Non probabilistic

Extending the Non-Probabilistic Model: Cycles and Crashes

The Epstein-Wilmott model from the previous two chapters gives us worst-case prices for interest rate products without assuming any probability distribution. But the basic version is, well, basic. It assumes rates move smoothly within bounds. Real interest rates jump. They follow cycles. They have a stochastic component that looks a lot like Brownian motion on short timescales. Chapter 70 adds bells and whistles to make the model more realistic while keeping its non-probabilistic spirit.

Pricing Derivatives Without Probability: The Sequel

In the previous chapter, Wilmott introduced the Epstein-Wilmott model for interest rates: no probability, just bounds on where rates can go and how fast they move. We saw how to value bonds and generate the Yield Envelope. Chapter 69 takes this framework and applies it to real portfolios and more complex derivatives. Bond options, index amortizing rate swaps, convertible bonds. The nonlinear, non-probabilistic approach handles them all.

Interest Rate Modeling Without Probabilities

Every interest rate model you have seen so far in this book assumes some form of random process. Brownian motion, mean reversion, stochastic volatility. They all start with “assume interest rates follow this stochastic differential equation” and then build a pricing framework on top. Chapter 68 of Wilmott’s book throws all of that out the window. No random walks. No probability distributions. No volatility parameters. Just bounds. This is the Epstein-Wilmott model, and it is refreshingly different.