For those of you into derivatives & hedging instruments, some utter nonsense that sums up just about everything this week.....

Pricing methodology depends on setting up a model of the probability distribution of the forward zero-coupon curve at the time of pricing and imposing that model on the forward-start IRSs' cashflow structure, with the aim of obtaining a probability distribution of the net present value of the cashflows. The zero-coupon curve is assumed to undergo a Markov process (which is a distinct class of stochastic process). A stochastic process literally means 'guessable' and can be described as a process which involves a random variable in which the successive values are inter-dependent in some way. The probability distribution of the forward curve depends amongst other factors on the swaption maturity, the appropriate interest rate for that period, the current forward curve and the implied volatility (the assumed rate of change of the curve). The present value of the forward swap will also obviously depend on the individual cashflows pertaining to the underlying structure of the swap, either accreting or amortising or both, on which the swaption is based. The probability distribution of the forward curve can be modelled by using a binomial numerical model, which uses binomial trees. Alternatively, it can be structured by modelling the stochastic process through one of a number of mathematical models, such as the Black and Scholes model.

The market standard tool for pricing swaptions is to simulate the route taken by the modified Black model. This is because of its ease of use and market acceptance. However, the modified Black formula has been subject to extensive criticism from various sources over the years. The more prominent shortcomings illuminated by these authors entail that the particular model looks at the underlying IRS simply as a forward rate; it does not encapsulate the structure of the swap, such as maturity, coupon frequency, etc. Indeed, the more complicated cashflow structures such as rollercoaster or accreting swaps will almost certainly yield incorrect results. In addition, it is shown to be theoretically imperfect, because of the fact that the modified Black model only allows for one stochastic. It also uses a fixed-yield curve, whereas swap traders know that the curve undergoes a stochastic process. Newer models, such as the Ho-Lee, Heath-Jarrow-Merton and Hull-White models, are called arbitrage-free models and are designed to avoid arbitrage possibilities due to changes in the yield curve. Some of the newer models also make the volatility itself a stochastic term.