This book provides an advanced treatment of option valuation. The general setting is that of 2D continuous-time models with stochastic volatility. Explicit equilibrium risk adjustments and many other new results are provided. Mathematica code for the more important formulas is included. For a...

This article analyzes the specifications of option pricing models based on time-changed Levy processes. We classify option pricing models based on (i) the structure of the jump component in the underlying return process, (ii) the source of stochastic volatility, and (iii) the specification of...

This book provides an advanced treatment of option valuation. The general setting is that of 2D continuous-time models with stochastic volatility. Explicit equilibrium risk adjustments and many other new results are provided. Mathematica code for the more important formulas is included. For a...

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...

The characteristic functions of many affine jump-diffusion models, such as Heston’s stochastic volatility model and all of its extensions, involve multivalued functions such as the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages,...

While the stochastic volatility (SV) generalization has been shown to improvethe explanatory power compared to the Black-Scholes model, the empiricalimplications of the SV models on option pricing have not been adequately tested.The purpose of this paper is to first estimate a multivariate SV...

In electricity markets, futures contracts typically function as a swap since they deliver the underlying over a period of time. In this paper, we introduce a market price for the delivery periods of electricity swaps, thereby opening an arbitrage-free pricing framework for derivatives based on...

We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns admits a Gram-Charlier A expansion with closed-form...

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs...