A path-integral approximation for non-linear diffusions

References

• Aït Sahalia, Y., Transition densities for interest rate and other nonlinear diffusions. J. Finance, 1999, 54, 1361. doi: 10.1111/0022-1082.00149
   Web of Science ®Google Scholar
• Andersen, L. and Piterbarg, V., Interest Rate Modeling, 2010 (Atlantic Financial Press: London).
   Google Scholar
• Antonov, A. and Spector, M., Analytical approximations for short rate models. Risk, 2011, 26, 66.
   Google Scholar
• Bennati, E., Rosa-Clot, M. and Taddei, S., A path integral approach to derivative security pricing I: Formalism and analytical results. Int. J. Theoret. Appl. Finance, 1999, 02(04), 381. doi: 10.1142/S0219024999000200
   Google Scholar
• Black, F. and Karasinski, P., Bond and option pricing when short rates are lognormal. Financ. Anal. J., 1991, 47, 52. doi: 10.2469/faj.v47.n4.52
   Google Scholar
• Capriotti, L., The exponent expansion: An effective approximation of transition probabilities of diffusion processes and pricing kernels of financial derivatives. Int. J. Theoret. Appl. Finance, 2006, 09(07), 1179. doi: 10.1142/S0219024906003925
   Google Scholar
• Cuccoli, A., Giachetti, R., Tognetti, V., Vaia, R. and Verrucchi, P., The effective potential and effective Hamiltonian in quantum statistical mechanics. J. Phys.: Condens. Matter, 1995, 7, 7891.
   Web of Science ®Google Scholar
• Daniluk, A. and Muchorski, R., Approximations of bond and swaption prices in a Black-Karasiński model. Int. J. Theoret. Appl. Finance, 2016, 19(03), 1. doi: 10.1142/S0219024916500175
   Google Scholar
• Devreese, J.P.A., Lemmens, D. and Tempere, J., Path integral approach to Asian options in the Black-Scholes model. Physica A, 2010, 389, 780. doi: 10.1016/j.physa.2009.10.020
   Web of Science ®Google Scholar
• Feynman, R.P., Space–time approach to non-relativistic quantum mechanics. Rev. Mod. Phys., 1948, 20, 367. doi: 10.1103/RevModPhys.20.367
   Web of Science ®Google Scholar
• Feynman, R., Hibbs, A. and Styer, D., Quantum Mechanics and Path Integrals. Dover Books on Physics, 2010 (Dover Publications: New York).
   Google Scholar
• Feynman, R.P. and Kleinert, H., Effective classical partition functions. Phys. Rev. A, 1986, 34, 5080. doi: 10.1103/PhysRevA.34.5080
   PubMed Web of Science ®Google Scholar
• Giachetti, R. and Tognetti, V., Variational approach to quantum statistical mechanics of nonlinear systems with application to Sine-Gordon chains. Phys. Rev. Lett., 1985, 55, 912. doi: 10.1103/PhysRevLett.55.912
   PubMed Web of Science ®Google Scholar
• Jamshidian, F., An exact bond option formula. J. Finance, 1989, 44, 205. doi: 10.1111/j.1540-6261.1989.tb02413.x
   Web of Science ®Google Scholar
• Kac, M., Wiener and integration in function spaces. Bull. Amer. Math. Soc., 1966, 72(Number 1, Part 2), 52. doi: 10.1090/S0002-9904-1966-11463-5
   Google Scholar
• Kakushadze, Z., Path integral and asset pricing. Quant. Finance, 2015, 15(11), 1759. doi: 10.1080/14697688.2015.1052092
   Web of Science ®Google Scholar
• Karatzas, I. and Shreve, S., Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, 1991 (Springer: New York).
   Google Scholar
• Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets. EBL-Schweitzer, 2009 (World Scientific: Berlin).
   Google Scholar
• Lee, J., Capriotti, Wrong way risk done right. Risk, 2015, 30, 67.
   Google Scholar
• Li, M., Mercurio, F. and Resnick, S., The GARCH linear SDE. Risk, 2019, 34, 68.
   Google Scholar
• Linetsky, V., The path integral approach to financial modeling and options pricing. Comput. Econ., 1997, 11, 129. doi: 10.1023/A:1008658226761
   Google Scholar
• O'Kane, D., Modelling Single-name and Multi-name Credit Derivatives. The Wiley Finance Series, 2010 (Wiley: London). ISBN 9780470696767.
   Google Scholar
• Stehlíková, B. and Capriotti, L., An effective approximation for Zero-coupon bonds and Arrow-Debreu prices in the Black-Karasinski model. Int. J. Theoret. Appl. Finance, 2014, 17(06), 1. doi: 10.1142/S021902491450037X
   Google Scholar
• Tourrucôo, F., Hagan, P. and Schleiniger, G.F., Approximate formulas for Zero-coupon bonds. Appl. Math. Finance, 2007, 14, 107. doi: 10.1080/13504860600858204
   Google Scholar
• Vasicek, O.A., An equilibrium characterization of the term structure. J. Financ. Econ., 1977, 5, 177. doi: 10.1016/0304-405X(77)90016-2
   Web of Science ®Google Scholar
• Wiener, N., The average of an analytic functional. Proc. Natl. Acad. Sci., 1921a, 7(9), 253. doi: 10.1073/pnas.7.9.253
   PubMedGoogle Scholar
• Wiener, N., The average of an analytic functional and the Brownian movement. Proc. Natl. Acad. Sci., 1921b, 7(10), 294. doi: 10.1073/pnas.7.10.294
   PubMedGoogle Scholar