In general, the risk of a financial instrument on a future valuation date depends on several stochastic variables. In the case of a currency swap, its value on a future date, can be modelled as a function of five stochastic variables. These represent the factors that determine the term structure...

We consider portfolios whose returns depend on at least three variables and show the effect of the correlation structure on the probabilities of the extreme outcomes of the portfolio return, using a multivariate binomial approximation. The portfolio risk is then managed by using derivatives. We...

In this paper we investigate models of the term structure where the factors are interest rates. As an example, we derive a no-arbitrage model of the term structure in which any two futures (as opposed to forward) rates act as factors. The term structure shifts and tilts as the factor rates vary....

We build a no-arbitrage model of the term structure, using two stochastic factors on each date, the short-term interest rate and the premium of the forward rate over the short-term interest rate. The model can be regarded as an extension to two factors of the lognormal interest rate model of...

The value of a currency swap, at a future valuation date, is modelled as a function of five stochastic variables. These represent the factors that determine the term structure of interest rates in the two currencies, and the foreign exchange rate between the currencies. The joint-probability...

In this paper, we suggest an efficient method of approximating a general, multivariate lognormal distribution by a multivariate binomial process. There are two important features of such multivariate distributions. First, the state variables may have volatilities that change over time. Second,...

We establish a necessary and sufficient condition for the risk aversion of an agent's derived utility function to increase with independent, zero-mean background risk. This condition is weaker than standard risk aversion. For small risks, the condition is that the ratio of the third to the first...

We consider portfolios whose returns depend on at least three variables and show the effect of the correlation structure on the probabilities of the extreme outcomes of the portfolio return, using a multivariate binomial approximation. The portfolio risk is then managed by using derivatives. We...

In this paper, we suggest an efficient method of approximating a general, multivariate lognormal distribution by a multivariate binomial process. There are two features of such multivariate distributions that are of interest. First, the state variables may have volatilities that change over...

The value and hedge ratio of an American-style option are shown to be closely approximated by a simple quadratic formula. The technique requires the estimation of the values and hedge ratios of just two options: a European option and a twice-exercisable option. These can be computed...