We discuss the Monte-Carlo valuation of American options, using a technique due to Rogers which furnishes an upper bound. The method is illustrated and possible improvements to its accuracy are considered.

We discuss the `continuity correction' that should be applied to relate the prices of discretely sampled barrier options and their continuously-sampled equivalents. Using a matched asymptotic expansions approach we show that the correction of Broadie, Glasserman \& Kou (\emph{Mathematical...

This paper develops a subordinated stochastic process model for the asset price, where the directing process is identified as information. Motivated by recent empirical and theoretical work, we make use of the under-used market statistic of transaction count as a suitable proxy for the...

We consider the pricing of volatility products and especially volatility and variance swaps. Under risk-neutral valuation we provide closed form formulae for volatility-average and variance swaps. Also we provide a general partial differential equation for derivatives that have an extra...

In this paper we derive analytic expressions for the value of European Put and Call options when the stock process follows an exponential Levy-Stable process. It is shown that the generalised Black-Scholes operator for the Levy-Stable case can be obtained as an asymptotic approximation of a...

Modern financial practice depends heavily on mathematics and a correspondingly large theory has grown up to meet this demand. This paper focuses on the use of matched asymptotic expansions in option pricing; it presents illustrations of the approach in `plain vanilla' option valuation, in...

In this paper we suggest derivative contracts related to the Greeks of options; we show how to value them and how they can be used to manage the risk of a portfolio of derivatives. We further describe certain types of these options, namely those related to the Delta and Gamma, which can be...

We consider the pricing of a range of volatility derivatives, including volatility and variance swaps. Under risk-neutral valuation we provide closed form formulae for volatility-average and variance swaps for a variety of diffusion and jump-diffusion models for volatility. We describe a general...

We discuss the `continuity correction' that should be applied to connect the prices of discretely sampled American put options (i.e.Bermudan options) and their continuously-sampled equivalents. Using a matched asymptotic expansions approach we compute the correction and relate it to that...

We report on a technique based on multi-agent games which has potential use in the prediction of future movements of financial time-series. A third-party game is trained on a black-box time-series, and is then run into the future to extract next-step and multi-step predictions. In addition to...