We derive closed form analytic formulas for European vanilla options in the driftless Oscillating Brownian Motion model defined by two semi-infinite regimes each with its own constant local volatility. In particular we solve the Ito and Stratonovich Fokker-Planck equations for the probability...

Financial time series are dynamic and influenced by different types of information from the market. In this study, we propose new models for SPX and VIX options using the Hawkes process, jump process with stochastic intensity, and tempered stable process to capture these changes in financial...

Numerical methods such as binomial and finite difference methods can be used to price options however the problem is when the options have early exercise features. In this research project, we investigate the effectiveness and accuracy of Monte Carlo methods in pricing American options. We...

This paper re-examines two volatility-related patterns in the cross-section of stock option returns: the low-volatility effect and the expensiveness effect. Intermediary asset pricing theory suggests specific linkages between these effects. As our empirical results show, the low-volatility...

The process of fitting mathematical finance (MF) models for option pricing — known as calibration — is expensive because evaluating the pricing function usually requires Monte-Carlo sampling. Inspired by the success of deep learning for simulation, we present a hypernetwork based approach to...

We present a mixture of normalizing flows (MoNF) approach to European option pricing with guarantees that its estimations are free from static arbitrage. In contrast to many existing methods that meet economic rationality constraints (e.g., non-arbitrage) by introducing auxiliary losses, our...

In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalized to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options with Gaussian weights. For the family of stochastic...

This paper proposes machine learning-based option pricing models that incorporate firm characteristics. We employ two semi-parametric models, one that uses machine learning to predict the implied volatility and the other to correct the pricing error of the Black-Scholes model and use 114 firm...

Equity index risk premia vary more than can be explained by market risks and pricing models. I show that index option intermediaries cause variation in risk premia to manage their option positions. When expected volatility is low, intermediaries hold risky short positions. Increasing risk and...

Presentation slides. WFE ClearThe uploaded slides provide a summary of the presentation titled ‘Optimal Bidder Selection in Clearing House Default Options’. The slides were presented at The WFE’s Clearing & Derivatives Conference 2023