On Two Transform Methods for the  Valuation of Contingent Claims

Nwozo, Chuma Raphael; Fadugba, Sunday Emmanuel

doi:10.4236/jmf.2015.52009

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…They also extended their results to derive the free boundary and the fundamental analytic valuation formula for perpetual American power put option. For mathematical backgrounds, sporadic applications of transform methods in financial contexts see [9]- [18] just to mention a few.…”

Section: Introductionmentioning

confidence: 99%

Valuation of European Call Options via the Fast Fourier Transform and the Improved Mellin Transform

Fadugba¹,

Nwozo²

2016

JMF

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This paper considers the valuation of European call options via the fast Fourier transform and the improved Mellin transform. The Fourier valuation techniques and Fourier inversion methods for density calculations add a versatile tool to the set of advanced techniques for pricing and management of financial derivatives. The Fast Fourier transform is a numerical approach for pricing options which utilizes the characteristic function of the underlying instrument's price process. The Mellin transform has the ability to reduce complicated functions by realization of its many properties. Mellin's transformation is closely related to an extended form of other popular transforms, particularly the Laplace transform and the Fourier transform. We consider the fast Fourier transform for the valuation of European call options. We also extend a framework based on the Mellin transforms and show how to modify the method to value European call options. We obtain a new integral equation to determine the price of European call by means of the improved Mellin transform. We show that our integral equation for the price of the European call option reduces to the Black-Scholes-Merton formula. The numerical results show that the tremendous speed of the fast Fourier transform allows option prices for a huge number of strikes to be evaluated very rapidly but the damping factor or the integrability parameter must be carefully chosen since it controls the intensity of the fluctuations and the magnitude of the functional values. The improved Mellin transform is more accurate than the fast Fourier transform, converges faster to the Black-Scholes-Merton model, provides accurate comparable prices and the approach can be regarded as a good alternative to existing methods for the valuation of European call option on a dividend paying stock.

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Section: Introductionmentioning

confidence: 99%

Valuation of European Call Options via the Fast Fourier Transform and the Improved Mellin Transform

Fadugba¹,

Nwozo²

2016

JMF

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On Deep-Fake Stock Prices and Why Investor Behavior Might Not Matter

2022

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We propose an agent-based model of financial markets with only one asset. Thirty-two agents follow very simple rules inspired by Wolfram’s Rule 110. They engage in buying, selling, and/or holding. Each agent is endowed with a starting balance sheet marked-to-market in each iteration. The simulation allows for margin calls for both buying and selling. During each iteration, the number of buy, hold, and sell positions is aggregated into a market price with the help of a simple, linear formula. The formula generates a price depending on the number of buy and sell positions. Various results are obtained by altering the pricing formula, the trading algorithm, and the initial conditions. When applying commonly used statistical tools, we find processes that are essentially indistinguishable from the price of real assets. They even display bubbles and crashes, just like real market data. Our model is remarkable because it can apparently generate a process of equivalent complexity to that of a real asset price, but it starts from a handful of initial conditions and a small number of very simple linear algorithms in which randomness plays no part. We contend our results have far-reaching implications for the debate around investor behavior and the regulation of financial markets.

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Alternative Approach for the Solution of the Black-Scholes Partial Differential Equation for European Call Option

Fadugba¹,

Ajayi²

2015

OALib

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In this paper we present an alternative approach for the solution of the Black-Scholes partial differential equation for European call option which pays dividend yield using the modified Mellin transform method. The approach used in this paper does not require variables transformation. We also extend the modified Mellin transform method for the valuation of European call option which pays dividend yield. The numerical results show that the modified Mellin transform is accurate, mutually consistent and agrees with the values of the Black-Scholes model.

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On Two Transform Methods for the Valuation of Contingent Claims

Cited by 3 publications

References 19 publications

Valuation of European Call Options via the Fast Fourier Transform and the Improved Mellin Transform

Valuation of European Call Options via the Fast Fourier Transform and the Improved Mellin Transform

On Deep-Fake Stock Prices and Why Investor Behavior Might Not Matter

Alternative Approach for the Solution of the Black-Scholes Partial Differential Equation for European Call Option

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