scholarly journals Finding the derivative price using the Vasicek model with multidimensional stochastic volatility

2020 ◽  
Vol 17 (4) ◽  
pp. 19-30
Author(s):  
Ivan Burtnyak ◽  
Anna Malytska
Keyword(s):  
Spectral Analysis ◽  
Stock Market ◽  
Interest Rates ◽  
Stochastic Volatility ◽  
Wave Theory ◽  
Liouville Theory ◽  
Fredholm Alternative ◽  
Vasicek Model ◽  
Financial Flows ◽  
Profitability Analysis

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.

scholarly journals Modelling of derivatives pricing using methods of spectral analysis

2020 ◽  
Vol 7 (3) ◽  
pp. 128-136
Author(s):  
Ivan Burtnyak ◽  
Anna Malytska
Keyword(s):  
Spectral Analysis ◽  
Stock Market ◽  
Spectral Theory ◽  
Asset Price ◽  
Analytical Formula ◽  
Wave Theory ◽  
Financial Instruments ◽  
Derivatives Pricing ◽  
Financial Flows ◽  
Adjoint Operators

In this article expands the method of finding the approximate price for a wide class of derivative financial instruments. Using the spectral theory of self-adjoint operators in Hilbert space and the wave theory of singular and regular perturbations, the analytical formula of the approximate asset price is established. Methods for calculating the approximate price of options using the tools of spectral analysis, singular and regular wave theory in the case of fast and slow factors are developed. Combining methods from the spectral theory of singular and regular perturbations, it is possible to estimate the price of derivative financial instruments as a schedule by eigenfunctions. The approximate value of securities and their rate of return are calculated. Applying the theory of Sturm-Liouville, Fredholm’s alternative and analysis of singular and regular perturbations at different time scales have enabled us to obtain explicit formulas for the approximate value of securities and their yield on the basis of the development of their eigenfunctions and eigenvalues of self-adjoint operators using boundary value problems for singular and regular perturbations. The theorem of closeness estimates for bond prices approximation is proved. An algorithm for calculating the approximate price of derivatives and the accuracy of estimates has been developed, which allows to analyze and draw precautionary conclusions and suggestions to minimize the risks of pricing derivatives that arise in the stock market. A model for finding the value of derivatives corresponding to the dynamics of the stock market and the size of financial flows has been developed. This model allows you to find the prices of derivatives and their volatility, as well as minimize speculative changes in pricing, analyze the progress of stock market processes and take concrete steps to improve the situation to optimize financial strategies. The used methodology of European options pricing based on the study of volatility behavior and analysis of the yield of financial instruments allows to increase the accuracy of the forecast and make sound management strategic decisions by stock market participants.

scholarly journals South Africa’s economic response to monetary policy uncertainty

2017 ◽  
Vol 44 (2) ◽  
pp. 282-293 ◽  
Author(s):  
Mehmet Balcilar ◽  
Rangan Gupta ◽  
Charl Jooste
Keyword(s):  
Monetary Policy ◽  
Interest Rates ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Economic Consequences ◽  
Policy Uncertainty ◽  
Dsge Model ◽  
Content Type ◽  
Volatility Model ◽  
Central Bankers

Purpose The purpose of this paper is to study the evolution of monetary policy uncertainty and its impact on the South African economy. Design/methodology/approach The authors use a sign restricted SVAR with an endogenous feedback of stochastic volatility to evaluate the sign and size of uncertainty shocks. The authors use a nonlinear DSGE model to gain deeper insights about the transmission mechanism of monetary policy uncertainty. Findings The authors show that monetary policy volatility is high and constant. Both inflation and interest rates decline in response to uncertainty. Output rebounds quickly after a contemporaneous decrease. The DSGE model shows that the size of the uncertainty shock matters – high uncertainty can lead to a severe contraction in output, inflation and interest rates. Research limitations/implications The authors model only a few variables in the SVAR – thus missing perhaps other possible channels of shock transmission. Practical implications There is a lesson for monetary policy: monetary policy uncertainty, in isolation from general macroeconomic uncertainty, often creates unintended adverse consequences and can perpetuate a weak economic environment. The tasks of central bankers are incredibly difficult. Their models project output and inflation with relatively large uncertainty based on many shocks emanating from various sources. It matters how central bankers react to these expectations and how they communicate the underlying risks associated with setting interest rates. Originality/value This is the first study that looks into monetary policy uncertainty into South Africa using a stochastic volatility model and a nonlinear DSGE model. The results should be very useful for the Central Bank as it highlights how uncertainty, that they create, can have adverse economic consequences.

scholarly journals PERHITUNGAN PREMI ASURANSI JOINT LIFE DENGAN MODEL VASICEK DAN CIR

2019 ◽  
Vol 8 (3) ◽  
pp. 246
Author(s):  
I MADE WAHYU WIGUNA ◽  
KETUT JAYANEGARA ◽  
I NYOMAN WIDANA
Keyword(s):  
Stochastic Process ◽  
Interest Rates ◽  
Life Insurance ◽  
Insurance Premium ◽  
Insurance Contract ◽  
Insurance Company ◽  
Vasicek Model ◽  
Cir Model ◽  
Premium Payment ◽  
Premium Price

Premium is a sum of money that must be paid by insurance participants to insurance company, based on  insurance contract. Premium payment are affected by interest rates. The interest rates change according to stochastic process. The purpose of this work is to calculate the price of joint life insurance premiums with Vasicek and CIR models. The price of a joint life insurance premium with Vasicek and CIR models, at the age of the insured 35 and 30 years has increased until the last year of the contract. The price of a joint life insurance premium with Vasicek model is more expensive than the premium price using CIR model.

Spectral analysis of stock market prices

1979 ◽  
Vol 3 (2) ◽  
pp. 201-208 ◽  
Author(s):  
Marc L. Bertoneche
Keyword(s):  
Spectral Analysis ◽  
Stock Market ◽  
Market Prices
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