Hedging of contingent claims written on non traded assets under Markov-modulated models. (English) Zbl 1343.60118

Wang, Wei; Qian, Linyi; Wang, Wensheng

Commun. Stat., Theory Methods 45, No. 12, 3577-3595 (2016).

Summary: This paper studies the hedging problem of European contingent claims when the underlying asset is non-traded. We assume that the share prices of the assets are governed by Markov-modulated processes, that is, the market parameters switch over time according to a finite-state continuous-time Markov chain. Due to the presence of the Markov chain in the non-traded asset, the market which we consider is incomplete. We shall use the local risk minimization method to obtain an optimal hedging strategy in a closed-form for an investor. Finally, numerical illustrations of an optimal hedging strategy are given by Monte Carlo simulations.

MSC:

60J28	Applications of continuous-time Markov processes on discrete state spaces
60J27	Continuous-time Markov processes on discrete state spaces
91B70	Stochastic models in economics
91G80	Financial applications of other theories
91G60	Numerical methods (including Monte Carlo methods)
65C05	Monte Carlo methods

Keywords:

hedging; contingent claims; non-traded assets; Markov-modulated models; local risk minimization; Monte Carlo simulations

References:

[1]	Buffington J., Lawrence, K.S., ed. Stochastic Theory and Control, Proceedings of a Workshop pp 73– (2002)
[2]	DOI: 10.1142/S0219024902001523 · Zbl 1107.91325 · doi:10.1142/S0219024902001523
[3]	DOI: 10.1016/j.insmatheco.2006.05.001 · Zbl 1141.91420 · doi:10.1016/j.insmatheco.2006.05.001
[4]	DOI: 10.1111/j.1467-9965.2009.00384.x · Zbl 1185.91092 · doi:10.1111/j.1467-9965.2009.00384.x
[5]	DOI: 10.1016/j.na.2009.02.105 · Zbl 1238.91067 · doi:10.1016/j.na.2009.02.105
[6]	DOI: 10.1016/j.jedc.2006.06.005 · Zbl 1163.91388 · doi:10.1016/j.jedc.2006.06.005
[7]	DOI: 10.1088/1469-7688/2/2/303 · doi:10.1088/1469-7688/2/2/303
[8]	DOI: 10.1080/07362990701857194 · Zbl 1133.91415 · doi:10.1080/07362990701857194
[9]	DOI: 10.1007/s10436-005-0013-z · Zbl 1233.91270 · doi:10.1007/s10436-005-0013-z
[10]	DOI: 10.1016/j.na.2009.03.085 · Zbl 1239.91145 · doi:10.1016/j.na.2009.03.085
[11]	Föllmer H., Hildenbrand, W., Mas-Colell, A. eds. Contributions to Mathematical Economics in Honor of Gerard Débreu pp 205– (1986)
[12]	Föllmer H., Applied Stochastic Analysis. In: Stochastic Monographs, vol. 5 pp 389– (1991)
[13]	DOI: 10.1081/STA-120025389 · Zbl 1028.62084 · doi:10.1081/STA-120025389
[14]	DOI: 10.1080/713665550 · doi:10.1080/713665550
[15]	DOI: 10.1137/S0363012996299302 · Zbl 0891.93081 · doi:10.1137/S0363012996299302
[16]	DOI: 10.1111/j.1467-9965.2002.tb00129.x · Zbl 1049.91072 · doi:10.1111/j.1467-9965.2002.tb00129.x
[17]	DOI: 10.1287/mnsc.48.8.1086.166 · Zbl 1216.91039 · doi:10.1287/mnsc.48.8.1086.166
[18]	DOI: 10.1016/j.jbankfin.2008.05.013 · doi:10.1016/j.jbankfin.2008.05.013
[19]	DOI: 10.1080/14697680601043191 · Zbl 1151.91523 · doi:10.1080/14697680601043191
[20]	Lee K., Commun. Stochastic Anal. 2 (1) pp 125– (2008)
[21]	DOI: 10.1016/0304-405X(76)90022-2 · Zbl 1131.91344 · doi:10.1016/0304-405X(76)90022-2
[22]	DOI: 10.2143/AST.28.1.519077 · Zbl 1168.91417 · doi:10.2143/AST.28.1.519077
[23]	DOI: 10.1007/s00780-003-0112-5 · Zbl 1062.93048 · doi:10.1007/s00780-003-0112-5
[24]	DOI: 10.1016/j.insmatheco.2011.10.001 · Zbl 1235.91104 · doi:10.1016/j.insmatheco.2011.10.001
[25]	DOI: 10.1016/j.insmatheco.2005.12.004 · Zbl 1168.91419 · doi:10.1016/j.insmatheco.2005.12.004
[26]	DOI: 10.1017/CBO9780511569708.016 · doi:10.1017/CBO9780511569708.016
[27]	DOI: 10.1016/j.insmatheco.2008.03.001 · Zbl 1141.91549 · doi:10.1016/j.insmatheco.2008.03.001
[28]	DOI: 10.1016/j.orl.2011.02.010 · Zbl 1219.91144 · doi:10.1016/j.orl.2011.02.010