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Recent literature seek to forecast implied volatility derived from equity, index, foreign exchange, and interest rate options using latent factor and parametric frameworks. Motivated by increased public attention borne out of the financialization of futures markets in the early 2000s, we investigate if these extant models can uncover predictable patterns in the implied volatility surfaces of the most actively traded …
In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are emb…
Financial decision systems require fast surrogate models for pricing, calibration, hedging, XVA, stress testing, and portfolio optimization. Standard neural surrogates reproduce prices or risk quantities, but downstream tasks depend as much on derivatives: deltas, vegas, curve and credit-spread sensitivities, exposure and objective gradients. We formulate a derivative-informed operator-learning framework in which the…
One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of Þtting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper we study whe…
Our primary goal is to forecast and empirically examine the evolution of the implied volatility (IV) surface, with particular focus on the dates of scheduled meetings of the Federal Open Market Committee (FOMC). Firstly, we check if IV increases before the announcement and if thes effect is stronger for short-dated, out-the-money (OTM) options in high volatility regimes. In the second part, we turn the focus to verif…
Neural and numerical policy solvers can produce feasible controls even when the optimal rule and its binding constraints are unavailable. A primal-dual bracket certifies value loss, but it does not locate the optimal policy or explain which constraints genuinely bind. We show that, on the same declared simulation grid, one bracket can support both conclusions. For polyhedral controls, an exact conditional budget iden…
This paper develops a unified mathematical theory of implied, local, and learned volatility surfaces. Total variance $w_t(k,τ)=τσ_t^2(k,τ)$ is an infinite-dimensional state constrained by positivity, calendar monotonicity, and the butterfly differential inequality. We establish the topology and tangent geometry of this arbitrage set and prove that a nondegenerate Gaussian shock at an active constraint exits with prob…
We propose an arbitrage-aware latent flow-matching framework for unconditional implied volatility surface generation. The method first compresses high-dimensional surfaces into a low-dimensional latent space using a variational autoencoder regularized by differentiable calendar-spread, call-spread and butterfly-arbitrage penalties. A flow-matching model then learns to transport a Gaussian prior toward the empirical l…
We present a convolutional variational autoencoder for cryptocurrency implied-volatility surfaces, together with a deployable predictor that combines it with a quadratic smile re-fit through a deterministic per-tenor routing rule. Trained on 6,034 fully-filled hourly Binance Options surfaces of BTC and ETH spanning May-October 2023 and parameterised on a common $6 \times 7$ tenor-delta grid, the model attains a hidde…
We study the reconstruction of implied volatility surfaces from sparse and noisy option quotes using deep learning models under no-arbitrage constraints. We compare multiple neural architectures, including multilayer perceptrons, convolutional networks, U-Nets, variational autoencoders, and Transformer-based models against classical SVI parameterizations on option market data. Results show that Transformer and U-Net …
The classical mean-variance framework characterizes portfolio risk solely through return variance and the covariance matrix, implicitly assuming that all relevant sources of risk are captured by second moments. In modern financial markets, however, shocks often propagate through complex networks of interconnections, giving rise to systemic and spillover risks that variance alone does not reflect. This paper develops …
We study the construction of SPX--VIX (multi\textendash product) option surfaces that are simultaneously free of static arbitrage and dynamically chain\textendash consistent across maturities. Our method unifies \emph{constructive} PCA--Smolyak approximation and a \emph{chain\textendash consistent} diffusion model with a tri\textendash marginal, martingale\textendash constrained entropic OT (c\textendash EMOT) bridge…
We formulate option market making as a constrained, risk-sensitive control problem that unifies execution, hedging, and arbitrage-free implied-volatility surfaces inside a single learning loop. A fully differentiable eSSVI layer enforces static no-arbitrage conditions (butterfly and calendar) while the policy controls half-spreads, hedge intensity, and structured surface deformations (state-dependent rho-shift and ps…
We present a deep learning framework for pricing options based on market-implied volatility surfaces. Using end-of-day S\&P 500 index options quotes from 2018-2023, we construct arbitrage-free volatility surfaces and generate training data for American puts and arithmetic Asian options using QuantLib. To address the high dimensionality of volatility surfaces, we employ a variational autoencoder (VAE) that compresses …
This paper presents a deep generative modeling framework for controllably synthesizing implied volatility surfaces (IVSs) using a variational autoencoder (VAE). Unlike conventional data-driven models, our approach provides explicit control over meaningful shape features (e.g., volatility level, slope, curvature, term-structure) to generate IVSs with desired characteristics. In our framework, financially interpretable…
For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is able to explore risk management usages by following the orthotical Delta-Gamma dynamic hedging framework. The realized local volatility surface is, mathematically, a generalized Wiene…
In this paper, we consider three stochastic-volatility models, each characterized by distinct dynamics of instantaneous volatility: (1) a CIR process for squared volatility (i.e., the classical Heston model); (2) a mean-reverting lognormal process for volatility; and (3) a CIR process for volatility. Previous research has provided semi-analytical approximations for these models in the form of simple (non-mean-reverti…
This article examines how emerging economies use countercyclical monetary policies to manage economic crises and fluctuations in dominant currencies, such as the US dollar and the euro. Global economic cycles are marked by phases of expansion and recession, often exacerbated by major financial crises. These crises, such as those of 1997, 2008 and the disruption caused by the COVID-19 pandemic, have a particular impac…
Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.
Local Volatility Model — Strike-dependent diffusion used to fit vanilla surfaces consistently.
Notional value is the face amount a derivative references — the exposure scale, not the cash outlay or the market value.
SVI Parameterization — Arbitrage-aware parameterization of volatility smiles for interpolation and trading.
Seigniorage is the real resources a sovereign (or a private issuer of money-like claims) obtains by issuing money whose production cost is below face value.
Par value is the face amount the issuer promises to repay at maturity — 100 cents on the dollar in bond language.
Expected value is the probability-weighted average of a random variable — the center of the distribution you actually face, not the mode or the ‘base case’ slide.
Vol-structure note for classifying rich vs cheap ATM IV and surface dispersion before choosing credit or debit templates.
Educational IV × Greeks × surface sandbox already mounted on the Blackboard — synthetic regimes for pedagogy beside the live scanner.
Expected value is the probability-weighted average of a random variable — the center of the distribution you actually face, not the mode or the ‘base case’ slide.
Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.
Local Volatility Model — Strike-dependent diffusion used to fit vanilla surfaces consistently.
Notional value is the face amount a derivative references — the exposure scale, not the cash outlay or the market value.
Par value is the face amount the issuer promises to repay at maturity — 100 cents on the dollar in bond language.
Seigniorage is the real resources a sovereign (or a private issuer of money-like claims) obtains by issuing money whose production cost is below face value.