This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these results are applied to value extendible options. Moreover, some special cases of …
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48 results for “compound options”
A new method solves complex financial problems using deep learning.
problem Optimal stopping and option pricing in finance.
method Compound BSDE method, based on reformulating BSDEs.
result The method offers accurate and efficient solutions for high-dimensional problems.
The paper introduces ESG valuation in option pricing using binomial trees.
problem Option pricing with ESG considerations and discrete compounding.
method Replicating binomial trees with ESG valuation and discrete compounding.
result The approach enhances yield and reflects market history.
Study short-maturity VIX and European option prices with jumps.
problem Analyzing VIX and European options with jumps in short-maturity models.
method Local-stochastic volatility models with compound Poisson jumps, leading-order asymptotics in closed-form.
result Closed-form solutions for VIX and European option prices in short-maturity models.
New MC-Tree method combines Monte Carlo and binomial tree for option pricing and CVA.
problem Combining Monte Carlo and binomial tree methods for accurate and efficient option pricing and CVA calculations.
method MC-Tree method that mixes Monte Carlo and binomial tree parameters, using maximum entropy distributions for compound densities.
result MC-Tree method provides accurate and efficient option pricing and CVA calculations.
New model prices options with complex market data structures.
problem Complex market data structures in option pricing.
method Compound CARMA(p,q)-Hawkes model.
result Model can replicate volatility smile in financial markets.
The paper develops Hawkes-based models for LOB and applies them to European, spread, and basket option pricing.
problem Developing accurate models for pricing options in the context of limit order books (LOB).
method Introduces multivariate Hawkes processes and their limit theorems, applies to European, spread, and basket options.
result Hawkes-based models provide more market forecast information than classical models.
Strategic valuation of efficient and well-timed network investments under uncertain electricity market environment has become increasingly challenging, because there generally exist multiple interacting options in these investments, and failing to systematically consider these options can lead to decisions that underva…
We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is except at the stopping boundary and that it is everywhere (i.e. the smooth pasting conditio…
A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of t…
The paper prices long-term options with a reflecting barrier model.
problem Pricing long-term options with asset price limits.
method Model asset price as geometric Brownian motion with a lower reflecting barrier, pricing options using compound options.
result Option prices can be determined using standard risk-neutral arguments, and hedging strategies are available.
A new method calculates accurate SABR model option prices and deltas.
problem Inaccurate and arbitrageable SABR model option prices and deltas.
method Gaussian quadrature integration scheme for the normal SABR model.
result Accurate and arbitrage-free SABR model option prices and deltas calculated with 49 points.
We investigate the pricing of cliquet options in a jump-diffusion model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a drifted Lévy process entailing a Brownian diffusion component as well as compound Poisson jumps. We also derive representations for the density…
We model the price of a stock via a Langévin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound Poisson processes with operator stable jump intensities. We derive exact relations f…
Study short maturity Asian options in jump-diffusion models with local volatility.
problem Analyzing Asian options pricing in models with jumps and local volatility.
method Asymptotic analysis for short maturity, considering fixed and floating strike options.
result Explicit results for Asian option prices in several models, including Merton, double-exponential, and Variance Gamma models.
Optimizing option exercise policies based on variance optimal martingale measure can lead to unappealing results.
problem Optimizing American option exercise policies under the variance optimal martingale measure can result in unappealing policies.
method Optimizing option exercise policies under the variance optimal martingale measure, then anchoring to the resulting value of this policy.
result Optimizing option exercise policies based on the variance optimal martingale measure can lead to unappealing results.
Derives a pricing formula for VIX options using a new stochastic volatility model.
problem Pricing VIX options under a new stochastic volatility model with volatility clustering.
method Derives a semi-analytical pricing formula using the Heston-Hawkes model with an independent compound Hawkes process.
result Derives an explicit expression for VIX^2 as a linear combination of variance and Hawkes intensity.
Option Pricing under Stochastic Volatility and Jumps:A PIDE Framework with Empirical Evidenceq-fin.PR
Develops a PIDE framework for option pricing with stochastic volatility and jumps.
problem Option pricing under stochastic volatility and jumps.
method PIDE framework derived from Lévy-type process, implemented via finite-difference discretization with FFT for nonlocal jump operator, calibrated using GMM.
result Stochastic volatility accounts for most pricing improvement, reducing implied-volatility RMSE by 39% compared to Black-Scholes.
We consider the problem of pricing derivatives written on some industrial loss index via utility indifference pricing. The industrial loss index is modelled by a compound Poisson process and the insurer can adjust her portfolio by choosing the risk loading, which in turn determines the demand. We compute the price of a…
This paper examines the problem of pricing spread options under some models with jumps driven by Compound Poisson Processes and stochastic volatilities in the form of Cox-Ingersoll-Ross(CIR) processes. We derive the characteristic function for two market models featuring joint normally distributed jumps, stochastic vol…
Motivation: Drug discovery demands rapid quantification of compound-protein interaction (CPI). However, there is a lack of methods that can predict compound-protein affinity from sequences alone with high applicability, accuracy, and interpretability. Results: We present a seamless integration of domain knowledges and …
In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with jumps, the Bates model. In this model the asset log-returns are assumed to follow a jump-diffusion model where the jump component consists of a Levy process of compound Poisson …
We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security prici…
Improved model for SOFR, SONIA, and ESTR caplets pricing.
problem Accurate pricing of options on backward-looking rates.
method Extended Turfus and Romero-Bermúdez model to include smile and skew.
result Simple effective variance formulae for caplet pricing.
The paper shows robustness of Hilbert space-valued stochastic volatility models to perturbations.
problem Robustness of Hilbert space-valued stochastic volatility models to measurement or approximation errors.
method Quantifying the error induced by volatility perturbations and studying robustness of volatility process with finite dimensional approximations.
result Explicit bounds for the induced error in terms of approximation of the underlying parameter.
Study prices energy derivatives using specific stochastic processes.
problem Pricing energy derivatives in markets driven by specific stochastic processes.
method Calculated characteristic functions, derived non-arbitrage conditions, and developed efficient algorithms for simulation.
result Developed methods for pricing various energy contracts.
When the underlying asset displays oscillations, spikes or heavy-tailed distributions, the lognormal diffusion process (for which Black and Scholes developed their momentous option pricing formula) is inadequate: in order to overcome these real world difficulties many models have been developed. Merton proposed a jump-…
Based on the concept of self-decomposable random variables we discuss the application of a model for a pair of dependent Poisson processes to energy facilities. Due to the resulting structure of the jump events we can see the self-decomposability as a form of cointegration among jumps. In the context of energy faciliti…
Study estimates Medallion's compounded return before fees at 31.8%.
problem Incorrectly using yearly returns for compounding leads to overestimation of fund performance.
method Used fund sizes and trading profits to estimate compounded return; used manager's wealth as proxy for Simons.
result Annualized compounded return of Medallion before fees is likely under 35%
Characterizes measures preserving compound mixed renewal process properties.
problem Preserving compound mixed renewal process properties under different probability measures.
method Characterization of progressively equivalent probability measures.
result Any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures.
We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix onto a non-random vector. The scaling index models prices of the individual financial asse…
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
We study T. Cover's rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $\$1$ deposit into the best of some finite set of (perhaps levered) rebalancing rules determined in hindsight. A r…
Generates natural product-like compounds using GPT models.
problem Challenges in generating and evaluating natural product-like compounds.
method Trained GPT-based chemical language models on natural product dataset.
result Generated compounds have similar distribution to natural products.
High throughput screening of compounds (chemicals) is an essential part of drug discovery [7], involving thousands to millions of compounds, with the purpose of identifying candidate hits. Most statistical tools, including the industry standard B-score method, work on individual compound plates and do not exploit cross…
Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. To this end, in this paper we present exact and fast methodologies for the simulation of the spot price dynamics modeled as the …
In this paper, we introduce a new model for the risk process based on general compound Hawkes process (GCHP) for the arrival of claims. We call it risk model based on general compound Hawkes process (RMGCHP). The Law of Large Numbers (LLN) and the Functional Central Limit Theorem (FCLT) are proved. We also study the ma…
Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general nonparametric regression models using normalized compound random measure mixture models. Posterior inference is made using a novel pseudo-marginal Metropolis-Hastings sampler for normalized comp…
A semi-supervised learning framework for quantitative structure-activity regression modellingstat.AP
Semi-supervised learning improves QSAR model predictions for novel compounds.
problem Improving model predictions for compounds not in the training set and adjusting for selection bias.
method Semi-supervised learning framework to estimate model quality and adjust for selection bias.
result Predictions for novel compounds are improved by accounting for compound similarity and selection bias.
Compound Finance optimizes risk metrics for V3 protocol using Chainrisk simulations.
problem Optimizing systemic risks in Compound V3 protocol.
method Millions of Chainrisk simulations to evaluate VaR and LaR, providing parameter adjustments.
result Optimization framework enhances protocol stability.
STMT predicts compounds in unknown areas with trend reflection.
problem Predicting properties of unknown compounds in the extrapolation area.
method Stochastic Threshold Model Trees (STMT) that reflects data trends.
result STMT improves prediction accuracy for one compound in the extrapolation area.
Riemannian geometry for Compound Gaussian distributions: application to recursive change detectionstat.ML
New Riemannian geometry for Compound Gaussian distributions applied to efficient change detection.
problem Change detection in multivariate image times series.
method Developed a recursive approach based on Riemannian optimization.
result Optimal performance achieved with computational efficiency.
ChemGrapher uses deep learning to automatically convert chemical compound images into accurate graphs.
problem Automatically converting chemical compound images into accurate graphs with correct bond multiplicity and stereochemical information.
method Developed a deep neural network model for optical compound recognition, including segmentation and classification models.
result Significant error reductions in bond multiplicity and stereochemical information compared to existing tools.
The study improves compound selection in in silico screening by focusing on model's ability to predict desirable outcomes.
problem Improving compound selection in in silico screening to reduce errors and enhance generalization.
method Extending learning theory, the study analyzes the impact of selection policies on generalization and proposes a method to mitigate challenges.
result Generalization can be enhanced by considering a model's ability to predict the fraction of desired outcomes in a batch.
With the rapid development of high-throughput technologies, parallel acquisition of large-scale drug-informatics data provides huge opportunities to improve pharmaceutical research and development. One significant application is the purpose prediction of small molecule compounds, aiming to specify therapeutic propertie…
Ethereum's Pectra upgrade introduces 0x02 compounding validators, offering higher stake and potential APR uplifts.
problem Staking rewards on Ethereum
method Analyzing compounding effects on consensus-layer rewards
result 0x02 validators achieve modestly higher median CL APR
The paper develops generalization bounds for deep compound Gaussian neural networks.
problem Developing theoretical guarantees for the performance of deep neural networks.
method Novel generalization error bounds using a compound Gaussian prior and Dudley's integral.
result Theoretical bounds show generalization error scales in signal dimension and in network size.
New MGCPP model for order flow in financial markets.
problem Modeling order flow dynamics in financial markets.
method Developed MGCPP, proved LLN and FCLTs, applied to real data.
result Validated MGCPP model with real trading data.