on estimated future market prices. The results of this study will be of particular significance to farmers, cooperatives and general investors.

Downloads

Download data is not yet available.

Author Biography

Patrick MUMU, Nairobi University

Undergraduate Student BSC Actuarial Science

References

A. Cartea and M. G. Figueroa, Pricing in electricity markets: a mean reverting jump di®usion model with seasonality," in Applied Mathematical Finance, Dec 2005, vol. 12, pp. 313{335.

Alison Etheridge, A course in Financial Calculus, Cambridge University Press, Cam-Bridge, UK, 2002.

Cox, John C., Jonathan E. Ingersoll, and Stephen A. Ross. 1985. A Theory of the Term Structure of Interest Rates. Econometrica 53, no. 2 (March): 385-407.

Ornstein, L. S., and G. E. Uhlenbeck. 1930. On the Theory of the Brownian Motion. Physical Review 36, no. 5: 823. doi:10.1103/PhysRev.36.823.

Schwartz, E. (1997 "˜The stochastic behaviour of commodity prices: Implications for valuation and hedging', Journal of Finance 52(3), 922-973.

Schwartz, E. and Smith, J. (2000), "˜Short-term variations and long-term dynamics in commodity prices', Management Science 46(7), 893-911.

Smith, W. (2010). On the simulation and estimation of the mean-reverting Ornstein-uhlenbeck process. Commodities Markets and Modelling.

Vasicek, Oldrich. 1977. An equilibrium characterization of the term structure. Journal of Financial Economics 5, no. 2 (November): 177-188. doi:10.1016/0304-405X (77)90016-2.

Downloads

Additional Files

Published

2016-09-23

How to Cite

MUMU, P. (2016). A Comparison of Prices Generated by The Derivative Commodity Model (Ornstein-Uhlenbeck Process) With Those Obtained by The Conventional Arbitrage-Free Method of Pricing Forward Derivatives with Respect to Tea in Nduti Tea Factory Kenya. Journal of Statistics and Actuarial Research, 1(1), 12–23. Retrieved from https://iprjb.org/journals/index.php/JSAR/article/view/86

Issue

Section

Articles