We price derivatives defined for different asset classes with a full stochastic dependence structure. We consider jointly geometric Brownian motions and mean-reversion processes with a a stochastic variance-covariance matrix driven by a Wishart process. These models cannot be treated within the...

This technical note provides a detailed description of a simple but effective modeling solution to mark and risk manage plain-vanilla options on dividend futures. We focus on equity indices, as dividend products for single stocks are less liquid and observable and we derive a simple pricing...

In over 40 years teaching finance, I have put together hundreds of PowerPoint slides for MBA and Undergraduate level courses on Futures, Options, Derivatives and related topics. I provide them here for download and use without restriction, with the caveat that while I have done my best to make...

We show that LME's (London Metal Exchange) listed forward contracts can be valued using usual formulas for forward contracts and that LME's listed Options, though legally American, are correctly treated as European Options

With the transitions to overnight benchmarks as the main benchmarks in some currencies, futures based on overnight rates are becoming more common. The most traded futures on overnight rates settle against compounded rates. The pricing of those futures requires some convexity adjustments with an...

In electricity markets, futures contracts typically function as a swap since they deliver the underlying over a period of time. In this paper, we introduce a market price for the delivery periods of electricity swaps, thereby opening an arbitrage-free pricing framework for derivatives based on...

This paper discusses how to obtain the Black-Scholes equation to evaluate options and how to obtain explicit solutions for Call and Put. The Black-Scholes equation, which is the basis for determining explicit solutions for Call and Put, is a rather sophisticated equation. It is a partial...

VIX futures and option are the most popular contracts traded in the Chicago Board Options Exchange. The bid-ask spreads of traded VIX derivatives remain to be wide, possibly due to lack of reliable pricing models. In this paper, we consider pricing VIX derivatives under the consistent model...

I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an American option. If this regression...

Empirical evidence shows that, in equity options markets, the slope of the skew is largely independent of the volatility level. Single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew. On the other hand, multifactor stochastic...