VaR-Optimal Risk Management in Regime-Switching Jump-Diffusion Models

Alessandro Ramponi

Department of Economics and Finance, University of Roma Tor Vergata, Roma, Italy.

DOI: 10.4236/jmf.2013.31009                

Abstract

In this paper we study a classical option-based portfolio strategy which minimizes the Value-at-Risk of the hedged position in a continuous time, regime-switching jump-diffusion market, by using Fourier Transform methods. However, the analysis of this hedging strategy, as well as the computational technique for its implementation, is fairly general, i.e. it can be applied to any dynamical model for which Fourier transform methods are viable.

Keywords

Regime Switching Jump-Diffusion Models; Value at Risk; Risk Management; Fourier Transform Methods

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. H. Ahn, J. Boudoukh, M. Richardson and R. F. Whitelaw, “Optimal Risk Management Using Options,” Journal of Finance, Vol. 54, No. 1, 1999, pp. 359-375. doi:10.1111/0022-1082.00108
[2]	J. Annaert, G. Deelstra, D. Heyman and M. Vanmaele, “Risk Management of a Bond Portfolio Using Options,” Insurance: Mathematics and Economics, Vol. 41, No. 3, 2007, pp. 299-316. doi:10.1016/j.insmatheco.2006.11.002
[3]	F. Antonelli, A. Ramponi and S. Scarlatti, “Option Based Risk Management of a Bond Portfolio under Regime Switching Interest Rates,” Decisions in Economics and Finance, 2011. doi:10.1007/s10203-011-0123-1
[4]	J. Hamilton, “A New Approach to the Economic Analysis of Non Stationary Time Series and the Business Cycle,” Econometrica, Vol. 57, No. 2, 1989, pp. 357-384. doi:10.2307/1912559
[5]	R. Cont and P. Tankov, “Financial Modelling with Jump Processes,” Chapman & Hall, CRC Press, Boca Raton, 2003. doi:10.1201/9780203485217
[6]	R. Kawata and M. Kijima, “Value at Risk in a Market Subject to Regime Switching,” Quantitative Finance, Vol. 7, No. 6, 2007, pp. 609-619. doi:10.1080/14697680601161795
[7]	A. Taamouti, “Analytical Value-at-Risk and Expected Shortfall under Regime-Switching,” Finance Research Letters, Vol. 6, No. 3, 2009, pp. 138-151. doi:10.1016/j.frl.2009.03.004
[8]	A. Ramponi, “On Fourier Transform Methods for Regime-Switching Jump-Diffusions and the Pricing of Forward Starting Options,” International Journal of Theoretical and Appplied Finance, Vol. 15, No. 5, 2012, 26 p.
[9]	D. Duffie and J. Pan, “Analytical Value-at-Risk with Jumps and Credit Risk,” Finance and Stochastics, Vol. 5, No. 2, 2001, pp. 155-180. doi:10.1007/PL00013531
[10]	O. Le Courtois and C. P. Walter, “A Study on Value-at-Risk and Lévy Processes,” 2009. http://ssrn.com/abstract=1598360 doi:10.2139/ssrn.1598360
[11]	Y. S. Kim, S. T. Rachev, M. L. Bianchi and F. J. Fabozzi, “Computing VaR and AVaR in Infinitely Divisible Distributions,” Probability and Mathematical Statistics, Vol. 30, No. 2, 2010, pp. 223-245.
[12]	M. Scherer,S.T.Rachev,Y.S.Kim and F.J. Fabozzi, “A FFT-Based Approximation of Tempered Stableand Tempered Infinitely Divisible Distributions,”2009. http://www.ams.sunysb.edu/~rachev/publication/StandardTSDistr_20100306final.pdf
[13]	P. Artzner, F. Delbaen, J. Eber and D. Heath, “Coherent Measures of Risk,” Mathematical Finance, Vol. 9, No. 3, 1999, pp. 203-228. doi:10.1111/1467-9965.00068
[14]	W. J. Runggaldier, “Jump-Diffusion Models,” In: S.T. Rachev, Ed., Handbook of Heavy Tailed Distributions in Finance, Elesevier/North-Holland, Amsterdam, 2003, pp. 169-209.
[15]	P. Carr and D. B. Madan, “Option Valuation Using the Fast Fourier Transform,” Journal of Computational Finance, Vol. 2, No. 4, 1999, pp. 61-73.
[16]	R. W. Lee, “Option Pricing by Transform Methods: Extensions, Unifications and Error Control,” Journal of Computational Finance, Vol. 7, No. 3, 2004, pp. 51-86.
[17]	A. Ramponi, “Computing Quantiles in Regime-Switching Jump-Diffusions with Application to Optimal Risk Management: A Fourier Transform Approach,” arXiv: 1207.6759, 2012.