The Evaluation of Financial Assets with Autocorrelations in Returns

Jegors Fjodorovs, Andrejs Matvejevs, Aigars Egle

Abstract


In this paper, we will describe an analytical solution to a problem of pricing financial assets with autocorrelations in returns. We will develop a continuous diffusion model for the case of autocorrelation in stock returns, obtain the European call option pricing formula written on a stock with autocorrelation in returns and show that even small levels of predictability due to autocorrelation can give a substantial deviation from the results obtained by Black-Sholes formula. Also, we will calculate the modified sensitivities of the value of European call option and show how in risk management widely used option hedging parameters depend on assumptions made about correlation in underlying asset returns. Finally, we will show convergence time for the stationary solution of the derived continuous diffusion model and test its distribution.


Keywords:
ARCH models; Black–Scholes model; discrete time stochastic difference equation systems; Markov chain; option Greeks

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References


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