An analytical perturbative solution to the Merton Garman model using symmetries.

@article{Calmet2019AnAP,
  title={An analytical perturbative solution to the Merton Garman model using symmetries.},
  author={X. Calmet and N. Shaw},
  journal={arXiv: Pricing of Securities},
  year={2019}
}
  • X. Calmet, N. Shaw
  • Published 2019
  • Economics, Mathematics
  • arXiv: Pricing of Securities
In this paper, we introduce an analytical perturbative solution to the Merton Garman model. It is obtained by doing perturbation theory around the exact analytical solution of a model which possesses a two-dimensional Galilean symmetry. We compare our perturbative solution of the Merton Garman model to Monte Carlo simulations and find that our solutions performs surprisingly well for a wide range of parameters. We also show how to use symmetries to build option pricing models. Our results… Expand

Figures and Tables from this paper

References

SHOWING 1-10 OF 39 REFERENCES
A path integral approach to option pricing with stochastic volatility : Some exact results
  • 63
  • PDF
Introducing Spin in 2D Quantum Tunneling
  • 1
  • PDF
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
  • 7,658
  • PDF
Theory of Rational Option Pricing
  • 7,148
  • PDF
Maximum likelihood estimation of non-affine volatility processes
  • 24
...
1
2
3
4
...