A stochastic local volatility technique for TARN options

References

• S.P. Alfonso, Estudio de modelos de volatilidad estocástica en el mercado FX, Master's thesis, Universidad Nacional de Colombia, 2016.
   Google Scholar
• D. Bates, Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options, Rev. Financ. Stud. 9 (1996), pp. 69–107. doi: 10.1093/rfs/9.1.69
   Web of Science ®Google Scholar
• F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), pp. 637–654. doi: 10.1086/260062
   Web of Science ®Google Scholar
• B. Borowski, Hedgingverfahren für Foreign Exchange Barrieroptionen, Master's thesis, T. U. München, 2005.
   Google Scholar
• C. Brown, J.C. Handley, C.T. Lin, and K.J. Palmer, Partial differential equations for Asian option prices, Quant. Finance 16 (2016), pp. 447–460. doi: 10.1080/14697688.2015.1052838
   Web of Science ®Google Scholar
• P. Carr and D.B. Madan, Option valuation using the fast Fourier transform, J. Comput. Finance 2 (1999), pp. 61–73. doi: 10.21314/JCF.1999.043
   Google Scholar
• I.J. Clark, Foreign Exchange Option Pricing: A Practitioners Guide, Wiley, West Sussex, 2011.
   Google Scholar
• J. Cox, S. Ross, and M. Rubinstein, Option pricing: A simplified approach, J. Financ. Econ. 7 (1979), pp. 229–264. doi: 10.1016/0304-405X(79)90015-1
   Web of Science ®Google Scholar
• G. Deelstra and G. Rayée, Local volatility pricing models for long-dated FX derivatives, 2012. Available at arXiv:1204.0633v1 [q-fin.RM].
   Google Scholar
• E. Derman and I. Kani, The volatility smile and its implied tree, Tech. Rep., Goldman Sachs, 1994.
   Google Scholar
• B. Dupire, Pricing with a smile, Risk 7 (1994), pp. 18–20.
   Google Scholar
• B. Dupire, A unified theory of volatility, 1996. Working paper.
   Google Scholar
• B. Engelmann, F. Koster, and D. Oeltz, Calibration of the Heston stochastic local volatility model: A finite volume scheme, 2012. Available at http://dx.doi.org/10.2139/ssrn.1823769.
   Google Scholar
• F. Fang and C.W. Oosterlee, A novel pricing method for European options based on Fourier-Cosine series expansions, SIAM J. Sci. Comput. 31 (2009), pp. 826–848. doi: 10.1137/080718061
   Web of Science ®Google Scholar
• F. Fang and C.W. Oosterlee, A Fourier-based valuation method for Bermudan and barrier options under Heston's model, SIAM J. Financ. Math. 2 (2011), pp. 439–463. doi: 10.1137/100794158
   Web of Science ®Google Scholar
• I. Florescu and F.G. Viens, Stochastic volatility: Option pricing using a multinomial recombining tree, Appl. Math. Finance 15 (2008), pp. 151–181. doi: 10.1080/13504860701596745
   Google Scholar
• P. Forsyth, K. Vetzal, and R. Zvan, A finite element approach to the pricing of discrete lookbacks with stochastic volatility, Appl. Math. Finance 6 (1999), pp. 87–106. doi: 10.1080/135048699334564
   Google Scholar
• P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, New York, 2003.
   Google Scholar
• P.S. Hagan, D. Kumar, A.S. Lesniewski, and D.E. Woodward, Managing smile risk, Wilmott Mag. 1 (2002), pp. 84–108.
   Google Scholar
• P. Henry-Labordère, Calibration of local stochastic volatility models to market smiles: A Monte-Carlo approach, 2009. Available at SSRN: https://ssrn.com/abstract=1493306.
   Google Scholar
• S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financ. Stud. 6 (1993), pp. 327–343. doi: 10.1093/rfs/6.2.327
   Web of Science ®Google Scholar
• J. Hull and A. White, An analysis of the bias in option pricing caused by a stochastic volatility, Adv. Futures Options Res. 3 (1988), pp. 29–61.
   Google Scholar
• J. Hull and A. White, One-factor interest-rate models and the valuation of interest-rate derivative securities, J. Financ. Quant. Anal. 28 (1993), pp. 235–254. doi: 10.2307/2331288
   Web of Science ®Google Scholar
• T. Kluge, Pricing derivatives in stochastic volatility models using the finite difference method, Ph.D. diss., Chemnitz Technical University, 2002.
   Google Scholar
• X. Luo and P. Shevchenko, Fast and simple method for pricing exotic options using Gauss–Hermite quadrature on a cubic spline interpolation, J. Financ. Eng. 1 (2014). Available at http://doi.org/10.1142/S2345768614500330.
   Google Scholar
• X. Luo and P. Shevchenko, Pricing TARNs using a finite difference method, J. Deriv. 23 (2015), pp. 62–72. doi: 10.3905/jod.2015.23.1.062
   Web of Science ®Google Scholar
• J. Morgan, Pricing exotics under smile, Risk 12 (1999), pp. 72–75.
   Google Scholar
• B. Salvador, Modelling, mathematical analysis and numerical simulation of problems related to counterparty risk and cva, Ph.D. diss., Universidade da Coru na, Spain, 2018.
   Google Scholar
• G. Tataru and T. Fisher, Stochastic Local Volatility, Quantitative Development Group, Bloomberg, Version 1, 2010.
   Google Scholar
• Y. Tian, The hybrid stochastic-local volatility model with applications in pricing FX options, Ph.D. diss., Monash University, 2013.
   Google Scholar
• Y. Tian, Z. Zhu, G. Lee, T. Lo, F. Klebaner, and K. Hamza, Pricing window barrier options with a hybrid stochastic-local volatility model, in Proc. 2014 IEEE Conference on Computational Intelligence for Financial Engineering and Economics, London, 2014.
   Google Scholar
• A.W. van der Stoep, L.A. Grzelak, and C.W. Oosterlee, The Heston stochastic-local volatility model: Efficient Monte Carlo simulation, Int. J. Theor. Appl. Finance 17 (2014), pp. 1450045–1–1450045–30. doi: 10.1142/S0219024914500459
   Google Scholar
• P. Wilmott, Paul Wilmott on Quantitative Finance, Wiley, West Sussex, 2006.
   Google Scholar
• U. Wystup, FX Options and Structured Products, Wiley, Chichester, 2017.
   Google Scholar
• R. Zvan, K.R. Vetzal, and P.A. Forsyth, PDE methods for pricing barrier options, J. Econ. Dyn. Control 24 (2000), pp. 1563–1590. doi: 10.1016/S0165-1889(00)00002-6
   Web of Science ®Google Scholar