Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models

References

• Alòs E, León JA (2016) On the short-maturity behaviour of the implied volatility skew for random strike options and applications to option pricing approximation. Quant. Finance 16(1):31–42.Crossref, Google Scholar
• Alòs E, Eydeland A, Laurence P (2011) A Kirk’s and a Bachelier’s formula for three-asset spread options. Energy Risk 9:52–57.Google Scholar
• Bates DS (1996) Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options. Rev. Financial Stud. 9(1):69–107.Crossref, Google Scholar
• Bichteler K, Gravereaux JB, Jacod J (1987) Davis M, ed. Malliavin Calculus for Processes with Jumps, Stochastic Monographs, Vol. 2 (Gordon and Breach, London).Google Scholar
• Cai N, Kou S (2012) Pricing Asian options under a hyper-exponential jump diffusion model. Oper. Res. 60(2):64–77.Link, Google Scholar
• Cai N, Li C, Shi C (2014) Closed-form expansions of discretely monitored Asian options in diffusion models. Math. Oper. Res. 39(3):789–822.Link, Google Scholar
• Cai N, Song Y, Kou S (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3):540–554.Link, Google Scholar
• Cai N, Song Y, Kou S (2016) A unified framework for options pricing under regime switching models. Working paper.Google Scholar
• Caldana R, Fusai G (2013) A general closed-form spread option pricing formula. J. Banking Finance 37(17):4893–4906.Crossref, Google Scholar
• Cass T (2009) Smooth densities for solutions to stochastic differential equations with jumps. Stochastic Processes Appl. 119(5):1416–1435.Crossref, Google Scholar
• Dadachanji Z (2015) Fx Barrier Options: A Comprehensive Guide for Industry Quants (Palgrave Macmillan, Basingstoke).Crossref, Google Scholar
• Delong L (2013) Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications (Springer, London).Crossref, Google Scholar
• Di Nunno G, Oksendal B, Proske F (2009) Malliavin Calculus for Lévy Processes with Applications to Finance (Springer, Berlin).Crossref, Google Scholar
• Eraker B (2004) Do stock prices and volatility jump? Reconciling evidence from spot and option prices. J. Finance 59(3):1367–1404.Crossref, Google Scholar
• Forster B, Lütkebohmert E, Teichmann J (2009) Absolutely continuous laws of jump-diffusions in finite and infinite dimensions with applications to mathematical finance. SIAM J. Math. Anal. 40(5):2132–2153.Crossref, Google Scholar
• Fusai G, Kyriakou I (2016) General optimized lower and upper bounds for discrete and continuous arithmetic Asian options. Math. Oper. Res. 41(2):531–559.Link, Google Scholar
• Fusai G, Meucci A (2008) Pricing discretely monitored Asian options under Lévy processes. J. Banking Finance 32(10):2076–2088.Crossref, Google Scholar
• Glasserman P (2004) Monte Carlo Methods in Financial Engineering (Springer, New York).Crossref, Google Scholar
• Hagan P, Kumar D, Lesniewski A, Woodward D (2002) Managing smile risk. Wilmott 1(September):84–108.Google Scholar
• Homescu C (2014) Local stochastic volatility models: calibration and pricing. Working paper, http://dx.doi.org/10.2139/ssrn.2448098.Google Scholar
• Jacod J, Kurtz TG, Méléard S, Protter P (2005) The approximate Euler method for Lévy driven stochastic differential equations. Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques 41(3):523–558.Crossref, Google Scholar
• Kunitomo N, Takahashi A (2001) The asymptotic expansion approach to the valuation of interest rate contingent claims. Math. Finance 11(1):117–151.Crossref, Google Scholar
• Kunitomo N, Takahashi A (2003) On validity of the asymptotic expansion approach in contingent claim analysis. Ann. Appl. Probab. 13(3):914–952.Crossref, Google Scholar
• Li C, Chen D (2016) Estimating jump-diffusions using closed-form likelihood expansions. J. Econometrics 195(1):51–70.Crossref, Google Scholar
• Liptser RSh, Shiryayev AN (1989) Theory of Martingales (Kluwer Academic, Dordrecht, Netherlands).Crossref, Google Scholar
• Mercurio F (2006) Swaption smile and CMS adjustment. Presentation paper, Derivatives and Risk Management Europe, Monte Carlo, June 7.Google Scholar
• Pagliarani S, Pascucci A (2013) Local stochastic volatility with jumps. Internat. J. Theoret. Appl. Finance 16(08):1350050.Crossref, Google Scholar
• Sepp A (2012) Achieving consistent modeling of VIX and equities derivatives. Presentation Paper, Global Derivatives Conf. Barcelona.Google Scholar
• Shiraya K, Takahashi A (2011) Pricing average options on commodity. J. Futures Markets 31(5):407–439.Crossref, Google Scholar
• Shiraya K, Takahashi A (2014) Pricing multi-asset cross currency options. J. Futures Markets 34(1):1–19.Crossref, Google Scholar
• Shiraya K, Takahashi A (2016) An approximation formula for basket option prices under local stochastic volatility with jumps, an application to commodity markets. J. Computational Appl. Math. 292(15):230–256.Crossref, Google Scholar
• Shiraya K, Takahashi A (2017) Pricing average and spread options under local-stochastic volatility jump-diffusion models (appendix). CARF Working Paper F-412.Google Scholar
• Shiraya K, Takahashi A (2017) An asymptotic expansion for local-stochastic volatility with jump models. Stochastics: An Internat. J. Probab. Stochastic Processes 89(1):65–88.Crossref, Google Scholar
• Shiraya K, Takahashi A (2017) A general control variate method for multi-dimensional SDEs: An application to multi-asset options under local stochastic volatility with jumps models in finance. Eur. J. Oper. Res. 258(1):358–371.Crossref, Google Scholar
• Shiraya K, Takahashi A, Toda M (2012) Pricing barrier and average options under stochastic volatility environment. J. Computational Finance 15(2):111–148.Crossref, Google Scholar
• Shiraya K, Takahashi A, Yamazaki A (2012) Pricing swaptions under the LIBOR market model of interest rates with local-stochastic volatility models. Willmott Magazine 61:48–63.Crossref, Google Scholar
• Takahashi A (1999) An asymptotic expansion approach to pricing financial contingent claims. Asia-Pacific Financial Markets 6(2):115–151.Crossref, Google Scholar
• Takahashi A, Yamada T (2015) On error estimates for asymptotic expansions with Malliavin weights: Application to stochastic volatility model. Math. Oper. Res. 40(3):513–541.Link, Google Scholar
• Takahashi A, Yamada T (2016) A weak approximation with asymptotic expansion and multidimensional Malliavin weights. Ann. Appl. Probab. 26(2):818–856.Crossref, Google Scholar
• Takahashi A, Takehara K, Toda M (2009) Computation in an asymptotic expansion method. CARF Working Paper F-149.Crossref, Google Scholar
• Yamazaki A (2014) Pricing average options under time-changed Lévy processes. Rev. Derivatives Res. 17(1):79–111.Crossref, Google Scholar
• Yoshida N (2003) Conditional expansions and their applications. Stochastic Processes Appl. 107(1):53–81.Crossref, Google Scholar
• Zeng P, Kwok YK (2016) Pricing bounds and approximation for discrete arithmetic Asian options under time-changed Lévy processes. Quant. Finance 16(9):1375–1391.Crossref, Google Scholar