Brownian-laplace Motion and Its Use in Financial Modelling
نویسنده
چکیده
Brownian-Laplace motion is a Lévy process which has both continuous (Brownian) and discontinuous (Laplace motion) components. The increments of the process follow a generalized normal Laplace (GNL) distribution which exhibits positive kurtosis and can be either symmetrical or exhibit skewness. The degree of kurtosis in the increments increases as the time between observations decreases. This and other properties render Brownian-Laplace motion a good candidate model for the motion of logarithmic stock prices. An option pricing formula for European call options is derived and it is used to calculate numerically the value of such an option both using nominal parameter values (to explore its dependence upon them) and those obtained as estimates from real stock price data.
منابع مشابه
The Normal-Laplace Distribution and its Relatives
The normal-Laplace (NL) distribution results from convolving independent normally distributed and Laplace distributed components. It is the distribution of the stopped state of a Brownian motion with normally distributed starting value if the stopping hazard rate is constant. Properties of the NL distribution discussed in the article include its shape and tail behaviour (fatter than the normal)...
متن کاملGeneralised Lévy Processes and their Applications in Insurance and Finance
For insurance risks, jump processes such as homogeneous/non-homogeneous Poisson process and Cox process have been used . In financial modelling, it has been observed that diffusion models are not robust enough to capture the appearance of jumps in underlying asset prices and interest rates. As a result, generalised Lévy processes, which are simply speaking, the combinations of Poisson process a...
متن کاملFractional Laplace Motion
Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional dist...
متن کاملAsymptotic Results for Renewal Risk Models with Risky Investments
We consider a renewal jump-diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin probabilities and related quantities, in models with light...
متن کاملSecurity Price Dynamics and Simulation in Financial Engineering
Applications in financial engineering have relied heavily on Brownian Motion as a workhorse model for pricing derivative securities and implementing risk management programs. When more than one state variable is required, the standard approach is to use a multivariate Brownian Motion with constant correlations. This article briefly summarizes several important reasons why this approach is not a...
متن کامل