Sep
26

## FFT computation of option prices

The Black-Scholes formula, one of the major breakthroughs of modern finance, allows for an easy and fast computation of option prices. But some of its assumptions, like constant volatility or log-normal distribution of asset prices, do not find justification in the markets. More complex models, which take into account the empirical facts, often lead to more computations and this time burden can become a severe problem when computation of many option prices is required, e.g. in calibration of the implied volatility surface. To overcome this problem Carr and Madan (1999) developed a fast method to compute option prices for a whole range of strikes.

Fast Fourier transform (FFT) is applied for this purpose, the use of the FFT is motivated by two reasons. On the one hand, the algorithm offers a speed advantage. This effect is even boosted by the possibility of the pricing algorithm to calculate prices for a whole range of strikes. On the other hand, the cf of the log price is known and has a simple form for many models considered in literature, while the density is often not known in closed form.

Here is an sample Matlab file for FFT computation of option prices, http://www.theponytail.net/CCFEA/lect01/lect01fftoptionnormal.m.

wiki(Fast Fourier transform)

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Fast Fourier transform (FFT) is applied for this purpose, the use of the FFT is motivated by two reasons. On the one hand, the algorithm offers a speed advantage. This effect is even boosted by the possibility of the pricing algorithm to calculate prices for a whole range of strikes. On the other hand, the cf of the log price is known and has a simple form for many models considered in literature, while the density is often not known in closed form.

Here is an sample Matlab file for FFT computation of option prices, http://www.theponytail.net/CCFEA/lect01/lect01fftoptionnormal.m.

wiki(Fast Fourier transform)

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