Finding the derivative price using the Vasicek model with multidimensional stochastic volatility
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DOIhttp://dx.doi.org/10.21511/dm.17(4).2019.02
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Article InfoVolume 17 2019, Issue #4, pp. 19-30
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Methods of calculating the approximate price of options using instruments of spectral analysis, singular and regular wave theory in the context of influence of fast and slow acting factors are developed. By combining methods from the spectral theory of singular and regular disturbances, one can approximate the price of derivative financial instruments as a schedule of its own functions. The article uses the theory of spectral analysis and the singular and regular theory of perturbations, which are applied to the short-term interest rates described by the Vasicek model with multidimensional stochastic volatility. The approximate price of derivatives and their profitability are calculated. Applying the Sturm-Liouville theory, the Fredholm alternative, and the analysis of singular and regular disturbances in different time scales, explicit formulas were obtained for the approximation of bond prices and yields based on the development of their own functions and eigenvalues of self-adjoint operators using boundary value problems for singular and regular perturbations. The theorem for estimating the accuracy of derivatives price approximation is established. Such a technique, in contrast to existing ones, makes it possible to study the stock market dynamics and to monitor the financial flows in the market. This greatly facilitates the statistical evaluation of their parameters in the process of monitoring the derivatives pricing and the study of volatility behavior for the profitability analysis and taking strategic management decisions on the stock market transactions.
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JEL Classification (Paper profile tab)C65, G11, G13
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References16
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Tables0
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- Black, F., & Scholes M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-659.
- Borodin, A., & Salminen, P. (2002). Handbook of Brownian motion: facts and formulae. Birkhauser.
- Brennan, M., & Schwartz, E. (1979). A continuous time approach to the pricing of bonds. Journal of banking and finance, 3, 133-155.
- Burtnyak, І., & Malytska, A. (2018). Spectral study of options based on CEV model with multidimensional volatility. Investment Management and Financial Innovations, 15(1), 18-25.
- Burtnyak, І., & Malytska, A. (2018). Taylor expansion for derivative securities pricing as a precondition for strategic market decisions. Problems and Perspectives in Management, 16(1), 224-231.
- Burtnyak, І., & Malytska, A. (2018). Application of the spectral theory and perturbation theory to the study of Ornstein-Uhlenbesck processes. Carpathian Math. Publ, 10(2), 273–287.
- Cox, J., Ingersoll, J., & Ross, S. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385-408.
- Gorovoi, V., & Linetsky, V. (2004). Black’s model of interest rates as options, eigenfunction expansions and japanese interest rates. Mathematical finance, 14(1), 49-78.
- Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. The Journal of Finance, 42(2), 281-300.
- Kumar, R. (2015). Effect of volatility clustering on indifference pricing of options by convex risk measures. Applied Mathematical Finance, 22(1), 63-82.
- Lewis, A. (1998). Applications of eigenfunction expansions in continuoustime finance. Mathematical Finance, 8, 349-383.
- Linetsky, V. (2004). The spectral decomposition of the option value. International Journal of Theoretical and Applied Finance, 7(3), 337-384.
- Linetsky, V. (2007). Chapter 6 spectral methods in derivatives pricing. In Birge, J. R., & Linetsky, V. (Eds.). Financial engineering. Volume 15 of handbooks in operations research and management science (pp. 223-299).
- Lorig, M. (2014). Pricing derivatives on multiscale diffusions: an eigenfunction expansion approach. Mathematical Finance, 24(2), 331-363.
- Merton, R. (1973). Theory of rational option pricing. Bell journal of economics and management science, 4, 141-183.
- Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177-188.