Active Hedging Greeks of an Options Portfolio integrating churning and minimization of cost of hedging using Quadratic & Linear Programing

Sinha, Pankaj and Gupta, Akshay and Mudgal, Hemant (2010): Active Hedging Greeks of an Options Portfolio integrating churning and minimization of cost of hedging using Quadratic & Linear Programing.

Abstract

This paper proposes a methodology for active hedging Greeks of an option portfolio integrating churning and minimization of cost of hedging. In the first section, hedging strategy is implemented by taking positions in other available options, while simultaneously minimizing the net premium paid for the hedging and then churning the portfolio to take into account the changed value of Greeks in the new portfolio. In the second section, the paper extends the model to incorporate the transaction cost while hedging the portfolio and churning it in Indian Scenario. Both constant and nonlinear shape of transaction cost has been considered as per the Security Transaction Tax and Brokerage charges in India. A quadratic programming has been presented which has been approximated by a linear programming solution. The prototype software has been developed in MS Excel using Visual Basic.

• Item Type: MPRA Paper
• Language: English
• Keywords: Options Portfolio, Hedging Greeks, Churning of Portfolio, Linear Programing, Transaction Cost
• Subjects: G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

[1] Papahristodoulou, C. (2004). Option strategies with linear programming, European Journal of Operational Research, 157, 246–256.

[2] Horasanlı, M. (2008). Hedging strategy for a portfolio of options and stocks with linear programming, Applied Mathematics and Computation, 199, 804–810.

[3] Hull, J. C. (2009). Options, Futures, and Other Derivatives, Prentice Hall.

[4] Rendleman, R. J. (1995). An LP approach to option portfolio selection, Advances in Futures and Options Research, 8, 31–52.

[5] Sinha, P & Johar, A. (2010). Hedging Greeks for a Portfolio of Options using Linear and Quadratic Programming, Journal of Prediction Markets. 4(1):17 -26

[6] Li, Z.F., Wang, S.Y., & Deng, X.T. (2000). A linear programming algorithm for optimal portfolio selection with transaction costs, International Journal of Systems Science, 2000, volume 31, number 1, pages 107 – 117