In the spirit of Arrow-Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to nonparametrically price and hed…
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48 results for “Exotic derivatives”
Overlay framework simplifies exotic derivative pricing.
problem Inconsistent pricing models for exotics.
method Combines path reweighting and conic optimisation.
result Practically model-independent price bands for exotics.
Study dynamic trading in options to improve price bounds for exotic derivatives.
problem Improving price bounds for exotic derivatives through dynamic option trading.
method Extend semi-static trading strategies to include dynamic option trading, analyze duality results and pricing rules.
result Improved price bounds for exotic derivatives compared to conventional methods.
We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called "implied expected signature" from such market prices, which are used to price other …
The study examines how including additional call option prices affects model-independent price bounds for exotic derivatives.
problem Improving model-independent price bounds for exotic derivatives using additional call option prices.
method Characterization of market settings that guarantee improved price bounds and exclusion of any improvement.
result The inclusion of additional call option prices can significantly impact model-independent price bounds.
Consistent pricing of bivariate interest rate exotics via constrained Schrödinger optimal transportq-fin.MF
Develops a framework for consistent pricing of interest rate derivatives.
problem Consistent pricing of bivariate interest rate exotics across interconnected markets.
method Schrödinger optimal transport problem with constraints.
result Demonstrates practical applicability and no-arbitrage bounds computation.
We use Karhunen-Loève expansion for efficient pricing of exotic derivatives.
problem Efficient pricing of path-dependent options.
method Karhunen-Loève expansion and Monte Carlo simulation.
result Fast and accurate computation of exotic derivatives pricing.
Efficient and Accurate Calibration to FX Market Skew with Fully Parameterized Local Volatility Modelq-fin.PR
Model accurately calibrates FX market skew for exotic options.
problem Inconsistent prices from different models for FX derivatives.
method Fully parameterized local volatility model with numerical methods.
result Model provides reliable prices for daily trading.
New exotic 4-manifolds with zero signature found.
problem Finding exotic 4-manifolds with specific properties.
method Special small Lefschetz fibrations built via positive factorizations in the mapping class group.
result Smallest known exotic closed simply connected 4-manifolds with signature zero.
This work illustrates how several new pricing formulas for exotic options can be derived within a Levy framework by employing a unique pricing expression. Many existing pricing formulas of the traditional Gaussian model are obtained as a by-product.
The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment …
A physicist explores exotic 7-spheres using fibre bundles and instantons.
problem Investigating the geometry and topology of exotic 7-spheres.
method Analytical and computational tools from theoretical physics, including fibre bundles and instantons.
result Derives an analytic expression for a family of Riemannian metrics on the Gromoll-Meyer sphere.
New method calibrates LV surfaces for exotic derivatives with smoother, more stable Greeks.
problem Challenges in LV calibration leading to spiky surfaces and unstable Greeks.
method Automatic local regression to pre-process market observables and smooth LV surfaces.
result Significantly smoother LV surfaces and greatly improved Greek stability with negligible additional cost.
Gamma Hedging and Rough Pathsq-fin.MF
Study of gamma-hedging using rough paths for European and exotic options.
problem Applying rough paths to gamma-hedging strategies for derivatives.
method Rough-path theory applied to discrete-time gamma-hedging strategy.
result Sure replication of European and exotic derivatives under regular pricing signals.
Study values American passport options in an exponential Lévy model.
problem Valuing an exotic derivative called the American passport option.
method Derived pricing equation using dynamic programming principle and proved viscosity solution.
result Option value is a viscosity solution of variational inequality and is convex.
Speeds up complex portfolio exposure calculations.
problem Calculating exposure of portfolios with exotic derivatives.
method Least Squares Monte Carlo (LSMC) technique.
result Significantly reduces computation time for nested Monte Carlo.
New invariants prove exotic slice disks for knots.
problem Proving exotic slice disks for knots.
method Involutive Khovanov homology and derived invariants.
result Reprove exotic slice disks for knots .
We explicitly construct a genus- Lefschetz fibration over whose total space is using the monodromy of Matsumoto's genus- Lefschetz fibration. We then construct more genus- Lefschetz fibrations whose total spaces are exotic mi…
This paper considers the valuation of exotic path-dependent options in Lévy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener--Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a Lév…
New 4-manifolds with exotic diffeomorphisms found.
problem Existence of exotic diffeomorphisms in 4-manifolds.
method Proves existence of infinitely many contractible 4-manifolds with exotic diffeomorphisms.
result Infinitely many contractible 4-manifolds with absolutely exotic diffeomorphisms.
On smile properties of volatility derivatives and exotic products: understanding the VIX skewq-fin.MF
We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to describe the properties of the at-the-money implied volatility (ATMI) in terms of the Malliavin derivatives of t…
Exotic submanifolds in 4-manifolds remain exotic after stabilizations.
problem Constructing exotic codimension-1 submanifolds in 4-manifolds.
method Constructing pairs of exotic codimension-1 submanifolds with diffeomorphic complements and showing they remain exotic after stabilizations.
result Exotic submanifolds remain exotic after any number of stabilizations.
Tensor networks improve exotic option pricing efficiency.
problem Challenges in pricing exotic financial derivatives using standard methods.
method Combining binomial pricing with tensor network techniques (Matrix Product States).
result Linear scaling with parameters and reduced computational complexity.
Heston vol-of-vol and the VVIXq-fin.PR
This paper explores the vol-of-vol parameter in the Heston model and its relation to VVIX.
problem Calibrating the Heston model to market data for stable exotic option pricing.
method Four approaches to estimate VVIX in the Heston model: transition density, analytical approximation, and PDE-based.
result Improved calibration stability of the Heston model using the estimated VVIX.
Study exotic Dehn twists in 4-manifolds, producing first known exotic diffeomorphisms.
problem Detecting exotic diffeomorphisms in 4-manifolds.
method 2-parameter families Seiberg-Witten theory over .
result Constructed the smallest closed 4-manifold with exotic diffeomorphisms.
New methods distinguish exotic 4-manifolds using Heegaard Floer homology.
problem Distinguishing exotic 4-manifolds from standard ones.
method Using Heegaard Floer homology to define new invariants.
result New invariants remain distinct in covers and can distinguish exotic manifolds.
Path signatures improve hedging of exotic derivatives in non-Markovian models.
problem Hedging exotic derivatives under non-Markovian stochastic volatility models.
method Investigates path signatures in deep and shallow learning contexts, comparing neural networks and regression approaches.
result Path signatures outperform LSTM in most cases and yield more accurate results in hedging.
Constructs exotic proper 2-knots from open 2-handles.
problem Proving topological equivalence of exotic proper knotted surfaces.
method Flexible construction of exotic open 2-handles, distinguishing through genus functions and end Floer homology.
result Constructs infinite families of irreducible exotic proper knotted surfaces.
The paper presents a new method to create exotic 4-manifolds and surfaces that remain exotic after stabilization.
problem Stabilization of exotic 4-dimensional phenomena and knotted surfaces.
method Elementary approach to constructing exotic 4-manifolds and surfaces, including examples in closed, simply connected 4-manifolds.
result The construction yields exotic surfaces in the 4-ball that remain exotic after stabilization, detected by Khovanov homology.
New actions found on exotic spheres using group theory.
problem Understanding smooth transformations on exotic spheres.
method Recent progress in stable homotopy groups of spheres and group theory.
result Smooth circle and cyclic group actions on exotic spheres produced.
A new model adds stochastic spot/volatility correlation to Heston model for better exotic pricing.
problem Improving exotic option pricing in foreign exchange markets.
method Developed a Double Heston model with stochastic spot/volatility correlation, an affine model.
result The new model increases prices of out-of-the-money knockout options and one touch options.
The paper constructs exotic knotted surfaces and curves in 4-manifolds.
problem Understanding exotic knotted surfaces and curves in 4-manifolds.
method Local knotting and construction of surfaces and curves.
result First examples of exotically knotted complex curves and symplectic 2-spheres.
In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivat…
Paper finds exotic diffeomorphisms on specific 4-manifolds.
problem Understanding exotic diffeomorphisms on 4-manifolds with .
method Comparing winding numbers of parameter families.
result 2\mathbb{C}\mathbb{P}^2 \# 10 (-\mathbb{C}\mathbb{P}^2) admits exotic diffeomorphisms.
Study optimal semi-static hedging for illiquid markets using dynamic cash and static quoted derivatives.
problem Optimal pricing of exotic derivatives in illiquid markets with bid-ask spreads.
method Use Galerkin method and integration quadratures to approximate hedging problem as convex optimization, solved by interior point method.
result Semi-static hedging improves pricing and reduces transaction costs compared to static or dynamic trading alone.
Investigates how multivariate Lévy models affect calibration and pricing.
problem How multivariate Lévy models affect calibration and pricing.
method Calibration methods of Luciano and Semeraro (2010) and Ballotta and Bonfiglioli (2016) are studied.
result Models can fit market data and price exotic derivatives with rich dependence structures.
Detects exotic embeddings in 4-manifolds with boundary.
problem Detecting exotic diffeomorphisms in 4-manifolds with boundary.
method Defined family versions of Kronheimer-Mrowka invariants and used them to find exotic embeddings.
result First example of exotic 3-spheres in a smooth closed 4-manifold with diffeomorphic complements.
Study exotic phenomena in small 4-manifolds using diffeomorphisms.
problem Understanding exotic smooth structures and embeddings in 4-manifolds.
method Using constraints from Seiberg-Witten theory on diffeomorphisms.
result New methods to detect and bound exotic phenomena.
We show how to construct absolutely exotic smooth structures on compact 4-manifolds with boundary, including contractible manifolds. In particular, we prove that any compact smooth 4-manifold W with boundary that admits a relatively exotic structure contains a pair of codimension-zero submanifolds homotopy equivalent t…
Since the first work on exotic smoothness in physics, it was folklore to assume a direct influence of exotic smoothness to quantum gravity. In the second paper, we calculate the "smoothness structure" part of the path integral in quantum gravity for the exotic R^4 as non-compact manifold. We discuss the influence of th…
New exotic structures found on 4-manifolds with specific groups.
problem Finding exotic smooth structures on 4-manifolds with certain fundamental groups.
method Constructing new smooth structures using definite intersection forms and fundamental groups.
result Infinitely many exotic smooth structures on 4-manifolds with fundamental group Z/2Z.
4-manifolds can be exotic after connected sum with S^2 x S^2.
problem Existence of exotic contractible 4-manifolds.
method Constructed a cork that remains exotic after connected sum with S^2 x S^2.
result Existence of exotic pair of contractible 4-manifolds.
New exotic 4-manifolds found with small trisection genus.
problem Finding exotic 4-manifolds with small trisection genus.
method Constructing genus-3 relative trisections for contractible 4-manifolds.
result Exotic 4-manifolds with boundary have trisection genus of 4.
This paper constructs exotic diffeomorphisms on reducible 4-manifolds with odd b+.
problem Detecting exotic diffeomorphisms on reducible 4-manifolds with odd b+.
method Using a families Bauer-Furuta invariant and pin-cobordism.
result Constructs exotic diffeomorphisms on reducible 4-manifolds with odd b+.
Hedging strategies and minimal variance portfolios for European and exotic options in a Levy marketq-fin.PM
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…
In this paper we introduce exotic twisted -equivariant K-theory of loop space depending on the (typically non-flat) holonomy line bundle on induced from a gerbe with connection on . We also define exotic twisted -equivariant Chern character that maps the exotic tw…
Classifies geodesic planes outside convex core of geometrically finite 3-manifolds.
problem Classifying geodesic planes in geometrically finite 3-manifolds.
method Constructive proof involving exotic rays and roofs.
result Existence of exotic roofs depends on the existence of exotic rays and bending lamination properties.
Exotic diffeomorphisms found on complex surfaces and 4-manifolds.
problem Finding exotic diffeomorphisms on 4-manifolds.
method Minimal complex surfaces and spin 4-manifolds with boundary.
result First known instances of exotic diffeomorphisms of irreducible 4-manifolds.