In the streaming era, music revenues distributed to rights holders have become more transparent. However, it is not yet clear how to quantify the risk and return characteristics of music royalty assets, as is done with equities. In this paper, we fit three discounted cashflow models to transactions on the Royalty Exchange platform. We use our best model to backtest the one year and five year performance of music royalty assets, after transaction costs. We find that Life of Rights (LOR) music assets had risk and return characteristics comparable to stocks in the S\&P500, when held over 5 years. Since the performance of stocks and music assets are likely to be uncorrelated, this result may help investors assess this asset class within the context of a more traditional stock and bond portfolio.
Abstract The number of median fin-rays is a readily quantifiable trait that has been previously studied due to its interspecific variation. I observed in F2 progeny from two inbred lines of medaka with differing anal fin-ray numbers (Kaga and Hd-rRII1) that individuals exhibited the same ray number but differed in the anteroposterior length of the anal fin and the interval between the anal fin-rays. Inducing vertebral fusion to shorten the anal fin anteroposterior length resulted in a decrease in ray number. Given reports of an increased ray number during low-temperature development, I reared Hd-rRII1 fry at 17°C post-hatching, which resulted in an increase in the number of rays. At this temperature, the anal fin anteroposterior length and the interval between the anal fin-rays were also slightly reduced. Since the posterior boundary of the anal fin is determined by Hox genes, I hypothesize that a temperature-sensitive signaling pathway exists downstream of these genes. Collectively, our results suggest that the medaka anal fin-ray number is determined by at least two genetic traits: the anal fin anteroposterior length and the interval between the anal fin-rays.
In this study, MLP models with dynamic structure are applied to factor models for asset pricing tasks. Concretely, the MLP pyramid model structure was employed on firm-characteristic-sorted portfolio factors for modelling the large-capital US stocks. It was further developed as a practicable factor investing strategy based on the predictions. The main findings in this chapter were evaluated from two angles: model performance and investing performance, which were compared from the periods with and without COVID-19. The empirical results indicated that with the restrictions of the data size, the MLP models no longer perform "deeper, better", while the proposed MLP models with two and three hidden layers have higher flexibility to model the factors in this case. This study also verified the idea of previous works that MLP models for factor investing have more meaning in the downside risk control than in pursuing the absolute annual returns.
We propose a convolution-FFT method for pricing European options under the Heston model that leverages a continuously differentiable representation of the joint characteristic function. Unlike existing Fourier-based methods that rely on branch-cut adjustments or empirically tuned damping parameters, our approach yields a stable integrand even under large frequency oscillations. Crucially, we derive fully analytical error bounds that quantify both truncation error and discretization error in terms of model parameters and grid settings. To the best of our knowledge, this is the first work to provide such explicit, closed-form error estimates for an FFT-based convolution method specialized to the Heston model. Numerical experiments confirm the theoretical rates and illustrate robust, high-accuracy option pricing at modest computational cost.
Jagdish Gnawali, W. Brent Lindquist, Svetlozar T. Rachev
We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets consist of a stock and a perpetual derivative of that stock. The option has the stock and its derivative as its underlying. Using a replicating portfolio, we develop prices for European options and generate the unique relationships between the risk-neutral and real-world parameters of the model. We discuss calibration of the model to empirical data in the cases in which the risky asset returns are treated as either arithmetic or logarithmic. From historical price and call option data for select large cap stocks, we develop implied parameter surfaces for the real-world parameters in the model.
Samuel Collins, Thomas James, Felicity Southworth
et al.
Abstract The decontamination of exposed persons is a priority following the release of toxic chemicals. Efficacious decontamination reduces the risk of harm to those directly affected and prevents the uncontrolled spread of contamination. Human studies examining the effectiveness of emergency decontamination procedures have primarily focused on decontaminating skin, with few examining the decontamination of hair and scalp. We report the outcome of two studies designed to evaluate the efficacy of current United Kingdom (UK) improvised, interim and specialist mass casualty decontamination protocols when conducted in sequence. Decontamination efficacy was evaluated using two chemical simulants, methyl salicylate (MeS) and benzyl salicylate (BeS) applied to and recovered from the hair of volunteers. Twenty-four-hour urinary MeS and BeS were measured as a surrogate for systemic bioavailability. Current UK decontamination methods performed in sequence were partially effective at removing MeS and BeS from hair and underlying scalp. BeS and MeS levels in urine indicated that decontamination had no significant effect on systemic exposure raising important considerations with respect to the speed of decontamination. The decontamination of hair may therefore be challenging for first responders, requiring careful management of exposed persons following decontamination. Further work to extend these studies is required with a broader range of chemical simulants, a larger group of volunteers and at different intervention times.
We develop a tractable equilibrium model for price formation in intraday electricity markets in the presence of intermittent renewable generation. Using stochastic control theory, we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in closed form for a finite number of agents as well as in the asymptotic framework of mean field games. Our model reproduces the empirical features of intraday market prices, such as increasing price volatility at the approach of the delivery date and the correlation between price and renewable infeed forecasts, and relates these features with market characteristics like liquidity, number of agents, and imbalance penalty.
This paper investigates how to measure common market risk factors using newly proposed Panel Quantile Regression Model for Returns. By exploring the fact that volatility crosses all quantiles of the return distribution and using penalized fixed effects estimator we are able to control for otherwise unobserved heterogeneity among financial assets. Direct benefits of the proposed approach are revealed in the portfolio Value-at-Risk forecasting application, where our modeling strategy performs significantly better than several benchmark models according to both statistical and economic comparison. In particular Panel Quantile Regression Model for Returns consistently outperforms all the competitors in the 5\% and 10\% quantiles. Sound statistical performance translates directly into economic gains which is demonstrated in the Global Minimum Value-at-Risk Portfolio and Markowitz-like comparison. Overall results of our research are important for correct identification of the sources of systemic risk, and are particularly attractive for high dimensional applications.
Collateralization with daily margining has become a new standard in the post-crisis market. Although there appeared vast literature on a so-called multi-curve framework, a complete picture of a multi-currency setup with cross-currency basis can be rarely found since our initial attempts. This work gives its extension regarding a general framework of interest rates in a fully collateralized market. It gives a new formulation of the currency funding spread which is better suited for the general dependence. In the last half, it develops a discretization of the HJM framework with a fixed tenor structure, which makes it implementable as a traditional Market Model.
We derive a general multivariate theory for realised characteristics of `model-free discretisation-invariant swaps', so-called because the standard no-arbitrage assumption of martingale forward prices is sufficient to derive fair-value swap rates for such characteristics which have no jump or discretisation errors. This theory underpins specific examples for swaps based on higher moments of a single log return distribution where exact replication is possible via option-implied `fundamental contracts' like the log contact. The common factors determining the S&P 500 risk premia associated with these higher-moment characteristics are investigated empirically at the daily, weekly and monthly frequencies.
In the paper we develop mathematical tools of quantile hedging in incomplete market. Those could be used for two significant applications: o calculating the \textbf{optimal capital requirement imposed by Solvency II} (Directive 2009/138/EC of the European Parliament and of the Council) when the market and non-market risk is present in insurance company. We show hot to find the minimal capital $V_0$ to provide with the one-year hedging strategy for insurance company satisfying $E\left[{\mathbf 1}_{\{V_1 \geq D\}}\right]=0.995$, where $V_1$ denotes the value of insurance company in one year time and $D$ is the payoff of the contract. o finding a hedging strategy for derivative not using underlying but an asset with dynamics correlated or in some other way dependent (no deterministically) on underlying. The work is a generalisation of the work of Klusik and Palmowski \cite{KluPal}. Keywords: quantile hedging, solvency II, capital modelling, hedging options on nontradable asset.
Bielecki and Rutkowski (2014) introduced and studied a generic nonlinear market model, which includes several risky assets, multiple funding accounts and margin accounts. In this paper, we examine the pricing and hedging of contract both from the perspective of the hedger and the counterparty with arbitrary initial endowments. We derive inequalities for unilateral prices and we give the range for either fair bilateral prices or bilaterally profitable prices. We also study the monotonicity of a unilateral price with respect to the initial endowment. Our study hinges on results for BSDE driven by continuous martingales obtained in Nie and Rutkowski (2014), but we also derive the pricing PDEs for path-independent contingent claims of European style in a Markovian framework.
Matthew Lorig, Oriol Lozano Carbasse, Rafael Mendoza-Arriaga
We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Lévy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Lévy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the Lévy subordinator that drives the underlying can be obtained directly by observing European call/put prices. To illustrate our general framework, we provide an explicit formula for the value of a variance swap when the underlying is modeled as (i) a Lévy subordinated geometric Brownian motion with default and (ii) a Lévy subordinated Jump-to-default CEV process (see \citet{carr-linetsky-1}). {In the latter example, we extend} the results of \cite{mendoza-carr-linetsky-1}, by allowing for joint valuation of credit and equity derivatives as well as variance swaps.
In this paper we propose a simple and efficient method to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. We give the analytical expressions for the ordered default time distributions with recursive formulas for the coefficients, which makes the calculation fast and efficient in finding rates of basket CDSs. In the homogeneous case, we explore the ordered default time in limiting case and further include the exponential decay and the multistate stochastic intensity process. The numerical study indicates that, in the valuation of the swap rates and their sensitivities with respect to underlying parameters, our proposed model outperforms the Monte Carlo method.
In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise premium can be cast into the form of a decoupled non-linear FBSDE. We numerically solve the FBSDE by applying an interacting particle method recently proposed by Fujii and Takahashi (2012d), which allows one to perform a Monte Carlo simulation in a fully forward-looking manner. We perform the fourth-order analysis for the Black-Scholes (BS) model and the third-order analysis for the Heston model. The comparison to those obtained from existing tree algorithms shows the effectiveness of the particle method.
The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the associated counter party credit risk. By introducing the collateral coverage ratio, our framework can handle these issues in an unified manner. Although the resultant pricing formula becomes non-linear FBSDE and cannot be solve exactly, the fist order approximation is provided using Gateaux derivative. We have shown that it allows us to decompose the price of generic contract into three parts: market benchmark, bilateral credit value adjustment (CVA), and the collateral cost adjustment (CCA) independent from the credit risk. We have studied each term closely, and demonstrated the significant impact of asymmetric collateralization through CCA using the numerical examples.
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the numéraire process causes significant changes in the market properties. In particular, an equivalent martingale measure is not unique for this market, and there are non-replicable claims. The martingale prices and the hedging error can vary significantly and take extreme values, for some extreme choices of the equivalent martingale measures. Some rational choices of the equivalent martingale measures are suggested and discussed, including implied measures calculated from observed bond prices. This allows to calculate the implied market price of risk process.
Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products that use these models for their underlying assets is a non-trivial exercise due to the incomplete nature of the corresponding market. In this paper we apply two volatility estimation techniques available in the literature for these models, namely Kalman filtering and the hierarchical-likelihood approach, in order to implement various pricing and dynamical hedging strategies. Our study shows that the local risk minimization scheme developed by Föllmer, Schweizer, and Sondermann is particularly appropriate in this setup, especially for at and in the money options or for low hedging frequencies.