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Results for “derivatives” · papers 18 · wiki 36
Academic Papers · 18arXiv q-fin live 8 · desk corpus 79
arXiv · arXiv · 2026

Replication-Consistent Liquidity Forecasting for Derivatives -- Forward Funding Sensitivities and a Liquidity Valuation Adjustment for Settlement Lags

We study cash-flow forecasting for derivatives used in liquidity management and clarify its relation to risk-neutral valuation and replication. While it is well known that expectations under different measures (e.g., $\mathbb{P}$ vs. $\mathbb{Q}$) can yield different undiscounted cash-flows, further inconsistencies arise when payment times are stochastic. We show that using discounting sensitivities (funding-curve he

Christian P. Fries
arXiv · arXiv · 2022

Systematization of Knowledge: Synthetic Assets, Derivatives, and On-Chain Portfolio Management

Synthetic assets are decentralized finance (DeFi) analogues of derivatives in the traditional finance (TradFi) world - financial arrangements which derive value from and are directly pegged to fluctuations in the value of an underlying asset (ex: futures and options). Synthetic assets occupy a unique niche, serving to facilitate currency exchange, giving traders a means to speculate on the value of crypto assets with

Abrar Rahman, Victor Shi, Matthew Ding, Elliot Choi
arXiv · arXiv · 2022

Time-zero Efficiency of European Power Derivatives Markets

We study time-zero efficiency of electricity derivatives markets. By time-zero efficiency is meant a sequence of prices of derivatives contracts having the same underlying asset but different times to maturity which implies that prices comply with a set of efficiency conditions that prevent profitable time-zero arbitrage opportunities. We investigate whether statistical tests, based on the law of one price, and tradi

Juan Ignacio Peña, Rosa Rodriguez
arXiv · arXiv · 2018

Consistent Time-Homogeneous Modeling of SPX and VIX Derivatives

This paper shows how to recover a stochastic volatility model (SVM) from a market model of the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore are better suited for pricing VIX futures and VIX derivatives. But the VIX itself is a derivative of the S&P500 (SPX) and it is common practice to price SPX derivatives using an SVM. Therefore, consistent modeli

Andrew Papanicolaou
arXiv · arXiv · 2011

Risk Premia and Optimal Liquidation of Credit Derivatives

This paper studies the optimal timing to liquidate credit derivatives in a general intensity-based credit risk model under stochastic interest rate. We incorporate the potential price discrepancy between the market and investors, which is characterized by risk-neutral valuation under different default risk premia specifications. We quantify the value of optimally timing to sell through the concept of delayed liquidat

Tim Leung, Peng Liu
arXiv · arXiv · 2011

Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR

We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review t

Marco Bianchetti, Mattia Carlicchi
arXiv · arXiv · 2009

A Dynamic Model for Credit Index Derivatives

We present a new model for credit index derivatives, in the top-down approach. This model has a dynamic loss intensity process with volatility and jumps and can include counterparty risk. It handles CDS, CDO tranches, Nth-to-default and index swaptions. Using properties of affine models, we derive closed formulas for the pricing of index CDS, CDO tranches and Nth-to-default. For index swaptions, we give an exact pric

Louis Paulot
arXiv · arXiv · 2009

Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves

We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations

Marco Bianchetti
arXiv · arXiv · 2026

Optimal Pricing and Hedging of SOFR Derivatives

Thousands of SOFR derivatives are available in exchanges and OTC, but the market remains illiquid and incomplete. Such a market is beyond the scope of classic risk-neutral approaches that imply linear pricing rules and, at best, approximate hedging strategies whose hedging error may be difficult to quantify. This paper develops an indifference pricing model which is consistent with observed derivative quotes, the age

Teemu Pennanen, Waleed Taoum
arXiv · arXiv · 2026

Semi-Static Variance-Optimal Hedging of Covariance Risk in Multi-Asset Derivatives

We develop a semi-static framework for the variance-optimal hedging of multi-asset derivatives exposed to correlation and covariance risk. The approach combines continuous-time dynamic trading in the underlying assets with a static portfolio of auxiliary contingent claims. Using a multivariate Galtchouk--Kunita--Watanabe decomposition, we show that the resulting global mean-variance problem decouples naturally into a

Konstantinos Chatziandreou, Sven Karbach
arXiv · arXiv · 2026

Feynman-Kac Derivatives Pricing on the Full Forward Curve

This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional numerical methods computationally prohibitive. To make the problem computationally tractable, I cast the stochastic pricing problem as a deterministic partial differential equatio

Kevin Mott
arXiv · arXiv · 2024

AD-HOC: A C++ Expression Template package for high-order derivatives backpropagation

This document presents a new C++ Automatic Differentiation (AD) tool, AD-HOC (Automatic Differentiation for High-Order Calculations). This tool aims to have the following features: -Calculation of user specified derivatives of arbitrary order -To be able to run with similar speeds as handwritten code -All derivatives calculations are computed in a single backpropagation tree pass -No source code generation is used, r

Juan Lucas Rey
arXiv · arXiv · 2024

PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)

In this article we derive partial differential equations (PDEs) for pricing interest rate derivatives under the generalized Forward Market Model (FMM) recently presented by A. Lyashenko and F. Mercurio in \cite{lyashenkoMercurio:Mar2019} to model the dynamics of the Risk Free Rates (RFRs) that are replacing the traditional IBOR rates in the financial industry. Moreover, for the numerical solution of the proposed PDEs

J. G. López-Salas, S. Pérez-Rodríguez, C. Vázquez
arXiv · arXiv · 2022

A semi-static replication approach to efficient hedging and pricing of callable IR derivatives

We present a semi-static hedging algorithm for callable interest rate derivatives under an affine, multi-factor term-structure model. With a traditional dynamic hedge, the replication portfolio needs to be updated continuously through time as the market moves. In contrast, we propose a semi-static hedge that needs rebalancing on just a finite number of instances. We show, taking as an example Bermudan swaptions, that

Jori Hoencamp, Shashi Jain, Drona Kandhai
arXiv · arXiv · 2021

Normal Tempered Stable Processes and the Pricing of Energy Derivatives

In this study we consider the pricing of energy derivatives when the evolution of spot prices is modeled with a normal tempered stable driven Ornstein-Uhlenbeck process. Such processes are the generalization of normal inverse Gaussian processes that are widely used in energy finance applications. We first specify their statistical properties calculating their characteristic function in closed form. This result is ins

Piergiacomo Sabino
arXiv · arXiv · 2021

Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein-Uhlenbeck Type

In this study we consider the pricing of energy derivatives when the evolution of spot prices follows a tempered stable or a CGMY driven Ornstein- Uhlenbeck process. To this end, we first calculate the characteristic function of the transition law of such processes in closed form. This result is instrumental for the derivation of non-arbitrage conditions such that the spot dynamics is consistent with the forward curv

Piergiacomo Sabino
arXiv · arXiv · 2020

Deep learning for CVA computations of large portfolios of financial derivatives

In this paper, we propose a neural network-based method for CVA computations of a portfolio of derivatives. In particular, we focus on portfolios consisting of a combination of derivatives, with and without true optionality, \textit{e.g.,} a portfolio of a mix of European- and Bermudan-type derivatives. CVA is computed, with and without netting, for different levels of WWR and for different levels of credit quality o

Kristoffer Andersson, Cornelis W. Oosterlee
arXiv · arXiv · 2018

Pricing Financial Derivatives Subject to Counterparty Risk and Credit Value Adjustment

This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the literature, we emphasize that the market value of a defaultable deriva

David Lee
Wiki Entities · 36
Derivatives

Binomial Tree Pricing

Binomial Tree Pricing — Discrete recombining tree for American and path-sensitive options.

Derivatives

Black-Scholes Model

Black-Scholes is the European option formula under lognormal spot, constant vol, and continuous hedging — a quoting convention more than a belief about the world.

Derivatives

Butterfly Spread

A butterfly is long one wing, short two bodies, long the other wing — a bet on a pin or on the curvature of the smile.

Derivatives

Calendar Spread

Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.

Derivatives

Call Option

A call option is the right, not the obligation, to buy the underlying at a strike by expiry — convex upside for a premium.

Derivatives

Collar

A collar is long stock, long a put, and short a call — a banded payoff, often structured to be zero-debit.

Derivatives

Covered Call

A covered call is long the stock and short a call — you sell upside for premium and keep the downside.

Derivatives

Dealer Gamma Positioning

Dealer gamma positioning describes whether option dealers are structurally long or short gamma, shaping how hedging flows amplify or dampen market moves.

Derivatives

Delta

Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.

Derivatives

Delta Hedging

Delta Hedging — Continuous rebalancing of directional exposure that links options markets to underlying liquidity.

Derivatives

Dispersion Trading

Dispersion Trading — Index vol versus single-name vol — a pure play on implied correlation.

Derivatives

Gamma

Gamma is the sensitivity of delta to the underlying — how fast the hedge ratio moves, and who is chasing whom.

Derivatives

Gamma Hedging

Gamma Hedging — Delta adjustments by dealers that can accelerate trends or pin prices near strikes.

Derivatives

GARCH Volatility Model

GARCH Volatility Model — Conditional heteroskedasticity framework for forecasting volatility clusters.

Derivatives

Implied Realized Spread

Implied Realized Spread — Gap between implied and realized vol that defines carry for short-vol books.

Derivatives

Implied Volatility

Implied volatility is the σ you plug into Black-Scholes to match the market price — a quote of the option, not a forecast you must believe.

Derivatives

Implied Volatility Surface

Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.

Derivatives

Iron Condor Structure

Iron Condor Structure — Short vol range trade expressing view of subdued movement between strikes.

Derivatives

LEAPS Options

LEAPS Options — Long-dated equity options used for leveraged directional or hedge overlays.

Derivatives

Local Volatility Model

Local Volatility Model — Strike-dependent diffusion used to fit vanilla surfaces consistently.

Derivatives

Moneyness

Moneyness is where spot sits versus strike — in, at, or out of the money — the first map of option value and of Greek shape.

Derivatives

Monte Carlo Option Pricing

Monte Carlo Option Pricing — Simulation pricing for path-dependent and multi-asset claims.

Derivatives

Move Index

The MOVE Index tracks implied volatility in the U.S. Treasury market and serves as a benchmark for rates uncertainty and macro stress.

Derivatives

Notional Value

Notional value is the face amount a derivative references — the exposure scale, not the cash outlay or the market value.

Derivatives

Option Greeks

Greeks are the sensitivities of option value to spot, vol, time, and rates — the risk report of a non-linear book.

Derivatives

Options Open Interest

Options Open Interest — Outstanding contracts revealing crowd positioning and potential gamma walls.

Derivatives

Protective Put

A protective put is long the asset and long a put — a floor under the position for a premium that bleeds.

Derivatives

Put Option

A put option is the right to sell the underlying at a strike — convex downside, or a hedge that costs carry.

Derivatives

Put-Call Parity

Put-call parity is the no-arbitrage link C − P = F − K (discounted) — a European call and put with the same K and T are one instrument plus cash.

Derivatives

Realized Volatility

Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.

Derivatives

Risk Reversal

Risk Reversal — Call-put spread package measuring directional skew in FX and equity options.

Derivatives

Skew

Skew measures the relative richness of downside versus upside implied volatility, helping track hedging demand and asymmetry in market risk pricing.

Derivatives

Stochastic Volatility Model

Stochastic Volatility Model — Models where volatility itself is random, capturing smile dynamics and VRP.

Derivatives

Straddle

A straddle is a call and a put at the same strike — a bet on a large move, long or short, without picking direction.

Derivatives

Strangle

A strangle is an OTM call plus an OTM put — cheaper than a straddle, needs a bigger move, same vol-vs-realized logic.

Derivatives

Strike Price

The strike is the contract price at which an option can be exercised — the hinge of moneyness and of the payoff kink.

Option Blackboard · 0
No Option Blackboard entries matched.
Encyclopedia · 24
Derivatives · Foundations

Binomial Tree Pricing

Binomial Tree Pricing — Discrete recombining tree for American and path-sensitive options.

Derivatives · Foundations

Black-Scholes Model

Black-Scholes is the European option formula under lognormal spot, constant vol, and continuous hedging — a quoting convention more than a belief about the world.

Derivatives · Foundations

Butterfly Spread

A butterfly is long one wing, short two bodies, long the other wing — a bet on a pin or on the curvature of the smile.

Derivatives · Foundations

Calendar Spread

Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.

Derivatives · Foundations

Call Option

A call option is the right, not the obligation, to buy the underlying at a strike by expiry — convex upside for a premium.

Derivatives · Foundations

Collar

A collar is long stock, long a put, and short a call — a banded payoff, often structured to be zero-debit.

Derivatives · Foundations

Covered Call

A covered call is long the stock and short a call — you sell upside for premium and keep the downside.

Derivatives · Foundations

Dealer Gamma Positioning

Dealer gamma positioning describes whether option dealers are structurally long or short gamma, shaping how hedging flows amplify or dampen market moves.

Derivatives · Foundations

Delta

Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.

Derivatives · Foundations

Delta Hedging

Delta Hedging — Continuous rebalancing of directional exposure that links options markets to underlying liquidity.

Derivatives · Foundations

Dispersion Trading

Dispersion Trading — Index vol versus single-name vol — a pure play on implied correlation.

Derivatives · Foundations

Gamma

Gamma is the sensitivity of delta to the underlying — how fast the hedge ratio moves, and who is chasing whom.

Derivatives · Foundations

Gamma Hedging

Gamma Hedging — Delta adjustments by dealers that can accelerate trends or pin prices near strikes.

Derivatives · Foundations

GARCH Volatility Model

GARCH Volatility Model — Conditional heteroskedasticity framework for forecasting volatility clusters.

Derivatives · Foundations

Implied Realized Spread

Implied Realized Spread — Gap between implied and realized vol that defines carry for short-vol books.

Derivatives · Foundations

Implied Volatility

Implied volatility is the σ you plug into Black-Scholes to match the market price — a quote of the option, not a forecast you must believe.

Derivatives · Foundations

Implied Volatility Surface

Implied Volatility Surface — Strike and tenor structure of implied vol, the core object for vol trading and risk.

Derivatives · Foundations

Iron Condor Structure

Iron Condor Structure — Short vol range trade expressing view of subdued movement between strikes.

Derivatives · Foundations

LEAPS Options

LEAPS Options — Long-dated equity options used for leveraged directional or hedge overlays.

Derivatives · Foundations

Local Volatility Model

Local Volatility Model — Strike-dependent diffusion used to fit vanilla surfaces consistently.

Derivatives · Foundations

Moneyness

Moneyness is where spot sits versus strike — in, at, or out of the money — the first map of option value and of Greek shape.

Derivatives · Foundations

Monte Carlo Option Pricing

Monte Carlo Option Pricing — Simulation pricing for path-dependent and multi-asset claims.

Derivatives · Foundations

Move Index

The MOVE Index tracks implied volatility in the U.S. Treasury market and serves as a benchmark for rates uncertainty and macro stress.

Derivatives · Foundations

Notional Value

Notional value is the face amount a derivative references — the exposure scale, not the cash outlay or the market value.

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