Risk neutral densities recovered from option prices can be used to infer market participants expectations of future stock returns and are a vital tool for pricing illiquid exotic options. Although there is a broad literature on the subject, most studies do not address the likelihood of default....

In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a "flexible" version of Joshi's tree,...

We study the convergence of the binomial, trinomial, and more generally $m$-nomial tree schemes when evaluating certain European path-independent options in the Black-Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for the...

Efficient pricing of American options is important. Many numerical schemes calculate their prices using Bermudan options, and the popular penalty method is equivalent to a randomized Bermudan option scheme. Outside the Black-Scholes setting, very few convergence speed results have been...