Research article

A recursive pricing method for autocallables under multivariate subordination

  • Received: 25 April 2019 Accepted: 05 June 2019 Published: 01 July 2019
  • JEL Codes: C02, G13

  • In this paper we develop a new class of models for pricing autocallables based on multivariate subordinate Orstein Uhlenbeck (OU) processes. Starting from d independent OU processes and an independent d-dimensional Lévy subordinator, we construct a new process by time changing each of the OU processes with a coordinate of the Lévy subordinator. The prices of underlying assets are then modeled as an exponential function of the subordinate processes. The new models introduce state-dependent jumps in the asset prices and the dependence among jumps is governed by the Lévy measure of the d-dimensional subordinator. By employing the eigenfunction expansion technique, we are able to derive the analytical formulas for the worst-of autocallable prices. We also numerically implement a specific model and test its sensitivity to some of the key parameters of the model.

    Citation: Kevin Z. Tong. A recursive pricing method for autocallables under multivariate subordination[J]. Quantitative Finance and Economics, 2019, 3(3): 440-455. doi: 10.3934/QFE.2019.3.440

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  • In this paper we develop a new class of models for pricing autocallables based on multivariate subordinate Orstein Uhlenbeck (OU) processes. Starting from d independent OU processes and an independent d-dimensional Lévy subordinator, we construct a new process by time changing each of the OU processes with a coordinate of the Lévy subordinator. The prices of underlying assets are then modeled as an exponential function of the subordinate processes. The new models introduce state-dependent jumps in the asset prices and the dependence among jumps is governed by the Lévy measure of the d-dimensional subordinator. By employing the eigenfunction expansion technique, we are able to derive the analytical formulas for the worst-of autocallable prices. We also numerically implement a specific model and test its sensitivity to some of the key parameters of the model.


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    [1] Alm T, Harrach D, Keller M (2013) A Monte Carlo pricing algorithm for autocallables that allows for stable differentiation. J Comput Financ 17: 43-70. doi: 10.21314/JCF.2013.265
    [2] Bouzoubaa M, Osseiran A (2010) Exotic options and hybrids, Wiley Finance.
    [3] Deng G, Mallett J, McCann C (2011) Modeling autocallable structured products. J Deriv Hedge Funds 17: 326-340. doi: 10.1057/jdhf.2011.25
    [4] Fries CP, Joshi MS (2011) Perturbation stable conditional analytic Monte-Carlo pricing scheme for autocallable products. Int J Theor Appl Financ 14: 197-219. doi: 10.1142/S0219024911006334
    [5] Glasserman P (2003) Monte-Carlo methods in financial engineering, Springer Finance.
    [6] Guillaume T (2015a) Autocallable structured products. J Deriv 22: 73-94.
    [7] Guillaume T (2015b) Analytical valuation of autocallable notes. Int J Financ Eng 2: 1-23.
    [8] Koster F, Rehmet A (2018) Monte Carlo payoff smoothing for pricing autocallable instruments. J Comput Financ 21: 59-77. doi: 10.21314/JCF.2018.340
    [9] Li J, Li L, Mendoza-Arriaga R (2016) Additive subordination and its applications in finance. Finance Stoch 20: 589-634. doi: 10.1007/s00780-016-0300-8
    [10] Li J, Li L, Zhang G (2017) Pure jump models for pricing and hedging VIX derivatives. J Econ Dyn Contro 74: 28-55. doi: 10.1016/j.jedc.2016.11.001
    [11] Li L, Linetsky V (2014) Time-changed Ornstein-Uhlenbeck processes and their applications in commodity derivative models. Math Financ 24: 289-330. doi: 10.1111/mafi.12003
    [12] Li L, Mendoza-Arriaga R, Mo Z, et al. (2016) Modelling electricity prices: a time change approach. Quant Financ 16: 1089-1109. doi: 10.1080/14697688.2015.1125521
    [13] Lim D, Li L, Linetsky V (2012) Evaluating callable and putable bonds: an eigenfunction expansion approach. J Econ Dyn Contro 36: 1888-1908. doi: 10.1016/j.jedc.2012.06.002
    [14] Linetsky V (2004) The spectral decomposition of the option value. Int J Theor Appl Financ 5: 337-384.
    [15] Linetsky V, Mitchell D (2008) pectral methods in derivatives pricing, in Birge, J.R. Author, Handbook of Financial Engineering, Amsterdam: Elsevier, 223-299.
    [16] Mendoza-Arriaga R, Carr P, Linetsky V (2010) Time changed Markov processes in unified credit-equity modeling. Math Financ 20: 527-569. doi: 10.1111/j.1467-9965.2010.00411.x
    [17] Mendoza-Arriaga R, Linetsky V (2013) Time-changed CIR default intensities with two-sided mean-reverting jumps. Ann Appl Probab 24: 811-856.
    [18] Mendoza-Arriaga R, Linetsky V (2016) Multivariate subordination of Markov processes with financial applications. Math Financ 26: 699-747. doi: 10.1111/mafi.12061
    [19] Prudnikov AP, Brychkov YA, Marichev OI (1986) Integrals and Series, Vol. 2, Gordon and Breach Science Publishers.
    [20] Sato K (1999) Lévy processes and infinitely divisible distribution, Cambridge: Cambridge University Press.
    [21] Tankov P, Cont R (2003) Financial modelling with jump processes, Chapman and Hall/CRC.
    [22] Tong KZ, Hou D, Guan J (2019) The pricing of dual-expiry exotics with mean reversion and jumps. J Math Financ 9: 25-41. doi: 10.4236/jmf.2019.91003
    [23] Tong Z, Liu A (2017) Analytical pricing formulas for discretely sampled generalized variance swaps under stochastic time change. Int J Financ Eng 4: 1-24.
    [24] Tong Z, Liu A (2018) Analytical pricing of discrete arithmetic Asian options under generalized CIR with time change. Int J Financ Eng 5: 1-21.
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