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The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
1-7
Received:
19 July 2014
Accepted:
5 August 2014
Published:
5 August 2014
Abstract: This paper presents the Mellin transform method as an alternative analytic solution for the valuation of geometric Asian option. Asian options are options in which the variable is the average price over a period of time. The analytical solution of the Black-Scholes partial differential equation for Asian option is known as an explicit formula, this is due to the fact that the geometric average of a set of lognormal random variables is lognormally distributed. We derive a closed form solution for a continuous geometric Asian option by means of the partial differential equations. We also provide an alternative method for solving geometric Asian options partial differential equations using the Mellin transform method.
Abstract: This paper presents the Mellin transform method as an alternative analytic solution for the valuation of geometric Asian option. Asian options are options in which the variable is the average price over a period of time. The analytical solution of the Black-Scholes partial differential equation for Asian option is known as an explicit formula, this...
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On Hybrid Model for the Valuation of Credit Risk
Fadugba Sunday Emmanuel,
Edogbanya Olaronke Helen
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
8-11
Received:
1 August 2014
Accepted:
6 August 2014
Published:
13 August 2014
Abstract: This paper presents hybrid model for the valuation of credit risk. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. It is closely tied to the potential return of investment, the most notable being that the yields on bonds correlate strongly to their perceived credit risk. Hybrid model combines the structural and intensity-based approaches. While avoiding their difficulties, it picks the best features of both approaches; the economic and intuitive appeal of the structural approach and the tractability and empirical fit of the intensity-based approach. In credit derivatives market there are quite a few securities that depend on more than one source of risk, like corporate bonds and convertible bonds, most attractive credit models should involve all these three sources of risk, and interest-rate risk. Our framework brings together these standard block.
Abstract: This paper presents hybrid model for the valuation of credit risk. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. It is closely tied to the potential return of investment, the most notable being that the yields on bonds correlate strongly to their perceived credit risk. Hybrid model combines the ...
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On Martingales and the Use of Optional Stopping Theorem to Determine the Mean and Variance of a Stopping Time
Ganiyu,
A. A.,
Fakunle,
I.
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
12-17
Received:
1 August 2014
Accepted:
6 August 2014
Published:
5 September 2014
Abstract: This paper examines the roles martingale property played in the use of optional stopping theorem (OST). It also examines the implication of this property in the use of optional stopping theorem for the determination of mean and variance of a stopping time. A simple example relating to betting system of a gambler with limited amount of money has been provided. The analysis of the betting system showed that the gambler leaves with the same amount of money as when he started and therefore satisfied martingale property. Linearity of expectation property was used as a reliable tool in the use of the martingale property.
Abstract: This paper examines the roles martingale property played in the use of optional stopping theorem (OST). It also examines the implication of this property in the use of optional stopping theorem for the determination of mean and variance of a stopping time. A simple example relating to betting system of a gambler with limited amount of money has bee...
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Performance Measure of Binomial Model for Pricing American and European Options
Fadugba Sunday Emmanuel,
Ajayi Olayinka Adedoyin,
Okedele Olanrewaju Hammed
Issue:
Volume 3, Issue 6-1, December 2014
Pages:
18-30
Received:
28 September 2014
Accepted:
6 October 2014
Published:
20 October 2014
Abstract: Binomial model is a powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes model and other option pricing models that require solutions to stochastic differential equations, the binomial option pricing model is mathematically simple. It is based on the assumption of no arbitrage. The assumption of no arbitrage implies that all risk-free investments earn the risk-free rate of return and no investment opportunities exists that requires zero amount of investment but yield positive returns. It is the activity of many individuals operating within the context of financial market that, in fact, upholds these conditions. The activities of the arbitrageurs or speculators are often maligned in the media, but their activities insure that financial markets work. They insure that financial assets such as options are priced within a narrow tolerance of their theoretical values. In this paper we use binomial model to derive the Black-Scholes equation using the risk-neutral expectation formula. We also use binomial model for the valuation of European and American options. Lastly, the primary reason why the binomial model is used is its flexibility compared to the Black-Scholes model and it is also used to price a wide variety of options.
Abstract: Binomial model is a powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes model and other option pricing models that require solutions to stochastic differential equations, the binomial option pricing model is mathematically simple. It is based on the assumption of no arbitrage. The assu...
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