Mellin Transform Method for the Valuation of Some Vanilla Power Options With Non-Dividend Yield

Nwozo, Chuma Raphael; Fadugba, Sunday Emmanuel

doi:10.12732/ijpam.v96i1.7

Cited by 10 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 2.2. The fundamental operational properties of the Mellin transforms such as scaling, shifting, derivatives, integrals, convolution, multiplicative convolution and Parseval's formula are well detailed in [9,12,17,18].…”

Section: Mellin Transformmentioning

confidence: 99%

Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function

Fadugba¹,

Adeniji²,

Kekana³

et al. 2022

Int. J. Anal. Appl.

View full text Add to dashboard Cite

This paper proposes a framework based on the celebrated transform of Mellin type (MT) for the direct solution of the Black-Scholes-Merton European Put Option Model (BSMEPOM) on Dividend Yield (DY) with Modified-Log Payoff Function (MLPF) under the geometric Brownian motion. The focal goal of this paper is to use MT to obtain a valuation formula for the European Put Option (EPO) which pays a DY with MLPF. By means of the MT and its inversion formula, the price of EPO on DY was expressed in terms of integral equation. The valuation formula of EPO was obtained with the help of the convolution property of MT and final time condition. MT was tested on an illustrative example in order to measure its performance, effectiveness and suitability. The MLPF was compared with other existing payoff functions. Hence, the effect of DY on the pricing of EPO with MLPF was also investigated.

show abstract

Section: Mellin Transformmentioning

confidence: 99%

Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function

Fadugba¹,

Adeniji²,

Kekana³

et al. 2022

Int. J. Anal. Appl.

View full text Add to dashboard Cite

show abstract

“…Standard arbitrage arguments show that any derivative ( ) , t u S t written on t S must satisfy the partial differential equation [19]. Theorem 1 [15]: Let n t S denote the price of the underlying asset, 0 σ > the volatility, r the riskless interest rate, n the power of the option, q the dividend yield and t W the Wiener process. If the underlying price of the asset n t S follows a random process (Geometric Wiener process) in…”

Section: Black-scholes-merton-like Valuation Formulamentioning

confidence: 99%

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

Fadugba¹,

Nwozo²

2016

JMF

View full text Add to dashboard Cite

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.

show abstract

“…• The first term in (20) is the integral representation for the price of the European power put option (stems from the minimum guaranteed payoff of the American power put) which pays no dividend yield (see [4]).…”

Section: American Power Put Option With Non-dividend Yieldmentioning

confidence: 99%

“…Mellin transforms in option theory were introduced by [2], [3] extended the results obtained in [2] and showed how the Mellin transform approach could be used to derive the valuation formula for the perpetual American put options on dividend-paying stocks. [4] considered the Mellin transform method for the valuation of some vanilla power options with non-dividend yield. They derived the fundamental valuation formula known as the Black-Scholes model using the convolution property of the Mellin transform method.…”

Section: Introductionmentioning

confidence: 99%

Mellin Transform Method for the Valuation of the American Power Put Option with Non-Dividend and Dividend Yields

Fadugba¹,

Nwozo²

2015

JMF

View full text Add to dashboard Cite

In this paper we present the Mellin transform method for the valuation of the American power put option with non-dividend and dividend yields, respectively. We use the Mellin transform method to derive the integral representations for the price and the free boundary of the American power put option. We also extend our results to derive the free boundary and the fundamental analytic valuation formula for perpetual American power put option which has no expiry date. Numerical experiments have shown that the Mellin transform method is a better alternative technique compared to the binomial model (BSM), recursive method (RM) and finite difference method (FDM) for the valuation of the American power put option. In general, the Mellin transform method is accurate, flexible and produces accurate prices for the optimal exercise boundary of the American power put option for a wide range of parameters. Hence the Mellin transform method is mutually consistent and agrees with the values of the analytic option valuation formula called the "Black-Scholes model".

show abstract

Mellin Transform Method for the Valuation of Some Vanilla Power Options With Non-Dividend Yield

Cited by 10 publications

References 11 publications

Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function

Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function

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

Mellin Transform Method for the Valuation of the American Power Put Option with Non-Dividend and Dividend Yields

Contact Info

Product

Resources

About