In this paper, we give a way to calculate a option implied volatility curve in closed form via the well known quadratic root formula. The closed form expression has 3 free parameters, which parsimoniously govern the assumed dynamics of implied volatility under forward swap measure. Preliminary...

A financial portfolio typically pays dividend based on its value. We show that there is a unique portfolio that pays the maximum dividend rate while remaining solvent, under appropriate assumptions. We also give a characterization of both the portfolio and the optimal dividend rate

We develop a new option pricing framework that tightly integrates with how institutional investors manage options positions. The framework starts with the near-term dynamics of the implied volatility surface and derives no-arbitrage constraints on its current shape. Within this framework, we...

We consider the hedging of options when the price of the underlying asset is always exposed to the possibility of jumps of random size. Working in a single factor Markovian setting, we derive a new spanning relation between a given option and a continuum of shorter-term options written on the...