Optimal limit order prices become constant when underlying price is mean reverting.
problem Optimal limit order prices tracking mean reverting price.
method Optimal control models with mean reverting price assumption.
result Optimal bid and ask prices become constant for far times from terminal.
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that daily LPPL returns are typically orders of magnitude smaller than measured price…
Paper presents fast methods for pricing energy derivatives using mean-reverting jump-diffusion models.
problem Pricing energy derivatives with mean-reverting and occasional spikes.
method Exact and fast simulation of spot price dynamics using Ornstein-Uhlenbeck and jump-diffusion processes.
result Apparent computational advantages of the proposed procedures for pricing Asian options, gas storages, and swings.
The paper analyzes optimal timing to sell assets under different price dynamics and utility functions.
problem Optimal timing to sell risky assets under different price dynamics and risk preferences.
method Two stochastic models (trending and mean-reverting) and three utility functions (exponential, power, log) are considered to derive optimal thresholds and certainty equivalents.
result The timing option can make the investor's value function and certainty equivalent non-concave in price.
New numerical method for non-linear asset price model with CEV volatility.
problem Describing stochastic volatility in asset price dynamics.
method Proposes a mean-reverting theta-rho model with CEV volatility, constructs a truncated EM method.
result Truncated EM solutions can evaluate path-dependent financial products.
Optimal purchasing policy for mean-reverting items with a finite deadline.
problem Minimizing cost of purchasing and holding mean-reverting items within a fixed time.
method Proved optimal policy as a time-variant threshold function, constructed with dynamic programming.
result Explicit equations for crossing time probability and overshoot expectation.
A one-factor asset pricing model with an Ornstein--Uhlenbeck process as its state variable is studied under partial information: the mean-reverting level and the mean-reverting speed parameters are modeled as hidden/unobservable stochastic variables. No-arbitrage pricing formulas for derivative securities written on a …
Trading styles affect long-run variance of asset prices, increasing under trend-following and decreasing under mean-reverting.
problem Understanding how different trading styles impact the long-run variance of asset prices.
method Probabilistic models designed to capture the direction of trading were used.
result Trading styles increase long-run variance under trend-following and decrease it under mean-reverting conditions.
The paper values perpetual callable American volatility options using a mean-reverting volatility model.
problem Valuation of callable American volatility put options.
method Modeling volatility dynamics as a mean-reverting 3/2 process and proposing a pricing formula.
result The value of perpetual callable American volatility put options is discussed under given conditions.
Optimal timing strategy for mean-reverting price spreads.
problem Trading price spreads with mean-reverting characteristics.
method Sequential optimal stopping framework with refined signature method.
result Precise entry and exit timings that maximize gains.
The paper reconciles rough volatility with fast mean reverting models.
problem Empirical evidence of rough volatility contradicts fast mean reverting models.
method Analyzes mean reverting rough volatility and compares it to fast mean reverting Markov volatilities.
result Price impact of rough volatility coincides with fast mean reverting models.
Two new models improve option valuation for negative or mean reverting futures markets.
problem Valuation of futures contracts with negative underlying prices.
method Proposed two models: Ornstein-Uhlenbeck and continuous time GARCH.
result Improved option values compared to Black 76, especially for negative or mean reverting markets.
The paper solves complex swing option pricing equations with numerical methods.
problem Valuation of swing options with jumps under a mean-reverting model.
method Proposes second-order numerical methods to solve PIDEs convection-dominated and with nonlocal integral terms.
result Numerical methods confirm second-order convergence behavior.
Model prices sovereign contingent convertible bonds during crises.
problem Pricing Sovereign Contingent Convertible bonds (S-CoCo) during crises.
method Model CDS spread regime switching as a hidden Markov process, coupled with a mean-reverting stochastic process. Use Longstaff-Schwartz American option pricing framework for simulation.
result Computed future state contingent S-CoCo prices for risk management.
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European opt…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility sur…
High-frequency traders manage inventories to exploit price information, leading to mean-reverting inventories and excess trading.
problem Managing inventories for high-frequency traders in imperfect competition.
method Analyzes Nash equilibria for inventory-averse HFTs using nonlinear equations and asymptotic analysis.
result Optimal inventories become mean-reverting and vanish in the continuous-time limit, while HFTs' profits converge to risk-neutral counterparts.
Proposes a new model for stock and dividend derivatives pricing.
problem Pricing stock and dividend derivatives with positive stock prices and non-negative dividends.
method Jointly specifies dynamics for stock price and dividend rate, using mean-reverting dividend rate.
result Closed-form expressions for stock and dividend futures prices, accurate option approximations.
A new model for short rates using pure-jump processes.
problem Modeling short rates with bounded behavior and affine bond prices.
method Sum of pure-jump Ornstein-Uhlenbeck processes for mean-reversion, with affine bond price representations.
result The model can be market-consistently calibrated and has an explicit option pricing formula.
The paper finds optimal levels for traders in mean-reverting markets.
problem Determining optimal levels for traders in mean-reverting markets.
method Analytical framework using heat potentials.
result Developed an analytical solution for optimal levels.
The price of electricity is far more volatile than that of other commodities normally noted for extreme volatility. The possibility of extreme price movements increases the risk of trading in electricity markets. However, underlying the process of price returns is a strong mean-reverting mechanism. We study this featur…
Study optimal trading strategies for mean-reverting spreads using integral equations.
problem Optimal timing for trading mean-reverting price spreads.
method Utilized local time-space calculus and nonlinear integral equations of Volterra-type.
result Derived optimal boundaries for trading strategies.
Optimizes a portfolio with mean-reverting assets using Ornstein-Uhlenbeck process.
problem Design a portfolio with high mean reversion and low variance.
method Penalized OU-Likelihood Estimation with specialized algorithm.
result Parsimonious portfolio selection with desirable characteristics.
A Monte Carlo method for pairs trading on mean-reverting spreads with Lévy processes.
problem Trading on mean-reverting spreads with flexible models.
method Monte Carlo simulation with variance gamma and alpha-gamma driving processes.
result Optimal trading strategies are affected by model parameters and correlation.
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for European option prices. The resulting pricing formulas are semi-analytic, in th…
In this note, we derive the characteristic function expansion for logarithm of the underlying asset price in corrected Heston model as proposed by Fouque and Lorig.
Hybrid LSMC-PDE method for Bermudan options under GDMR model.
problem Pricing Bermudan options under the GDMR model.
method Adapted Hybrid LSMC-PDE framework, combining Monte Carlo and PDE methods.
result Hybrid approach yields more accurate and lower error estimates than plain LSMC.
We study an optimal execution problem in the presence of market impact where the security price follows a geometric Ornstein-Uhlenbeck process, which implies the mean-reverting property, and show that the optimal strategy is a mixture of initial/terminal block liquidation and gradual intermediate liquidation. The mean-…
Optimal trading incorporates signals to reduce costs and price dynamics disruptions.
problem Minimizing trading costs and price dynamics disruptions in large orders.
method Incorporates a Markovian signal into optimal trading framework, proving existence and uniqueness of optimal strategies.
result Explicit singular optimal strategy derived for an Ornstein-Uhlenbeck signal and exponentially decaying market impact.
We discuss stochastic modeling of volatility persistence and anti-correlations in electricity spot prices, and for this purpose we present two mean-reverting versions of the multifractal random walk (MRW). In the first model the anti-correlations are modeled in the same way as in an Ornstein-Uhlenbeck process, i.e. via…
New method uses Hermite polynomials for American option valuation.
problem Valuation of American options with complex jump-diffusion dynamics.
method Hermite polynomial expansions of transition density and early exercise premium.
result Converging approximations to true option prices and exercise boundaries.
The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validat…
Optimizes trading in markets with unpredictable price impacts.
problem Optimizing trading strategies in markets with stochastic price impacts.
method Singular perturbation methods to approximate optimal control problem.
result Proves approximations are accurate to specified order using sub- and super-solutions.
Modeling horse race betting odds with Ornstein-Uhlenbeck process.
problem Analyzing how herding and informed bettors affect odds movements.
method Deriving an Ornstein-Uhlenbeck process from vote shares and odds movements data.
result Identified microscopic and macroscopic patterns in odds convergence.
The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process (X,D) of a diffusion state variable X driving default intensity and a default indicator process D and time change it wi…
Study reveals patterns in US stock opening and closing auctions.
problem Investigating the dynamics of US equities opening and closing auctions.
method Analysis of historical data and conditional analysis of auction prices.
result Opening and closing auctions have distinct price reactions to order placements/cancellations.
We analyze long-term memory properties of hourly prices of electricity in the Czech Republic between 2009 and 2012. As the dynamics of the electricity prices is dominated by cycles -- mainly intraday and daily -- we opt for the detrended fluctuation analysis, which is well suited for such specific series. We find that …
The paper analyzes futures trading under mean-reverting spot prices, incorporating timing and chooser options.
problem Trading futures with transaction costs under mean-reverting spot prices.
method Modeling spot dynamics with OU, CIR, or XOU models; deriving futures term structure; solving optimal double stopping problems.
result The option to choose between long or short positions delays market entry compared to pre-committing.
Optimizes portfolios in fast mean-reverting markets, achieving asymptotic efficiency.
problem Optimizing portfolios in markets with fast mean-reverting returns and volatility.
method Proposes a zeroth order strategy and uses singular perturbation method for asymptotic optimality.
result Shows asymptotic optimality of the proposed strategy under specific assumptions.
We analyze analytic approximation formulae for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a volatility nonlinearly depending on the interest rate itself. We derive the order of accuracy of the analytical approximation due to Choi and Wir…
Optimizes sparse mean-reverting portfolios for higher returns.
problem Finding optimal stock weights for mean-reverting portfolios.
method Transformed optimization problem into SDP, added constraints.
result Sparse mean-reverting portfolios provide higher returns with transaction costs.
In this paper, a finite-state mean-reverting model for the short-rate, based on the continuous time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and the special symmetric cases. Its limiting relationship to the Vasicek model will be examined wit…
We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order, that consistently generalizes previously proposed pro…
Study optimal trading times for mean-reverting prices with deadlines.
problem Optimal timing strategies for mean-reverting price processes with deadlines.
method Solve optimal double stopping problems with sequential deadlines using local time-space calculus.
result Derive optimal trading boundaries for long-short, short-long, and chooser strategies.
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local volatility/stochastic volatility mixture model, where the mixture parameter tunes that covariance. T…
In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indiffere…
Study optimal portfolio in intraday electricity markets using Lévy-Ornstein-Uhlenbeck processes.
problem Maximizing expected terminal utility in a single risky asset market.
method Model power prices with mean-reverting additive process, solve HJB equation for logarithmic utility.
result Explicit solution for optimal strategy, numerical and analytical methods available.
Model predicts Bitcoin prices influenced by market attention.
problem Predicting Bitcoin prices considering market attention.
method Model uses a mean-reverting Cox-Ingersoll-Ross process to model market attention, affecting Bitcoin volatility with a delay.
result The model provides semi-closed formulae for European call and put prices, and compares favorably to other models.