Option valuation using the fast Fourier transform

@article{Carr1999OptionVU,
  title={Option valuation using the fast Fourier transform},
  author={Peter Carr and Dilip B. Madan},
  journal={Journal of Computational Finance},
  year={1999},
  volume={2},
  pages={61-73}
}
This paper shows how the fast Fourier Transform may be used to value options when the characteristic function of the return is known analytically. 

Figures and Tables from this paper

Fast Fourier Transform and Option Pricing

This article is a concise introduction to applications of Fourier transform and FFT in option pricing.

Fourier-Based Approach for Power Options Valuation

This study price options whose underlying asset is raised to a constant using the Fourier-Cosine (COS) method, where numerical experiments show that the COS method is more efficient than other known option pricing techniques.

Radial basis function methods for pricing multi-asset options

The price of an option can under some assumptions be determined by the solution of the Black–Scholes partial differential equation. Often options are issued on more than one asset. In this case it ...

Option Pricing: Theory and Numerical Methods

In this article we will describe models, theory, and numerical methods for pricing derivative securities.

Options Pricing Efficiency with Fractional Fast Fourier Transform

The global minimization algorithms are adapted to calibrate the parameter based on the characteristic function and the Fractional Fast Fourier Transform and it is found the option pricing efficiency of Variance Gamma outperform Black-Sholes model.

Pricing Options Under Stochastic Volatility with Fourier-Cosine Series Expansions

An option pricing method for European options based on the Fouriercosine series, called the COS method, is presented. It can cover underlying asset processes for which the characteristic function is

Closed Formulas for the Price and Sensitivities of a Vanilla European Option Under a Jump Diffusion Model

We derive closed formulas for the prices of European options and their sensitivities when the underlying asset follows a jump diffusion model.

Pricing Extendible Options Using the Fast Fourier Transform

The valuation of the extendible options is determined as sums of expectations of indicator functions, leading to a semianalytic expression for the value of the options over a range of strikes.

Pricing Bermudan Options in Lévy Process Models

A Hilbert transform method for pricing Bermudan options in Levy process models is presented and the corresponding optimal stopping problem can be solved using a backward induction.
...

References

SHOWING 1-10 OF 19 REFERENCES

Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods

Fast closed form solutions for prices on European stock options are developed in a jump‐diffusion model with stochastic volatility and stochastic interest rates. The probability functions in the

A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and

Pricing Interest Rate Options in a Two-Factor Cox–Ingersoll–Ross model of the Term Structure

Solutions are presented for prices on interest rate options in a two-factor version of the Cox-Ingersoll-Ross model of the term structure. Specific solutions are developed for caps on floating

Spanning and Derivative-Security Valuation

This paper proposes a methodology for the valuation of contingent securities. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans

ASSET PRICES ARE BROWNIAN MOTION: ONLY IN BUSINESS TIME

AbstractThis paper argues that asset price processes arising from market clearing conditions should be modeled as pure jump processes, with no continuous martingale component. However, we show that

An Alternative Valuation Model for Contingent Claims

The fundamental valuation equation of Cox, Ingersoll and Ross was expressed in terms of the indirect utility of wealth function. As closed-form solution for the indirect utility is generally

Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options

An efficient method is developed for pricing American options on combination stochastic volatility/jump-diffusion processes when jump risk and volatility risk are systematic and nondiversifiable,

The Variance Gamma (V.G.) Model for Share Market Returns

A new stochastic process, termed the variance gamma process, is proposed as a model for the uncertainty underlying security prices. The unit period distribution is normal conditional on a variance

The Pricing of Options and Corporate Liabilities

If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this

The Variance Gamma Process and Option Pricing

A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. Theprocess is obtained by