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

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Pankaj Sinha
Akshay Gupta Akshay Gupta
Hemant Mudgal Hemant Mudgal

Abstract

This paper proposes a methodology for active hedgingGreeks 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.

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References

Papahristodoulou, C. (2004). Option strategies with linear programming, EuropeanJournal of Operational Research, 157, 246–256.

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

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

Rendleman, R. J. (1995). An LP approach to option portfolio selection, Advances inFutures and Options Research, 8, 31–52.

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

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