Analytical solutions found for a modified Black-Scholes equation for European put options.
problem Finding solutions for a modified Black-Scholes equation for European put options.
method Used Maple to compute analytical solutions in terms of associated Laguerre polynomials.
result The modified Black-Scholes equation with European put options is exactly solvable.
The paper shows that benchmark-neutral pricing minimizes option prices.
problem Pricing extreme-maturity European put options on diversified indices.
method Benchmark-neutral pricing applied to a drifted time-transformed squared Bessel process.
result Benchmark-neutral price is the minimal possible price, risk-neutral price is more expensive.
Optimal exercise boundary for put options with delivery lags identified.
problem Analyzing the optimal exercise time for American put options with delivery lags.
method Decomposing the option into a European put and a new American-style derivative, using free boundary techniques.
result The optimal exercise boundary exists and is a strictly increasing and smooth curve.
New high-order compact scheme improves basket option pricing accuracy.
problem Improving accuracy in pricing European Put options on a basket of assets.
method Developed a second-order accurate in time and fourth-order accurate in space high-order compact scheme.
result Standard second-order schemes are significantly outperformed by the new scheme.
We consider the pricing of American put options in a model-independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting…
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.
Researchers develop explicit approximations for European put options in stochastic volatility models.
problem Developing accurate approximations for European put option prices in stochastic volatility models.
method Exploits expansions of the mixing representation of the put option price using Malliavin calculus.
result Explicit formulas for option prices and error bounds are derived, with closed-form solutions under piecewise-constant parameters.
The paper explains option pricing using simple calculus for undergraduates.
problem Pricing European and American options in discrete time.
method Binomial model and elementary calculus.
result Put-call parity formulas and bounds for options.
We derive explicit formulas for time decay, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical studies of financial marke…
Study provides short-time expansions for LETF options using Lévy models.
problem Analyzing small-time behavior of LETF option prices with local volatility and jumps.
method Closed-form expressions for leading order terms of LETF option prices near expiration.
result Price of out-of-the-money LETF options is asymptotically equivalent to underlying ETF options with modified prices.
In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff (y−x)+ is replaced by φ(x,y). It turns out that the duality still holds under monotonicity and concavity assumptions on φ. The specific analytical form of the …
Analyzes pricing formulas for barrier options with discrete dividends.
problem Complexity introduced by discrete dividends in pricing formulas.
method Compares Buryak and Guo's analytic approach for European options with Dai and Chiu's barrier option formulas.
result Analytic approach effective for European puts and calls, but performance varies for barrier options.
The paper solves a pricing problem for a multiple reset put option using integral equations.
problem Valuation of a multiple reset put option with reset rights.
method Formulated as a multiple optimal stopping problem, reduced to single optimal stopping problems, solved by induction and integral equations.
result Characterized optimal reset boundaries as solutions to nonlinear integral equations and derived reset premium representations.
The paper prices options using a novel finite element method.
problem Pricing European and American options under the Heston model.
method Discontinuous Galerkin finite element method (dGFEM) with interior penalty and Rannacher smoothing.
result Efficient and accurate pricing of options, demonstrated through comparisons and experiments.
Derives a dual equation for various option types, leading to new pricing and hedging insights.
problem Pricing and hedging of various option types.
method Derives a dual equation with the same form as the Black-Scholes-Merton equation, applicable to homogeneous degree one payoffs.
result Provides simple analytic formulas for delta and gamma, and reveals put-call equality for various options.
The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student's t-distribution, which we call a …
Study on currency option valuation in crisis markets.
problem Valuation of currency options in financial crisis markets.
method Modified Black-Scholes model with augmented stochastic volatility.
result Closed-form solution for European call and put options.
It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper inv…
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…
The article provides formulas to hedge impermanent loss in decentralized markets.
problem Impermanent loss in concentrated liquidity provision in decentralized markets.
method Analytical characterizations and static replication formulas using European calls or puts.
result Static replication formulas accurately hedge impermanent loss.
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.
Quantum algorithm for pricing European call options.
problem Accurate valuation of financial derivatives, especially for complex models and options.
method Transforms classical FFT into quantum QFT for pricing European call options.
result Quantum algorithm outperforms classical Monte Carlo simulation in NISQ era.
The general and special repo rates are related with the prices of the European call- and American put-options. The evaluation takes into account specific business models of the parties in the repo agreement and the law restrictions. Using the repo-option relation, an alternative to the Black-Scholes method of option pr…
Optimized options portfolio with a specific payoff function.
problem Optimizing an options portfolio with a fixed payoff function.
method Formulated as an integer linear programming problem, including an objective payoff function and constraints.
result Optimum solution for European call and put options on Taiwan Futures Exchange.
The study uses Fisher information to estimate volatility uncertainty in Heston model.
problem Estimating volatility uncertainty in financial models like Heston.
method Fit likelihood function on VIX options, compute Fisher information matrices from Heston model Greeks.
result Option prices can reliably estimate volatility when it's large, but become unreliable below a critical value.
In this paper we show how to relate European call and put options on multiple assets to certain convex bodies called lift zonoids. Based on this, geometric properties can be translated into economic statements and vice versa. For instance, the European call-put parity corresponds to the central symmetry property, while…
Analytical pricing formulas and Greeks are obtained for European and American basket put options using Mellin transforms. We assume assets are driven by geometric Brownian motion which exhibit correlation and pay a continuous dividend rate. A novel approach to numerical Mellin inversion is achieved via the fast Fourier…
New formulas for Black-Scholes option prices and Greeks derived.
problem Calculating accurate prices and Greeks for European options.
method Uniformly convergent series expansions for option prices and precise boundaries for convergence speed.
result New formulas for option prices and Greeks with precise convergence rates.
Method extends option valuation for 2D Lévy models.
problem Valuation of European options under 2-asset infinite-activity Lévy models.
method Developed numerical method extending Wang et al. (2007) for 1D to 2D, using Fourier transform for integral term and semi-Lagrangian theta-method for temporal discretization.
result Favourable second-order convergence for Normal Tempered Stable dynamics.
The issue of developing simple Black-Scholes type approximations for pricing European options with large discrete dividends was popular since early 2000's with a few different approaches reported during the last 10 years. Moreover, it has been claimed that at least some of the resulting expressions represent high-quali…
Improved option pricing for assets with jumps and spikes.
problem Inaccurate pricing of European and American options using lognormal diffusion.
method Developed a jump-diffusion model and reduced complexity of pricing algorithms.
result Reduced complexity of European option pricing from O(n^3) to O(n ln n).
Complex volatility leads to chaotic fractals in option pricing.
problem Exploring the implications of complex volatility in Black-Scholes model.
method Analyzing the function for pricing European options with complex volatility and solving for implied volatility.
result Chaotic fractals emerge in the calculation of complex implied volatility.
This work analyzes impermanent loss in decentralized markets and provides a hedging strategy.
problem Impermanent loss in automated market makers (AMMs).
method Analytical derivation of a static replication formula using European options, and numerical example with real data.
result Guaranteed hedging coverage for all final prices within a predefined interval.
Maximizes American put price bounds using European put prices.
problem Finding upper bounds for American put prices.
method Model-free approach using European put prices and martingale transport.
result Derives a model with maximal American put price.
This paper analyzes model risk in American put options using Heston volatility model.
problem Model risk in optimal exercise of American put options.
method Benchmark methodology of Hull and Suo [2002], Heston stochastic volatility model, numerical finite difference methods.
result Optimal exercise behavior is influenced by stochastic volatility dynamics and return-volatility correlation, creating model risk.
The paper analyzes option pricing under subdiffusive fractional Brownian motion.
problem Option pricing with a short rate following subdiffusive fractional Merton model.
method Incorporates stochastic short rate into fractional Black-Scholes equation and derives explicit formulas.
result Explicit formulas for call and put options derived under subdiffusive fractional Merton model.
The aim of this chapter is to show how option prices in jump-diffusion models can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial integro-differential equation (PIDE) in one-dimension for the American put and the European va…
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is possible to give explicit formulae for the variance of European option returns (vani…
This paper provides formulas for minimum cost super-hedging in a multi-asset binomial market.
problem Finding minimum cost super-hedging strategies in a multi-asset, incomplete market model.
method Explicit formulas for minimum cost super-hedging strategies for various European type multi-asset contingent claims.
result Explicit formulas for non-negative local residuals of super-hedging strategies.
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options are traded at certain maturities, and the forward price implied by these option pr…
A new method for pricing exchange options under stochastic volatility and jumps.
problem Pricing European and American exchange options with stochastic volatility and jumps.
method Equivalent martingale measure, numeraire choice, integral transforms, Kolmogorov backward equation, integral equations.
result Reduced exchange option pricing to a one-dimensional problem of a call option.
Analytic methods for option pricing under a novel Lévy model.
problem Developing pricing models for exotic options under a hyperexponential Lévy process.
method Series expansions and Laplace transform techniques.
result Analytic expressions for option prices and Greeks, including an asymptotic expansion of implied volatility.
The paper efficiently solves a complex option valuation equation for two assets.
problem Valuation of European options under a two-asset Kou jump-diffusion model.
method Extends an efficient algorithm for a one-dimensional integral to a two-dimensional one, using operator splitting schemes for time discretization.
result The method achieves optimal computational cost and stable convergence for various operator splitting schemes.
New ADI scheme speeds up option pricing in stochastic models.
problem Efficiently pricing options in models with stochastic volatility.
method High-order ADI scheme combining spatial and time discretizations.
result Fourth-order accuracy in space and second-order in time.
We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the possibility of default and correlation between different assets. We show how to…
Calibrating American options is sped up using model reduction techniques.
problem Calibrating American options is computationally challenging due to their flexibility and constraints.
method Two model reduction strategies: reduced basis method and de-Americanization.
result Calibration process is significantly faster with reduced model complexity.
Introduces a new stochastic volatility model using Jacobi processes.
problem Modeling asset return volatility with improved accuracy and tractability.
method Uses Jacobi processes to model squared volatility, deriving closed-form option pricing formulas.
result Option prices can be accurately approximated using series representations.
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton …