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A Stochastic Programming Model for Currency Option Hedging

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  • Jason Wu
  • Suvrajeet Sen

Abstract

In this paper we use a stochastic programming approach to develop currency option hedging models which can address problems with multiple random factors in an imperfect market. The portfolios considered in our model are rebalanced at the end of each time period, and reinvestments are allowed during the hedging process. These sequential decisions (reinvestments) are based on the evolution of random parameters such as exchange rates, interest rates, etc. We also allow the inclusion of a variety of instruments in the hedging portfolio, including short term derivative securities, short term options, and futures. These instruments help generate strategies that provide good liquidity and low trade intensity. One of the important features of the model is that it incorporates constraints on sensitivity measures such as Delta and Gamma. By ensuring that these hedge parameters track a desired trajectory (e.g., the parameters of a target option), the new model provides investment strategies that are robust with respect to the perturbations measured by Delta and Gamma. In order to manage the explosion of scenarios due to multiple random factors, we incorporate sampling within a scenario aggregation algorithm. We illustrate that when compared with other myopic hedging methods in imperfect markets, the new stochastic programming model can provide better performance. Our examples also illustrate stochastic programming as a practical computational tool for realistic hedging problems. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Jason Wu & Suvrajeet Sen, 2000. "A Stochastic Programming Model for Currency Option Hedging," Annals of Operations Research, Springer, vol. 100(1), pages 227-249, December.
    • Handle: RePEc:spr:annopr:v:100:y:2000:i:1:p:227-249:10.1023/a:1019296422231
    DOI: 10.1023/A:1019296422231
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    Citations

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    Cited by:

    1. Libo Yin & Liyan Han, 2013. "Options strategies for international portfolios with overall risk management via multi-stage stochastic programming," Annals of Operations Research, Springer, vol. 206(1), pages 557-576, July.
    2. Blomvall, Jörgen & Hagenbjörk, Johan, 2022. "Reducing transaction costs for interest rate risk hedging with stochastic programming," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1282-1293.
    3. Valeriy Ryabchenko & Sergey Sarykalin & Stan Uryasev, 2004. "Pricing European Options by Numerical Replication: Quadratic Programming with Constraints," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 301-333, September.
    4. Libo Yin & Liyan Han, 2015. "Hedging International Foreign Exchange Risks via Option Based Portfolio Insurance," Computational Economics, Springer;Society for Computational Economics, vol. 45(1), pages 151-181, January.
    5. Suvrajeet Sen & Lihua Yu & Talat Genc, 2006. "A Stochastic Programming Approach to Power Portfolio Optimization," Operations Research, INFORMS, vol. 54(1), pages 55-72, February.
    6. Gao, Pei-wang, 2009. "Options strategies with the risk adjustment," European Journal of Operational Research, Elsevier, vol. 192(3), pages 975-980, February.
    7. Xiangling Hu & Charles Munson & Stergios Fotopoulos, 2012. "Purchasing decisions under stochastic prices: Approximate solutions for order time, order quantity and supplier selection," Annals of Operations Research, Springer, vol. 201(1), pages 287-305, December.
    8. Barro, Diana & Consigli, Giorgio & Varun, Vivek, 2022. "A stochastic programming model for dynamic portfolio management with financial derivatives," Journal of Banking & Finance, Elsevier, vol. 140(C).
    9. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2020. "Integrated dynamic models for hedging international portfolio risks," European Journal of Operational Research, Elsevier, vol. 285(1), pages 48-65.

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