January  2014, 10(1): 207-218. doi: 10.3934/jimo.2014.10.207

Variance-optimal hedging for target volatility options

1. 

School of Mathematical Sciences, Nankai University, Tianjin 300071, China

2. 

School of Business, Nankai University, Tianjin 300071, China

Received  March 2012 Revised  March 2013 Published  October 2013

In this paper, we consider a variance-optimal hedge for target volatility options, under exponential Lévy dynamics. Since the payoff of target volatility options is related with realized volatility of some underlying asset, which is path-dependent, it is difficult to price this instrument. Here we will derive an explicit Föllmer-Schweizer decomposition of the contingent claim of target volatility options and then give the explicit expressions of hedging strategies in both discrete time and continuous time.
Citation: Xingchun Wang, Yongjin Wang. Variance-optimal hedging for target volatility options. Journal of Industrial & Management Optimization, 2014, 10 (1) : 207-218. doi: 10.3934/jimo.2014.10.207
References:
[1]

Finance and Stochastics, 16 (2012), 335-355. doi: 10.1007/s00780-011-0157-9.  Google Scholar

[2]

International Journal of Theoretical and Applied Finance, 15 (2012), 1250005-1-1250005-17. doi: 10.1142/S0219024911006474.  Google Scholar

[3]

Applied Mathematical Finance, 14 (2007), 41-62. doi: 10.1080/13504860600659222.  Google Scholar

[4]

American Economic Review, 94 (2004), 405-420. doi: 10.1257/0002828041464597.  Google Scholar

[5]

in "Applied Stochastic Analysis" (eds. M. Davis and R. Elliott), Gordon and Breach, (1991), 389-414.  Google Scholar

[6]

preprint, (2012). Google Scholar

[7]

Applied Mathematical Finance, 11 (2004), 317-346. doi: 10.1080/1350486042000254024.  Google Scholar

[8]

Annals of Applied Probability, 16 (2006), 853-885. doi: 10.1214/105051606000000178.  Google Scholar

[9]

Second edition. Applications of Mathematics (New York), 21. Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin, 2004.  Google Scholar

[10]

Cambridge University Press, Cambridge, 2001. Google Scholar

[11]

Annals of Probability, 22 (1994), 1536-1575. doi: 10.1214/aop/1176988611.  Google Scholar

[12]

Mathematics of Operations Research, 20 (1995), 1-32. doi: 10.1287/moor.20.1.1.  Google Scholar

[13]

preprint, (2011). Google Scholar

[14]

Mathematical Finance, 21 (2011), 233-256. doi: 10.1111/j.1467-9965.2010.00436.x.  Google Scholar

show all references

References:
[1]

Finance and Stochastics, 16 (2012), 335-355. doi: 10.1007/s00780-011-0157-9.  Google Scholar

[2]

International Journal of Theoretical and Applied Finance, 15 (2012), 1250005-1-1250005-17. doi: 10.1142/S0219024911006474.  Google Scholar

[3]

Applied Mathematical Finance, 14 (2007), 41-62. doi: 10.1080/13504860600659222.  Google Scholar

[4]

American Economic Review, 94 (2004), 405-420. doi: 10.1257/0002828041464597.  Google Scholar

[5]

in "Applied Stochastic Analysis" (eds. M. Davis and R. Elliott), Gordon and Breach, (1991), 389-414.  Google Scholar

[6]

preprint, (2012). Google Scholar

[7]

Applied Mathematical Finance, 11 (2004), 317-346. doi: 10.1080/1350486042000254024.  Google Scholar

[8]

Annals of Applied Probability, 16 (2006), 853-885. doi: 10.1214/105051606000000178.  Google Scholar

[9]

Second edition. Applications of Mathematics (New York), 21. Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin, 2004.  Google Scholar

[10]

Cambridge University Press, Cambridge, 2001. Google Scholar

[11]

Annals of Probability, 22 (1994), 1536-1575. doi: 10.1214/aop/1176988611.  Google Scholar

[12]

Mathematics of Operations Research, 20 (1995), 1-32. doi: 10.1287/moor.20.1.1.  Google Scholar

[13]

preprint, (2011). Google Scholar

[14]

Mathematical Finance, 21 (2011), 233-256. doi: 10.1111/j.1467-9965.2010.00436.x.  Google Scholar

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