Abstract
Motivated by new financial markets where there is no canonical choice of a risk-neutral measure, we compared two different methods for pricing options: calibration with an entropic penalty term and valuation by the Esscher measure. The main aim of this paper is to contrast the outcomes of those two methods with real-traded call option prices in a liquid market like NASDAQ stock exchange, using data referring to the period 2019–2020. Although the Esscher measure method slightly underperforms the calibration method in terms of absolute values of the percentage difference between real and model prices, it could be the only feasible choice if there are not many liquidly traded derivatives in the market.
Highlights
Empirical studies show that real financial markets are incomplete, which means that not all derivative securities like options are replicable by means of some initial capital plus the value process of some self-finance trading strategy, and hold unhedgeable and undiversifiable risks
We introduce, discuss, and compare two methods for the simulation of European call option prices: one based on the Esscher martingale measure and the other on the calibration to real-traded securities with an entropic penalty term
The main purpose of this research is to quantify the performances of two option pricing methods in a liquid market like NASDAQ
Summary
Empirical studies show that real financial markets are incomplete, which means that not all derivative securities like options are replicable by means of some initial capital plus the value process of some self-finance trading strategy, and hold unhedgeable and undiversifiable risks. The range of option prices composes the total range between the inf and the sup of expected values with respect to martingale measures, and is too large for practical purposes, see (Eberlein and Hammerstein 2004, Theorem 11.55). We introduce, discuss, and compare two methods for the simulation of European call option prices: one based on the Esscher martingale measure and the other on the calibration to real-traded securities with an entropic penalty term. We implemented them in the programming language R and contrast the simulated derivative prices with real data retrieved from NASDAQ option chains
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