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Before the 2008 financial crisis, most research in financial mathematics focused on pricing options without considering the effects of counterparties' defaults, illiquidity problems, and the role of the sale and repurchase agreement (Repo) market. Recently, models were proposed to address this by computing a total valuation adjustment (XVA) of derivatives; however without considering a potential crisis in the market.…
We investigate the optimal execution of contracts that are used in merger\&acquisition deals. We consider cash-settled and physically delivered contracts between a broker and a counterpart. Contracts are linear (total returns swaps), nonlinear (collar contracts) or Asian type (TWAP based contracts). We derive the optimal execution strategy and the optimal fee through indifference utility arguments allowing for linear…
Financial markets such as bond, derivatives, and repo markets form networks of interdependent obligations. Existing multilateral netting methods typically trade off the extent of netting against preservation of counterparty exposure: central clearing reallocates exposure to a central counterparty, while trade compression may alter bilateral counterparty relationships. TradeMech is a mechanism for markets in which one…
We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, i.e., one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semi-linear BSDEs and PDEs, and thus it is necessary to solve the equations numerically. However, once it can be gua…
Cash collateral is perfect in that it provides simultaneous counterparty credit risk protection and derivatives funding. Securities are imperfect collateral, because of collateral segregation or differences in CSA haircuts and repo haircuts. Moreover, the collateral rate term structure is not observable in the repo market, for derivatives netting sets are perpetual while repo tenors are typically in months. This arti…
A new modelling approach that directly prescribes dynamics to the term structure of VIX futures is proposed in this paper. The approach is motivated by the tractability enjoyed by models that directly prescribe dynamics to the VIX, practices observed in interest-rate modelling, and the desire to develop a platform to better understand VIX option implied volatilities. The main contribution of the paper is the derivati…
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…
VIX term structure tracks the shape of volatility futures across maturities and helps identify whether the market is pricing stable conditions or near-term stress.
Skew measures the relative richness of downside versus upside implied volatility, helping track hedging demand and asymmetry in market risk pricing.
Dealer gamma positioning describes whether option dealers are structurally long or short gamma, shaping how hedging flows amplify or dampen market moves.
VIX Index measures implied volatility in S&P 500 options and is widely used as a shorthand for equity market fear and risk aversion.
The MOVE Index tracks implied volatility in the U.S. Treasury market and serves as a benchmark for rates uncertainty and macro stress.
Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.
Variance Risk Premium — Gap between implied and realized volatility that systematic vol sellers harvest.
Vanna Charm Flow — Second-order greek hedging flows that amplify or dampen spot moves around expiries.
Gamma Hedging — Delta adjustments by dealers that can accelerate trends or pin prices near strikes.
Delta Hedging — Continuous rebalancing of directional exposure that links options markets to underlying liquidity.
Vega Exposure — Sensitivity to implied volatility changes — core risk for vol books and structured products.
Theta Decay — Time decay of option premium, the carry engine for systematic short-vol strategies.
Options Open Interest — Outstanding contracts revealing crowd positioning and potential gamma walls.
Put Call Ratio — Relative demand for downside protection versus upside participation.
Volatility of Volatility — Uncertainty about future volatility, critical for tail hedges and vol-of-vol products.
Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.
GARCH Volatility Model — Conditional heteroskedasticity framework for forecasting volatility clusters.
Local Volatility Model — Strike-dependent diffusion used to fit vanilla surfaces consistently.
Stochastic Volatility Model — Models where volatility itself is random, capturing smile dynamics and VRP.
SVI Parameterization — Arbitrage-aware parameterization of volatility smiles for interpolation and trading.
Volatility Arbitrage — Trading discrepancies between implied, realized, and cross-asset volatility.
Dispersion Trading — Index vol versus single-name vol — a pure play on implied correlation.
Variance Swap — Contract paying realized variance versus strike, core institutional vol transfer instrument.
VIX Futures Term Structure — Curve shape driving roll yield for vol ETNs and systematic short-vol carry.
Volatility Carry Trade — Selling implied vol or rolling VIX futures in contango — crowded but regime-sensitive.
Gamma Scalping — Trading realized vol against a long gamma book via delta hedging.
Pin Risk — Settlement risk when spot gravitates toward large open-interest strikes.
Iron Condor Structure — Short vol range trade expressing view of subdued movement between strikes.
Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.
Risk Reversal — Call-put spread package measuring directional skew in FX and equity options.
Implied Volatility — Market-implied expected volatility embedded in option prices.
Historical Volatility — Realized return dispersion used as a benchmark versus implied.
Implied Realized Spread — Gap between implied and realized vol that defines carry for short-vol books.
Volatility Risk Premium — Average excess of implied over subsequent realized volatility.
Volatility Smile — Strike-dependent implied vol pattern reflecting crash and demand premia.
Volatility Skew (Derivatives).
0DTE Options Flow (Derivatives).
Autocallable Risk 10Y (Derivatives).
Autocallable Risk 1M (Derivatives).
Autocallable Risk 1Y (Derivatives).
Autocallable Risk 20Y (Derivatives).
Autocallable Risk 2Y (Derivatives).
Autocallable Risk 30Y (Derivatives).
Autocallable Risk 3M (Derivatives).
Autocallable Risk 5Y (Derivatives).
Autocallable Risk 6M (Derivatives).
Autocallable Risk 7Y (Derivatives).
Autocallable Risk ATM (Derivatives).
Autocallable Risk belly (Derivatives).
Autocallable Risk front (Derivatives).
Autocallable Risk index (Derivatives).
Autocallable Risk long-end (Derivatives).
Autocallable Risk NDX (Derivatives).
Autocallable Risk NKY (Derivatives).
Autocallable Risk OTM (Derivatives).
Autocallable Risk RUT (Derivatives).
Autocallable Risk single-name (Derivatives).
Autocallable Risk SPX (Derivatives).
Autocallable Risk SX5E (Derivatives).
Autocallable Risk ultra-long (Derivatives).