Fourier Transform Methods for Heston Option Pricing

Summary

The document asks for a more accessible derivation of the semi-closed-form price of a European call under the Heston stochastic-volatility model. It does not derive the pricing formula itself; instead, the replies point readers toward a paper with a derivation in an appendix and an explanation of Fourier-transform option pricing that includes Heston among several models. A book on option valuation under stochastic volatility is also suggested.

The substance is therefore a short guide to learning resources and the Fourier-transform approach to pricing under stochastic volatility. The replies do not compare the sources in detail, reproduce assumptions or equations, or provide numerical evidence. One respondent explicitly cannot guarantee the cited derivation is error-free, so readers should verify the derivation and model conventions in the original references.

Key ideas

• The question concerns deriving the semi-closed-form European call price under the Heston model.
• A reply recommends an appendix containing a relatively direct derivation, with an explicit caveat about possible errors.
• Fourier-transform methods are identified as a way to explain option pricing under Heston and other models.
• The document points to further reading but contains no derivation, numerical results, or source comparison.

Tags

# Option Prices under the Heston Stochastic Volatility Model


# Option Prices under the Heston Stochastic Volatility Model












I was wondering if anyone has come across a more straightforward derivation of the semi-closed form solution for the price of a european call under the Heston model than the one proposed by Heston (1993) ?

## Answer by sets (score 2)

https://quant.stackexchange.com/a/16387

I cannot guarantee that it is error-free, but this paper (appendix A) has a relatively straightforward derivation of the Heston price for a european call.

## Answer by Mark Joshi (score 1)

https://quant.stackexchange.com/a/15216

I try to give what I at any rate think is a clear explanation of the Fourier transform approach to option pricing for various models including Heston in More Mathematical Finance.

You could also try Lewis's book Option Valuation Under Stochastic Volatility.

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