Part 1 (Peter Buchen)
The traditional method for pricing barrier and lookback options in the Black-Scholes framework is by discounted expectations, under the Equivalent Martingale Measure, of the joint distribution of the underlying asset and its running minimum (or maximum) over some specified time window. This joint distribution can be determined using the Reflection Principle for zero-drift Brownian motion and employing Girsanov's Theorem for the non-zero drift case. The calculations, it must be admitted, are difficult, cumbersome and highly non-intuitive. We show in the first part of the workshop how the pde Method of Images, associated parity relations and other specialised tools lead to rather simpler equivalent European payoffs for all the standard barrier and lookback options.

Part 2 (Otto Konstandatos)
We show in the second part of the workshop how to price some of the exotic extensions of standard barrier and lookback options, using the Method of Images. In particular, we show how to price partial time barrier options, double barrier options and partial price lookback options. We also indicate the huge array of related extensions that are readily priced using these methods, including hybrids such as Bermin's (1996) extreme spread lookback options and look-barrier option. Ultimately, once the pricing tools are in place, prices for many of these exotics are obtained without actually performing a single transformation or complicated integration. Furthermore, many of the ideas underlying the method are not restricted to the Black-Scholes framework.

Slides