We derive a simple formula for the cost of the ESO to the firm at the grant date under the assumption that the executive has a constant market-to-strike multiple. The market-to-strike multiple is defined as the ratio of the market price on exercise to the strike price of the ESO. The expected...

We analyze the American option valuation problem with the forward performance criterion introduced by Musiela and Zariphopoulou (2008). In this framework, utility evolves forward in time without reference to a specific future time horizon. Moreover, risk preferences change with stochastic market...

An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical...

We derive a closed-form expansion of option prices in terms of Black-Scholes prices and higher-order Greeks. We show how the true price of an option less its Black-Scholes price is given by a series of premiums on higher-order risks that are not priced under the Black-Scholes model assumptions....

This paper presents an extensive test of the Libor Market on the Euro Cap and Swaption market. The deterministic LIBOR market model prices OTC cap exactly and prices OTC swaptions with errors well below two basis points. Tests for the hedging performance show that the deterministic LIBOR market...

This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [arXiv:1906.06478]. We introduce a PDE...

Measuring the performance of stock portfolios that include options is challenging due to options' nonlinearity in the underlying, their exposure to volatility risk, and their time decay. Our contribution to the literature is twofold: First, we provide a theoretically rigorous derivation of the...

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the...

This paper determines the cost of employee stock options (ESOs) to shareholders. I present a pricing method that seeks to replicate the empirics of exercise and cancellation as good as possible. In a first step, an intensity-based pricing model of El Karoui and Martellini is adapted to the needs...