Taking a portfolio perspective on option pricing and hedging, we show that within the standard Black-Scholes-Merton framework large portfolios of options can be hedged without risk in discrete time. The nature of the hedge portfolio in the limit of large portfolio size is substantially different...

The “practitioner Black-Scholes delta” for hedging options is a delta calculated from the Black-Scholes-Merton model (or one of its extensions) with the volatility parameter set equal to the implied volatility. As has been pointed out by a number of researchers, this delta does not minimize...

Hedging at-the-money digital options near maturity, remains a challenge in quantitative finance. In the present work, we carry out a hedging strategy by means of a bull spread. We study the probability of super- and sub-hedge the digital option and minimize the probability of a sub-hedge...

In this paper we derive the locally risk-minimizing hedging for a general contingent claim in an incomplete market via the generalized Clark-Ocone formula. Using this result in a stochastic volatility model, we study its connection with the hedge obtained via PDE approach. We see these hedging...

The Markov Tree model is a discrete-time option pricing model that accounts for short-term memory of the underlying asset. In this work, we compare the empirical performance of the Markov Tree model against that of the Black-Scholes model and Heston's stochastic volatility model. Leveraging a...

In this paper, we introduce two methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural networks to simultaneously compute both the lower and upper bounds of...

The majority of quasi-analytic pricing methods for American options are efficient near-maturity but are prone to larger errors when time-to-maturity increases. A new methodology, called the "extension"-method, is introduced to increase the accuracy of almost any existing quasi-analytic approach...