Alternative closed-form formula for spread call option prices under log-normal models.
problem Valuation of spread call options under log-normal models.
method Developed an alternative closed-form formula for spread call option prices.
result Our formula performs better for certain range of model parameters than existing closed-form formula.
Formula calculates bond prices between payments.
problem No new bond pricing formula available.
method Closed-form formula derivation.
result Formula accurately calculates bond prices.
The paper uses moment matching method for pricing spread options under Lévy models.
problem Pricing spread options under Lévy models with mean-variance mixture.
method Moment matching method applied to Lévy models with mean-variance mixture.
result Obtains semi-closed form formulas for spread option prices.
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where…
New option pricing formulas for American and Bermudan options.
problem Traditional option pricing models assume constant volatility and interest rate.
method Relaxing assumptions, using square root of Brownian motion, providing closed-form formulas.
result Simple, closed-form pricing formulas for American and Bermudan options.
Improved option pricing formula using relativistic mechanics.
problem Improving Black-Scholes formula for better option pricing accuracy.
method Developed a relativistic version of the Black-Scholes formula and derived a closed-form solution.
result New formula offers significant improvements over existing solutions and better fits empirical data.
Paper proposes a closed-form formula for geometric Istanbul call options.
problem Pricing geometric Istanbul call options under the Black-Scholes model.
method Second-order Taylor expansion to derive a closed-form approximation.
result The proposed formula accurately approximates GIC values compared to Monte-Carlo simulations.
We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for short-time asymptotic expansions of heat kernels, and obtain a family of general…
New formulas for geodesics on Stiefel and flag manifolds using trust-region method.
problem Computing geodesics and logarithms on Stiefel and flag manifolds.
method Closed-form geodesic formulas, trust-region solver, Fréchet derivatives.
result Efficient computation of geodesic distance and logarithm map.
Develops first closed-form portfolio formula for GARCH spot assets.
problem Optimizing portfolio allocation for assets with time-varying volatility.
method Closed-form solution for CRRA utility maximization under HN-GARCH model.
result Optimal strategy is independent of asset volatility development.
New statistical Minkowski distances for Gaussian mixtures with closed-form formulas.
problem Computing distances for Gaussian mixture models efficiently.
method Proposed novel statistical distances based on Minkowski's inequality for Gaussian mixtures.
result Closed-form formula for Gaussian mixture models with integer exponents.
The paper calculates option prices using Mellin transform for stochastic volatility models.
problem Calculating prices for path-dependent options under stochastic volatility.
method Asymptotic approach and Mellin transform for deriving closed-form formulas.
result Derives closed-form formulas for option prices with first-order approximation.
Closed form formulas for swaption prices in HJM model are derived. These formulas are used for nonparametric fit of deterministic forward volatility. It is demonstrated that this formula and non-parametric fit works very well and can be used to identify arbitrage opportunities
We develop closed-form approximations for European put options under stochastic volatility models.
problem Tackling the pricing of European put options under stochastic volatility models with time-dependent parameters.
method Using a second-order Taylor expansion around the mean of the argument, we write the option price as an expectation of a Black-Scholes formula. We then simplify the resulting expectations and derive closed-form pricing formulas under the assumption of piecewise-constant parameters.
result We derive closed-form pricing formulas and bounds on the remainder term generated by the Taylor expansion, showing that the errors are well within acceptable ranges for practical applications.
Study examines pricing of target volatility options in fractional SABR model.
problem Pricing target volatility options in the lognormal fractional SABR model.
method Used Ito's calculus for a theoretical replicating strategy and derived approximations and closed-form expressions.
result Accuracy of approximations for target volatility option pricing in various parameter ranges.
Kristensen and Mele developed a method for closed-form derivatives pricing approximations.
problem Derivatives pricing models are often intractable, making approximation methods necessary.
method Power series expansion of pricing bias between models, leading to closed-form approximations.
result The method provides stable numerical approximations for various derivatives models.
The paper develops a new model-free formula for option initial margins.
problem Calculating initial margins for option portfolios is complex and risky.
method The authors derive a new approximation formula for VaR without assuming a model.
result The new formula performs better than existing methods in simulations.
Derives exact formula for Minkowski sum of ellipsoids in N-space.
problem Finding volume bounds for Minkowski sum of ellipsoids.
method Closed-form parametric equation derivation and volume bounds calculation.
result Upper and lower volume bounds for Minkowski sum of ellipsoids.
New formulas for barrier options in stochastic volatility models with nonzero correlation.
problem Calculating barrier options prices in models with nonzero correlation.
method Derivation of two novel closed-form formulas: Hull and White type and Alòs-like decomposition.
result Closed-form formulas for barrier options in stochastic volatility models with nonzero correlation.
In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the dr…
This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate the validity of our app…
Paper improves basket option pricing for log-normal models.
problem Challenges in pricing basket options with negative weights.
method Moment matching and solving a unary cubic equation.
result Highly accurate closed form solution for basket options.
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form represe…
We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied lognormal volatility in te…
Derives integral formula for ReLU networks with limited weights.
problem Finding optimal neural network weights with limited L1-norm. method Derives integral representation formula for shallow ReLU networks under L1-norm constraint. result Explicitly solves the least L1-norm neural network representation for a given function. We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
New method denoises images without clean reference using Tweedie distributions.
problem Image denoising without clean reference images.
method Combining Tweedie distributions, Noise2Score, and saddle point approximation.
result General closed-form denoising formula for various noise distributions.
Dividend discount models have been developed in a deterministic setting. Some authors (Hurley and Johnson, 1994 and 1998; Yao, 1997) have introduced randomness in terms of stochastic growth rates, delivering closed-form expressions for the expected value of stock prices. This paper extends such previous results by dete…
Develops explicit formulas for minimal immersions in 5D space.
problem Minimal surface models in 5D space.
method Holomorphic null curves in C^5.
result Concrete formulas for conformal minimal immersions in R^5.
Closed-form formulas for path-independent options in a specific Lévy model.
problem Valuation of path-independent options in the exponential NIG model.
method Closed-form pricing formulas derived using a factorized representation in Mellin space and complex analysis.
result Valid closed-form formulas with quickly convergent series for various options.
Improved portfolio optimization using VaR and CVaR with NMVM models.
problem Optimizing portfolios with VaR and CVaR under NMVM distributions.
method Transformed mean-CVaR-skewness problems into quadratic optimization with closed-form solutions for NMVM models.
result Approximate closed-form expressions for VaR and CVaR of NMVM portfolios.
We develop a Chern-Weil theory for compact Lie group action whose generic stabilizers are finite in the framework of equivariant cohomology. This provides a method of changing an equivariant closed form within its cohomological class to a form more suitable to yield localization results. This work is motivated by our w…
New formulas derived for variance gamma model option pricing.
problem Option pricing for the variance gamma model.
method Combining randomization method and fractional derivatives.
result Closed-form formulas for European options.
We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elastic…
Derives adjoint formulas for matrix operations and applies them to specific cases.
problem Computing adjoints for matrix operations and specific matrix types.
method Derives adjoint formulas for matrix operations and applies them to specific cases.
result Closed-form expressions for adjoints in specific matrix types.
The paper extends holomorphic forms on generalized Hermitian manifolds.
problem Understanding holomorphic forms on generalized Hermitian manifolds.
method Developed a criterion for holomorphic forms and used it to extend ∂-closed forms. result Invariance of generalized Hodge numbers in deformations of compact generalized Hermitian manifolds.
Python package ajdmom simplifies moment formula derivation for jump diffusions.
problem Deriving moment formulae for complex jump diffusion processes.
method Automatically generates closed-form expressions and derivatives for any order of moments.
result Enhances usability and usability of affine jump diffusion models.
Study leading-order asymptotics for VIX option prices in Bergomi models.
problem Understanding VIX option pricing in Bergomi models.
method Analytical approach to derive leading-order asymptotics for VIX option prices in Bergomi models.
result Closed-form solutions for VIX option prices in Bergomi models are derived.
Let G_R be a Lie group acting on an oriented manifold M, and let ω be an equivariantly closed form on M. If both G_R and M are compact, then the integral ∫Mω is given by the fixed point integral localization formula (Theorem 7.11 in [BGV]). Unfortunately, this formula fails when the acting Lie group G_R is not…
This paper studies an optimal investment problem under M-CEV with power utility function. Using Laplace transform we obtain explicit expression for optimal strategy in terms of confluent hypergeometric functions. For obtained representations we derive asymptotic and approximation formulas contains only elementary funct…
The classical integral localization formula for equivariantly closed forms (Theorem 7.11 in [BGV]) is well-known and requires the acting Lie group to be compact. It is restated here as Theorem 2. In this article we extend this result to NONcompact groups. The main result is Theorem 20. Then, using this generalization, …
In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by Wüthrich et a…
The paper finds formulas for special surface shapes in 3D space.
problem Creating formulas for constant mean curvature surfaces.
method Weierstrass representations for discrete surfaces in isotropic space.
result Constructs examples of surfaces with discrete parametrizations.
We prove that the control polygon of a Bezier curve B becomes homeomorphic and ambient isotopic to B via subdivision, and we provide closed-form formulas to compute the number of iterations to ensure these topological characteristics. We first show that the exterior angles of control polygons converge exponentially to …
Formula found for braid index of n-bridge braids.
problem Finding a formula for the braid index of n-bridge braids. method Elementary, effective, self-contained proof.
result Closed form formula for braid index of n-bridge braids. Stochastic dividend discount models (Hurley and Johnson, 1994 and 1998, Yao, 1997) present expressions for the expected value of stock prices when future dividends evolve according to some random scheme. In this paper we try to offer a more precise view on this issue proposing a closed-form formula for the variance of …
Closed-form pricing method for multi-asset options.
problem Pricing multi-asset contingent claims in an incomplete market.
method Proving extremal martingale measures and constructing algorithms for bounds and hedging.
result Closed-form formulas for no-arbitrage price intervals and hedging strategies.
Paper approximates free boundary for optimal investment stopping problems.
problem Optimal investment stopping problems with utility maximization.
method Dual control method to derive asymptotic properties and construct a global closed-form approximation.
result Global closed-form approximation of dual free boundary reduces computational cost.