Classical Merton model assumes that an asset is modelled by Brownian motion or geometric Brownian motion. However, these models lack some empirical properties of usual financial series. If jumps are allowed into the model, it becomes much more appropriate. In this note, jump processes are briefly introduced. Subsequently, the impact of jumps on the optimal consumption and portfolio choice is st...

In Merton (1987), idiosyncratic risk is priced in equilibrium as a consequence of incomplete diversification. We modify his model to allow the degree diversification vary with average volatility. This simple recognition results state‐dependent premium that higher when volatility low, and vice versa. The data appear be consistent positive for both US other developed markets.

We discuss the parameter estimation of probability default (PD), correlation between obligors, and a phase transition. In our previous work, we studied problem using beta-binomial distribution. A non-equilibrium transition with an order occurs when temporal decays by power law. this study, adopt Merton model, which uses asset as correlation, find that When index is less than one, PD estimator c...

BACKGROUND Recently, the frequency of audit inspections of health services for people with intellectual disability (ID) in the UK has increased, from occasional inquiries to a systematic audit of all services. From 2008, a process of continuous audit 'surveillance' of specialist health services is to be introduced. Similar regimes of inspection are in place for social care services. AIM To ex...

This is a short comment on Kung and Lee’s paper. In this note, we show that the formulae given in Kung and Lee(2009) for European call and put option under Merton’s model of the short rate are incorrect. We give the correct derivations making use of the ”change of numeraire” technique which is simpler and more standard. Key-words: Stochastic Interest rates, Change of Numeraire, Call option pric...

In this paper, we develop a new capital adequacy buffer model (CABM) which is sensitive to dynamic economic circumstances. The model, which measures additional bank capital required to compensate for fluctuating credit risk, is a novel combination of the Merton structural model, which measures distance to default, and the timeless capital asset pricing model (CAPM) which measures additional ret...