On the Data-Driven COS Method

Rodriguez, Alvaro Leitao; Oosterlee, Cornelis W.; Ortiz-Gracia, Luis; Bohté, Sander M.

doi:10.2139/ssrn.2917536

Cited by 2 publications

(3 citation statements)

References 34 publications

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“…In order to illustrate the performance and efficiency of the method we start with the assumption that the underlying asset price process S t follows the GBM process and then apply the MOL to compute the value of certain types of European options, a basic European call option, a powered option, and finally a cash-or-nothing option; all of which are special cases of the standard Bermudan option defined earlier, where the number of exercise opportunities, E, is set to one. We then report results for a Bermudan put option and numerically study its convergence when an increasing number of spatial grid points are used 2 . The following parameters are used throughout for the European styled options: σ = 0.3, r = 0.03 , initial stock price S 0 = 100, strike price K = 100 and T = 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…When fast and accurate evaluation of the option price is the objective, the Fourier based methods are commonly used numerical techniques. Some of the proposed Fourier based pricing methods include the COS method [1], data-driven COS [2], and fast Fourier transform-based approach [3]. Monte Carlo based schemes are popular for pricing the early exercise options under multidimensional stochastic processes.…”

Section: Introductionmentioning

confidence: 99%

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Method of lines for valuation and sensitivities of Bermudan options

Banerjee¹,

Murthy²,

Jain³

2021

Preprint

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In this paper, we present a computationally efficient technique based on the Method of Lines (MOL) for the approximation of the Bermudan option values via the associated partial differential equations (PDEs). The MOL converts the Black Scholes PDE to a system of ordinary differential equations (ODEs). The solution of the system of ODEs so obtained only requires spatial discretization and avoids discretization in time. Additionally, the exact solution of the ODEs can be obtained efficiently using the exponential matrix operation, making the method computationally attractive and straightforward to implement. An essential advantage of the proposed approach is that the associated Greeks can be computed with minimal additional computations. We illustrate, through numerical experiments, the efficacy of the proposed method in pricing and computation of the sensitivities for a European call, cash-or-nothing, powered option, and Bermudan put option.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Method of lines for valuation and sensitivities of Bermudan options

Banerjee¹,

Murthy²,

Jain³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…When fast and accurate evaluation of the option price is the objective, the Fourier-based methods are commonly used numerical techniques. Some of the proposed Fourier-based pricing methods include the Fourier-Cosine method (Fang & Oosterlee, 2009),data-driven Fourier-Cosine method (Leitao Rodriguez et al, 2017), and fast Fourier transformbased approach (Carr & Madan, 1999). Monte Carlo based schemes are popular for pricing the early exercise options under multidimensional stochastic processes.…”

Section: Introductionmentioning

confidence: 99%

Method of Lines for Valuation and Sensitivities of Bermudan Options

2022

View full text Add to dashboard Cite

In this paper, we present a computationally efficient technique based on the Method of Lines for the approximation of the Bermudan option values via the associated partial differential equations. The method of lines converts the Black Scholes partial differential equation to a system of ordinary differential equations. The solution of the system of ordinary differential equations so obtained only requires spatial discretization and avoids discretization in time. Additionally, the exact solution of the ordinary differential equations can be obtained efficiently using the exponential matrix operation, making the method computationally attractive and straightforward to implement. An essential advantage of the proposed approach is that the associated Greeks can be computed with minimal additional computations. We illustrate, through numerical experiments, the efficacy of the proposed method in pricing and computation of the sensitivities for a European call, cash-or-nothing, powered option, and Bermudan put option.

show abstract

On the Data-Driven COS Method

Cited by 2 publications

References 34 publications

Method of lines for valuation and sensitivities of Bermudan options

Method of lines for valuation and sensitivities of Bermudan options

Method of Lines for Valuation and Sensitivities of Bermudan Options

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