Abstract
A Fast Fourier transform approach has been presented by Carr & Madan (2009) on a single underlying asset. In this current research paper, we present fast Fourier transform algorithm for the valuation of Multi-asset Options under Economic Recession Induced Uncertainties. The issue of multi-dimension in both finite and infinite case of Options is part of the focus of this research. The notion of economic recession was incorporated. An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of economic recession compared to the period of recession-free. Nigeria economic recession outbreak in 2016 and its effects on the uncertainty of the payoffs of Nigeria Stocks Exchange (NSE) among other investments was among the motivating factors for proposing economic recession induced volatility in options pricing. The application of the proposed Fast Fourier Transform algorithm in handling multi-assets options was shown. A new result on options pricing was achieved and capable of yielding efficient option prices during and out of recession. Numerical results were presented on assets in 3-dimensions as an illustration taking Black Scholes prices as a bench mark for method effectiveness comparison. The key findings of this research paper among other crucial contributions could be seen in computational procedure of options valuation in multi-dimensions and uncertainties in options payoffs under the exposure of economic recession.
Highlights
An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of economic recession compared to the period of recession-free
Fast Fourier Transform algorithm for valuation of multi-assets in both finite and infinite dimension was presented in this research work
An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of Economic recession compared to the period of normalcy
Summary
The focus of most researchers is limited to two dimensions in the valuation of multi-asset options Some authors such as Yuwei Chen [3] gave their formulation in terms of Black Scholes Partial Differential Equation (PDE) and considered numerical method for obtaining the prices. We gave a framework for extending Carr & Madan [6] Fast Fourier Transform approach of valuating an option on a single underlying asset to valuation of multi-assets options. Our major contribution is seen in valuation of multi-assets option in both finite and infinite dimensions and incorporation of economic recession factor on the volatility of assets during the state of economic recession.
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