We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit...

The illiquidity of long-maturity options has made it difficult to study the term structures of option spanning portfolios. This paper proposes a new estimation and inference framework for these option-implied term structures that addresses long-maturity illiquidity. By building a sieve estimator...

The paper studies estimation of implied volatility and the impact of the choice of the corresponding risk-free rate proxy. We suggest to analyze the implied volatility and the risk-free rate proxy inferred in conjunction from the observed option prices. We formulate and solve an overdefined...

Many models have been suggested to describe how investors manage risk and value risky cash flows. Among them, the most widely used is the Sharpe-Lintner-Black Capital Asset Pricing Model (CAPM). However many anomalies and evidence against this version have been presented. To assume that the CAPM...

The aims of this paper are twofold. Firstly, we present an approximating formula for pricing basket and multi-asset spread options, which genuinely extends Caldana and Fusai (2013) two-asset spread options formula. Secondly, under the lognormal setting, we show that our formula becomes a Black...

This technical note provides a detailed description of a simple but effective modeling solution to mark and risk manage plain-vanilla options on dividend futures. We focus on equity indices, as dividend products for single stocks are less liquid and observable and we derive a simple pricing...

Risk premia are related to price probability ratios or for continuous time pure jump processes the ratios of jump arrival rates under the pricing and physical measures. The variance gamma model is employed to synthesize densities with risk premia seen as the ratio of the three parameters. The...

By exploiting the flexibility of the Wishart process, we propose an application of this framework to the pricing of Chicago Board Options Exchange (CBOE) volatility index (VIX) options. Our methodology is analytically tractable and yet flexible enough to efficiently price CBOE VIX options. In...

This paper implements an algorithm that can be used to solve systems of Black-Scholes equations for implied volatility and implied risk-free rate of return. After using a seemingly unrelated regressions (SUR) model to obtain point estimates for implied volatility and implied risk-free rate, the...