Starting with observable annually compounded forward rates we derive a term structure model of interest rates. The model relies upon the assumption that a specific set of annually compounded forward rates is log-normally distributed. We derive solutions for interest rate caps and floors as well...

The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates. However, imposing this assumption on the continuously compounded interest rate has a serious drawback: rates explode and expected rollover returns are...

We derive a unified model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds. The crucial assumption is that forward rates with a compounding period that matches the contract, which we want to price, is...

Assuming constant interest rates Brennan and Schwartz (1976, 1979) obtained the rational insurance premium on an equity-linked insurance contract through the application of the theory of contingent claims pricing. Further considerations with deterministic interest rates have been discussed in...

The extension of the Black-Scholes option pricing theory to the valuation of barrier options is reconsidered. Working in the binomial framework of CRR we show how various types of barrier options can be priced either by backward induction or by closed binomial formulas. We also consider...

The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates ... The purpose of this paper is to show that the problem with lognormal models result from modelling the wrong rate, namely the continuously compounded...

We review the continuous-time literature on the so-called direct approach to bond option pricing. Going back to Ball and Torous (1983), this approach models bond price processes directly (i.e. without reference to interest rates or state variable processes) and applies methods that Black and...

This paper analyses the relationship between the level of a return guarantee in an equity-linked pension scheme and the proportion of an investor’s contribution needed to finance this guarantee. Three types of schemes are considered: investment guarantee, contribution guarantee and surplus...