Reference Bibliography

References

  • Barndorff-Nielsen, O. E. (1997). Processes of normal inverse Gaussian type. Finance and Stochastics 2, 41–68. ↩1
  • Behrens, T.; Junike, G. and Schoutens, W. (2023). Failure of Fourier pricing techniques to approximate the Greeks, arXiv:2306.08421. ↩1
  • Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654. ↩1
  • Broadie, M. and Glasserman, P. (1996). Estimating security price derivatives using simulation. Management Science 42, 269–285. ↩1
  • Cranley, R. and Patterson, T. N. (1976). Randomization of number theoretic methods for multiple integration. SIAM Journal on Numerical Analysis 13, 904–914. ↩1
  • De Olivera, F. and Mordecki, E. (2014). Computing Greeks for Lévy models: the Fourier transform approach, arXiv:1407.1343. ↩1
  • Eberlein, E.; Glau, K. and Papapantoleon, A. (2010). Analysis of Fourier transform valuation formulas and applications. Applied Mathematical Finance 17, 211–240, arXiv:0809.3405. ↩1 ↩2
  • Giles, M. B. (2009). Vibrato Monte Carlo sensitivities. In: Monte Carlo and Quasi-Monte Carlo Methods 2008, edited by L'Ecuyer, P. and Owen, A. B. (Springer); pp. 369–382. ↩1 ↩2
  • Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering (Springer). ↩1
  • Glasserman, P. and Liu, Z. (2010). Sensitivity estimates from characteristic functions. Operations Research 58, 1611–1623. ↩1
  • Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies 6, 327–343. ↩1
  • Kou, S. G. (2002). A jump-diffusion model for option pricing. Management Science 48, 1086–1101. ↩1
  • Longstaff, F. A. and Schwartz, E. S. (2001). Valuing American options by simulation: a simple least-squares approach. The Review of Financial Studies 14, 113–147. ↩1
  • Madan, D. B.; Carr, P. P. and Chang, E. C. (1998). The variance gamma process and option pricing. European Finance Review 2, 79–105. ↩1 ↩2
  • Marcinkiewicz, J. (1939). Sur une propriété de la loi de Gauß. Mathematische Zeitschrift 44, 612–618. ↩1
  • Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3, 125–144. ↩1
  • Pagès, G.; Pironneau, O. and Sall, G. (2018). Vibrato and automatic differentiation for high order derivatives and sensitivities of financial options. Journal of Computational Finance 22, arXiv:1606.06143. ↩1 ↩2
  • Scaramuzzino, N. (2017). Differenziazione automatica: teoria ed applicazioni in finanza. Master's thesis, Politecnico di Milano. Supervisor C. Sgarra, academic year 2016/2017. Vibrato Saltando is in Section 7.6. ↩1 ↩2 ↩3 ↩4 ↩5 ↩6 ↩7
  • Stein, C. M. (1981). Estimation of the mean of a multivariate normal distribution. The Annals of Statistics 9, 1135–1151. ↩1