An Orthogonal Series Expansions Method to Hedge and Price European-Type Options

Chan, Ron

doi:10.2139/ssrn.2852033

Cited by 5 publications

(5 citation statements)

References 49 publications

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“…where c 1 , c 2 , and c 4 are the first, second and fourth cumulants, respectively, of the stochastic process. For simple, less-complicated financial models, we also obtain closed-form formulas for c 1 , c 2 , and c 4 , which can be found in Chan (2017Chan ( , 2018 and Fang and Oosterlee (2009a,b). As Fang and Oosterlee (2009b) suggest, any maturity time longer than 0.1 years is acceptable, and thus we use L = 8 as an appropriate value for the Lévy processes considered.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In this section, we briefly revise the CFS option pricing formula for European options to prepare for pricing early-exercise options in the next section. For further details on applying the CFS method in pricing European options, we refer readers to Chan (2017).…”

Section: The Complex Fourier Series Pricing Formulae For European Optmentioning

confidence: 99%

“…In this paper, we extend the theory of the complex Fourier series (CFS) method-the full-range Fourier series-proposed by Chan (2017) to circumvent the aforementioned problems. We use the CFS method to price early-exercise options to demonstrate that the CFS method is better than the FFT method while requiring less computational cost and offering higher accuracy and is a more sensible method than the COS method for options with longer maturity.…”

Section: Introductionmentioning

confidence: 99%

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Hedging and pricing early-exercise options with complex fourier series expansion

Chan

2020

The North American Journal of Economics and Finance

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We introduce a new numerical method called the complex Fourier series (CFS) method proposed by Chan (2017) to price options with an early-exercise feature-American, Bermudan and discretely monitored barrier options-under exponential Lévy asset dynamics. This new method allows us to quickly and accurately compute the values of early-exercise options and their Greeks. We also provide an error analysis to demonstrate that, in many cases, we can achieve an exponential convergence rate in the pricing method as long as we choose the correct truncated computational interval. Our numerical analysis indicates that the CFS method is computationally more comparable or favourable than the methods currently available. Finally, the superiority of the CFS method is illustrated with real financial data by considering Standard & Poor's depositary receipts (SPDR) exchange-traded fund (ETF) on the S&P 500 R index options, which are American options traded

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Section: Numerical Resultsmentioning

confidence: 99%

Section: The Complex Fourier Series Pricing Formulae For European Optmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hedging and pricing early-exercise options with complex fourier series expansion

Chan

2020

The North American Journal of Economics and Finance

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“…Regarding the CFS expansion method, Chan [22] applied it to actuarial field for the first time, obtained the explicit pricing formula of European options, and proved the exponential convergence rate of this method. Chan [23] extended this method to the pricing calculation of price options with early movement characteristics under the index Lévy asset dynamics.…”

Section: Introductionmentioning

confidence: 99%

Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Huang

Liu

et al. 2021

Mathematics

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This paper considers the estimation of ruin probability in an insurance risk model with stochastic premium income. We first show that the ruin probability can be approximated by the complex Fourier series (CFS) expansion method. Then, we construct a nonparametric estimator of the ruin probability and analyze its convergence. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

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“…Another approach is to use Fourier series to expand a PDF in terms of a partial sum of orthogonal basis functions. The basis function can be complex an exponential, e.g., Chan (2016), or COS, e.g. Fang and Oosterlee (2009a), function.…”

Section: Introductionmentioning

confidence: 99%

Singular Fourier–Padé series expansion of European option prices

Chan

2018

Quantitative Finance

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We apply a new numerical method, the singular Fourier-Padé (SFP) method invented by Driscoll and Fornberg (2001, 2011), to price European-type options in Lévy and affine processes. The motivation behind this application is to reduce the inefficiency of current Fourier techniques when they are used to approximate piecewise continuous (non-smooth) probability density functions. When techniques such as fast Fourier transforms and Fourier series are applied to price and hedge options with non-smooth probability density functions, they cause the Gibbs phenomenon; accordingly, the techniques converge slowly for density functions with jumps in value or derivatives. This seriously adversely affects the efficiency and accuracy of these techniques. In this paper, we derive pricing formulae and their option Greeks using the SFP method to resolve the Gibbs phenomenon and restore the global spectral convergence rate. Moreover, we show that our method requires a small number of terms to yield fast error convergence, and it is able to accurately price any European-type option deep in/out of the money and with very long/short maturities. Furthermore, we conduct an error-bound analysis of the SFP method in option pricing. This new method performs favourably in numerical experiments compared with existing techniques.

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An Orthogonal Series Expansions Method to Hedge and Price European-Type Options

Cited by 5 publications

References 49 publications

Hedging and pricing early-exercise options with complex fourier series expansion

Hedging and pricing early-exercise options with complex fourier series expansion

Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Singular Fourier–Padé series expansion of European option prices

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