Studies of the sensitivity of the prices of interest rate claims to alternative specifications of the volatility of spot and forward interest rates have drawn different conclusions. One possible explanation for this is that it is difficult to adjust the volatility structure without disturbing the initial set of bond prices. In this chapter we use a term structure-constrained model that lets us ...

We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. ...

This paper utilizes the saddlepoint approximation as an efficient tool to estimate the portfolio credit loss distribution in the Vasicek model. Value-atrisk (VaR), the risk measure chosen in the Basel II Accord for the evaluation of capital requirement, can then be found by inverting the loss distribution. The VaR contribution (VaRC), expected shortfall (ES) and ES contribution (ESC) can all be...

In this paper, we address the issue of determining the optimal contribution rate of a stochastic defined benefit pension fund. The affiliate’s mortality is modelled by a jump process and the benefits paid at retirement are function of the evolution of stochastic salaries. Assets of the fund are invested in cash, stocks and a rolling bond. Interest rates are driven by a Vasicek model. The object...

In the changing financial market, price of products fluctuates continuously over time. The study static term structure interest rate on market can no longer satisfy actual needs, and dynamic model is imperative. Compared with structure, introduces a stochastic differential basis rate. This paper shows some relevant models including Vasicek Model, Single-Factor Dynamic Multi-Factor Kalman Filter...

The Black Scholes model of option pricing constitutes the cornerstone of contemporary valuation theory. However, the model presupposes the existence of several unrealistic and rigid assumptions including, in particular, the constancy of the return on the “hedge portfolio”. There, now, subsists ample justification to the effect that this is not the case. Consequently, several generalisations of ...