We study the price of Asian options with floating-strike when the underlying asset price follows a Markov-modulated (or regime-switching ) geometric Brownian motion and both the interest rate and diffusion coefficient depend on an independent continuous-time finite-state Markov chain. We propose an iterative procedure that converges to the option prices without recourse to solving a coupled PDE system. The method can also be applied to fixed-strike Asian options. Our approach makes use of path properties of Brownian motion and the Fixed-Point Theorem .
We characterize the price of an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the underlying asset price, namely the interest rate and the volatility, to model sudden exogenous events in the economy. Asian options are particularly interesting because the payoff depends on the integrated asset price. We study the case of both floating- and fixed-strike Asian call options with arithmetic averaging when the asset follows a regime-switching geometric Brownian motion with coefficients that depend on a Markov chain. The typical approach to finding the value of a financial option is to solve an associated system of coupled partial differential equations. Alternatively, we propose an iterative procedure that converges to the value of this contract with geometric rate using a classical fixed-point theorem .
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an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the underlying asset price, namely the interest rate and the volatility, to model sudden exogenous events in the economy. Asian options are particularly interesting because the payoff depends on the integrated asset price. We study the case of both floating- and fixed-strike Asian call options with arithmetic averaging when the asset follows a
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and both the interest rate and diffusion coefficient depend on an independent continuous-time finite-state
with coefficients that depend on a
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The typical approach to finding the value of a financial option is to solve an associated system of coupled partial differential equations. Alternatively, we
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option prices without recourse to solving a coupled PDE system. The method can also be applied to fixed-strike Asian options. Our approach makes use of path properties of Brownian motion and the Fixed-Point Theorem
value of this contract with geometric rate using a classical fixed-point theorem