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A Framework for Derivative Pricing in the Fractional Black-Scholes Market
-- Ciprian Necula
This paper aims at developing a framework for evaluating derivatives if the underlying clause of the
derivative contract is supposedly driven by a fractional Brownian motion (fBm) with Hurst parameter greater than
0.5. For this purpose, some results regarding the quasi-conditional expectation, especially the behavior to
a Girsanov transform, are proved. The risk-neutral valuation formula and the fundamental evaluation
equation in the case of the fractional Black-Scholes (BS) market, are then obtained.
© 2009 IUP. All Rights Reserved.
Derivatives Hedging: SASOL (Pty) Ltd. as an Example
-- Tumellano Sebehela
The empirical study analyzes derivative hedging strategies that can be implemented for an investor who
has been holding SASOL (Pty) Ltd.'s stocks before February 1999, in relation to that of Johannesburg
Securities Exchange (JSE) Top 40 Index. Moreover, as the relationship between SASOL's stock and the JSE Top 40
Index changes, this empirical report recommends a different derivative hedging strategy based on calculations
and the relationship of the two variables—SASOL (Pty) Ltd. and the JSE Top 40 Index. A correct execution of
a derivative hedging strategy does not mean that no losses will be incurred, but that ideally, the overall
net position of the derivative hedging strategy should be positive. Each investment portfolio needs a
tailor-made derivative strategy that fits it well. Furthermore, for hedging strategy to work well, it needs proper
monitoring by a skilled professional.
© 2009 IUP. All Rights Reserved.
Monitoring the Upsurge of Biofuels in Commodity Futures Markets
-- Takashi Kanamura
The paper investigates the interaction between energy futures and agriculture commodity futures
prices, focusing on the recent upsurge of biofuels. The correlation model of price returns between energy and
agriculture is proposed here. Empirical studies on the DJ-AIG (Dow Jones AIG) commodity indices document that
the increase of correlations between energy and grain price returns occurs during high energy price
periods, which supports the correlation model. By using petroleum as energy, and soybean and soybean oil as
biofuels, the paper observes that there is a sharp rise in the correlations after 2004. In addition, the
relationship between petroleum and the three agricultural sources of bioethanol—sugar, wheat, and corn—has
been examined here.
© 2009 IUP. All Rights Reserved.
Pricing Basket Credit Default Swap: An Empirically-Based Simulation Study
-- Fathi Abid and Nader Naifar
This paper deals with the impact of structure of dependency and the choice of procedures for
rare-event simulation, on the pricing of multi-name credit derivatives such as basket credit default swap. A
copula-based simulation procedure for pricing basket credit default swaps, under different structure of
dependency, is presented here. The choice of copula and procedures for rare-event simulation govern the pricing of
the basket credit default swap. Alternatives to the Gaussian copula are the Clayton copula and
t-student copula under importance sampling procedures for simulation, which capture the dependence structure between
the underlying variables at extreme values and certain values of the input random variables in a simulation,
and have more impact, than others, on the parameter being estimated.
© 2009 IUP. All Rights Reserved.
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