We consider the fair valuation of a participating life insurance policy with surrender options when the market values of the asset are modelled by Markov-modulated Geometric Brownian Motion (GBM). We reduce the dimension of the optimal stopping problem for the policy by changing probability measures. We also provide a decomposition result for the value of the policy. The Barone-Adesi-Whaley app...

A jump-diffusion log-return process with log-normal jump amplitudes is presented. The probability density and other properties of the theoretical model are rigorously derived. This theoretical density is fit to empirical log-returns of Standard & Poor’s 500 stock index data. The model repairs some failures found from the log-normal distribution of geometric Brownian motion to model features of ...

As one of the main areas value investing, stock market attracts attention many investors. Among investors, index movements are a focus attention. In this paper, combining efficient hypothesis and fractal hypothesis, prediction model based on mixed fractional Brownian motion (MFBM) an improved fractional-order particle swarm optimization algorithm is proposed. First, MFBM constructed by adjustin...

Stock market is one of the fields where randomness prominent factor to be considered. Although many stochastic process deals which found in nature through interdisciplinary subject like Econophysics, them exhibits cumbersome trends. So, Geometric Brownian motion (GBM) used analyze scenario Nepal on basis parameter; NEPSE Index along with prediction indices python programming platform. Python si...

We propose a two-sided jump model for credit risk by extending the Leland-Toft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1) The jump and endogenous default can produce a variety of non-zero credit sprea...

We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al [5] that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion ...

Spread options are notoriously difficult to price without the use of Monte Carlo simulation. Some strides have been made in recent years through application Fourier transform methods; however, date, these methods only applied specific underlying processes including two-factor geometric Brownian motion (gBm) and three-factor stochastic volatility models. In this paper, we derive characteristic f...