We consider a trader who is responsible for managing a portfolio of derivatives that evolves stochastically and depends on a single underlying asset. We use reinforcement learning to develop a strategy for bringing options into the portfolio to manage gamma and vega risk. The options are subject...

This paper shows how reinforcement learning can be used to derive optimal hedging strategies for derivatives when there are transaction costs. The paper illustrates the approach by showing the difference between using delta hedging and optimal hedging for a short position in a call option when...

A common approach to valuing exotic options involves choosing a model and then determining its parameters to fit the volatility surface as closely as possible. We refer to this as the model calibration approach (MCA). A disadvantage of MCA is that some information in the volatility surface is...

We employ neural networks to understand volatility surface movements. We first use daily data on options on the S&P 500 index to derive a relationship between the expected change in implied volatility and three variables: the return on the index, the moneyness of the option, and the remaining...

Das internationale führende Standardwerk richtet sich an Studenten und Graduierte der Betriebswirtschaft und Volkswirtschaft. Auch für viele Praktiker, die anwendbare Kenntnisse über Futures- und Optionsmärkte erlangen wollen, ist das Werk von großem Nutzen.

Researchers such as Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) have proposed a one-factor model for asset prices that is exactly consistent with all European option prices. In this model, which we refer to as the implied volatility function (IVF) model, the asset price...

This paper presents a number of new ideas concerned with the implementation of theLIBOR market model and its extensions. It develops and tests an analytic approximationfor calculating the volatilities used by the market to price European swap options fromthe volatilities used to price interest...