arXiv subjects

Arunangshu Biswas

Publications and source records attributed to Arunangshu Biswas.

4 recordsLinked to original sources

arXiv2018

Option Pricing in a Regime Switching Stochastic Volatility Model

In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model has been successfully used where the volatility is expressed as a stochastic differential equation. In addition, we consider a regime switching model where the stock volatility dynamics depends on an underlying process which is possibly a non-Markov pure jump process. Under this model assumption, we find the locally risk minimizing pricing of European type vanilla options. The price function is shown to satisfy a Heston type PDE.

q-fin.PR↗

arXiv2015

Langevin type limiting processes for Adaptive MCMC

Adaptive Markov Chain Monte Carlo (AMCMC) is a class of MCMC algorithms where the proposal distribution changes at every iteration of the chain. In this case it is important to verify that such a Markov Chain indeed has a stationary distribution. In this paper we discuss a diffusion approximation to a discrete time AMCMC. This diffusion approximation is different when compared to the diffusion approximation as in Gelman, Gilks and Roberts (1997) where the state space increases in dimension to infinity. In our approach the time parameter is sped up in such a way that the limiting distribution (as the mesh size goes to 0) is to a non-trivial continuous time diffusion process.

math.PR↗

arXiv2014

Diffusive Limits for Adaptive MCMC for Normal Target densities

In this paper we apply the Diffusion approximation procedure to a discrete time Adaptive Markov Chain Monte Carlo (AMCMC) method when the target distribution is standard Normal. We show that the limiting distribution of the diffusion admits a density which we identify as the standard Normal distribution.

math.ST↗

arXiv2010

Process convergence of self normalized sums of i.i.d. random variables coming from domain of attraction of stable distributions

In this paper we show that the continuous version of the self normalised process $Y_{n,p}(t)= S_n(t)/V_{n,p}+(nt-[nt])X_{[nt]+1}/V_{n,p}$ where $S_n(t)=\sum_{i=1}^{[nt]} X_i$ and $V_{(n,p)}= \sum_{i=1}^{n}|X_i|^p)^{\frac{1}{p}}$ and $X_i$ i.i.d. random variables belong to $DA(α)$, has a non trivial distribution iff $p=α=2$. The case for $2 > p > α$ and $p \le α< 2$ is systematically eliminated by showing that either of tightness or finite dimensional convergence to a non-degenerate limiting distribution does not hold. This work is an extension of the work by Csörgö et al. who showed Donsker's theorem for $Y_{n,2}(\cdot)$, i.e., for $p=2$, holds iff $α=2$ and identified the limiting process as standard Brownian motion in sup norm.

math.PR↗