Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boun...Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boundary value problems to be found at just one point, if required (with associated saving in computation), whereas deterministic methods necessarily find the solution at large number of points simultaneously. This property can be particularly useful in problems such option pricing, where the value of an option is required only at the time of striking, and for the state of the market at that time. In this work we consider a European multi-asset options which mathematically described by the system of stochastic differential equations. We will apply Monte Carlo method for the solution of that system which is the price of Multi-asset rainbow options.展开更多
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-asse...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.展开更多
文摘Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boundary value problems to be found at just one point, if required (with associated saving in computation), whereas deterministic methods necessarily find the solution at large number of points simultaneously. This property can be particularly useful in problems such option pricing, where the value of an option is required only at the time of striking, and for the state of the market at that time. In this work we consider a European multi-asset options which mathematically described by the system of stochastic differential equations. We will apply Monte Carlo method for the solution of that system which is the price of Multi-asset rainbow options.
文摘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.
