Risk-neutral Model Research Articles

Does risk-sensitivity transfer across movements?

An intriguing finding in motor control studies is the marked effect of risk on movement decision making. However, there are inconsistent reports of risk-sensitivity across different movements and tasks, with both risk-seeking and risk-averse behavior observed. This raises the question of whether risk-sensitivity in movement decision making is context dependent and specific to the movement or task being performed. We investigated whether risk-sensitivity transfers between dissimilar movements within a single task. Healthy young adults made arm-reaching movements or whole-body leaning movements to move a cursor as close to the edge of a virtual cliff as possible without moving beyond the edge. They received points on the basis of the cursor's final proximity to the cliff edge. Risk was manipulated by increasing the point penalty associated with the cliff region and/or adding Gaussian noise to the cursor. We compared subjects' movement endpoints with endpoints predicted by a subject-specific, risk-neutral model of movement planning. Subjects demonstrated risk-seeking behavior in both movements that was consistent across risk environments, moving closer to the cliff than the model predicted. However, subjects were significantly more risk-seeking in whole-body movements. Our results present the first evidence of risk-sensitivity in whole-body movements. They also demonstrate that the direction of risk-sensitivity (i.e., risk-seeking or risk-averse) is similar between arm-reaching and whole-body movements, although degree of risk-sensitivity did not transfer from one movement to another. This finding has important implications for the ability of quantitative descriptions of decision making to generalize across movements and, ultimately, decision-making contexts.

The ABC of Long-Term Capital Budgeting

Our paper tests whether the expected rate-of-return estimates for long-term capital budgeting from the FFM and CAPM could outperform those from a simpler risk-neutral term-structure-based model. Our paper first estimates reasonable shrinkage (input parameters) based on historical data. We find1. Factor exposures drift(ed) significantly over longer horizons2. Since 1970, the arithmetic (geometric) equity premium relative to long- term Treasuries has been only 1.7% (0.8%) per year. This decline was primarily due to higher long-term Treasury yields, not lower average stock returns.Together, this evidence suggest that a user of the FFM and CAPM should drastically shrink the model-input parameters to the point where project cost- of-capital is often no longer meaningfully heterogeneous, i.e., different from that of a risk-neutral pricing model. In addition, the data suggests that3. Textbook application of both the FFM and CAPM failed to predict subse- quent rates of returns given estimated inputs, often even with the wrong sign.This evidence is fundamentally opposite to the recommendations in all major finance textbooks and curriculums in use today.

Hedge Backtesting for Model Validation

Derivative pricing models and risk-neutral EPE models can be assessed for their appropriateness using a nonparametric technique known as hedge backtesting, in which one looks at the quality of the hedging performance generated by the model. In this article, we give a precise definition of a hedge backtest and show what it tells us about a pricing model, how it inform parameter markings, and how it can be used to calculate model reserves. We also relate hedge backtesting theory to martingale and PDE methods for no-arbitrage pricing.

Pricing corporate loans under the risk-neutral measure

Corporate loans trade infrequently, and most methods for discounting loan cashflows ignore the effects of default and prepayment and are unable to value revolving loans. To improve loan valuation and risk management, we develop a risk neutral model to value corporate loans and revolving credit lines. The method models the credit-dependent prepayment option and revolver usage patterns using a lattice of risk-neutral credit transitions determined from historical data and modified to be consistent with market prices of credit default swaps. The model calculates average lives of loans, their average times to default, and loan-price sensitivities to market movements.

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Model risk of the implied GARCH-normal model

Model risk causes significant losses in financial derivative pricing and hedging. Investors may undertake relatively risky investments due to insufficient hedging or overpaying implied by flawed models. The GARCH model with normal innovations (GARCH-normal) has been adopted to depict the dynamics of the returns in many applications. The implied GARCH-normal model is the one minimizing the mean square error between the market option values and the GARCH-normal option prices. In this study, we investigate the model risk of the implied GARCH-normal model fitted to conditional leptokurtic returns, an important feature of financial data. The risk-neutral GARCH model with conditional leptokurtic innovations is derived by the extended Girsanov principle. The option prices and hedging positions of the conditional leptokurtic GARCH models are obtained by extending the dynamic semiparametric approach of Huang and Guo [Statist. Sin., 2009, 19, 1037–1054]. In the simulation study we find significant model risk of the implied GARCH-normal model in pricing and hedging barrier and lookback options when the underlying dynamics follow a GARCH-t model.

Who Said Large Banks Don't Experience Scale Economies? Evidence from a Risk-Return-Driven Cost Function

Earlier studies found little evidence of scale economies at large banks; later studies using data from the 1990s uncovered such evidence, providing a rationale for very large banks seen worldwide. Using more recent data, we estimate scale economies using two production models. The standard risk-neutral model finds little evidence of scale economies. The model using more general risk preferences and endogenous risk-taking finds large scale economies. We show that these economies are not driven by too-big-to-fail considerations. We evaluate the cost implications of breaking up the largest banks into banks of smaller size.

Risk-Neutral Models for Emission Allowance Prices and Option Valuation

The existence of mandatory emission trading schemes in Europe and the United States, and the increased liquidity of trading on futures contracts on CO2 emissions allowances, led naturally to the next step in the development of these markets: These futures contracts are now used as underliers for a vibrant derivative market. In this paper, we give a rigorous analysis of a simple risk-neutral reduced-form model for allowance futures prices, demonstrate its calibration to historical data, and show how to price European call options written on these contracts. This paper was accepted by Haitao Li, guest editor, finance.

Heterogeneous Agents and the Indifference Pricing of Property Index Linked Swaps

Swap spreads predicted by the traditional risk-neutral valuation models are much lower than the quoted market spreads for property index linked swaps (Patel and Pereira, Journal of Real Estate Finance and Economics, 36:5-21, 2008). This paper attempts to develop a utility indifference-based model for evaluating the reservation spreads of swap receivers and payers based on the principle of expected wealth utility equivalence rather than the traditional risk-neutral argument. Under the proposed model framework, this paper addresses the determination of the swap spreads. When the incompleteness of real estate markets and heterogeneity of representative agents are taken into consideration, it is shown that heterogeneous risk preferences and beliefs about expected future property returns are the remarkable determinants for the swap spreads. Our model also identifies market power and the settlement rules in the event of counterparty default as important factors in determining the swap spreads. Our model provides a possible interpretation for the difference between the spreads predicted by the traditional models and the actual market spreads.

Mean-downside-risk and mean-variance newsvendor models: Implications for sustainable fashion retailing

Abstract Newsvendor models have been well-established for studying supply chain management problems with fashionable products. In this paper, we explore the mean-downside-risk (MDR) and mean-variance (MV) newsvendor models under both the exogenous and endogenous retail price decision cases. We first construct analytical models with the MDR and MV objectives. We then show that the analytical solution schemes for both the MDR and MV problems are the same. With the measures for sustainability such as the expected quantity of goods leftover, the expected sales to expected goods leftover ratio, the rate of return on investment, and the probability of achieving a pre-determined profit target, we proceed to compare the levels of sustainability by the fashion retailers which employ the mean-risk and the risk neutral models. Insights are generated.

Financial and operational decisions in the electricity sector: Contract portfolio optimization with the conditional value-at-risk criterion

The restructuring of electricity markets around the world have caused increased volatility and uncertainty of the price power. As a result, providers of power now face increased uncertainty and risk in the operational and financial decisions related to procurement. Providers must seek optimal ways to deliver the required volume of power to retailers and end users while managing risk. We consider a mixed-integer programming model for a power providing agent that jointly considers the problem of selecting custom electricity contracts and finding the optimal procurement strategy of meeting contract obligations under spot price uncertainty. A two-stage stochastic integer programming (SIP) model with a conditional value-at-risk (CVaR) constraint to incorporate risk aversion is developed. Computational results are presented that demonstrates the CVaR approach and the results are compared with a corresponding expected cost minimization approach. The SIP model with CVaR will allow acceptance of contracts at lower prices compared to an approach based on a corresponding risk-neutral model as a hedge against uncertainty and mis-specified arbitrage.

A UNIFIED FRAMEWORK FOR PRICING CREDIT AND EQUITY DERIVATIVES

We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find a risk neutral model that matches a set of observed market prices. This risk neutral model can then be used to price more exotic, illiquid, or over-the-counter derivatives. We observe that our model matches the equity option implied volatility surface well since we properly account for the default risk in the implied volatility surface. We demonstrate the importance of accounting for the default risk and stochastic interest rate in equity option pricing by comparing our results to Fouque et al., which only accounts for stochastic volatility.

A Risk-Based Approach for Transmission Network Expansion Planning Under Deliberate Outages

This paper presents a risk-based approach for the transmission network expansion problem under deliberate outages. Malicious attacks expose network planners to a new challenge: how to expand and reinforce the transmission network so that the vulnerability against intentional attacks is mitigated while meeting budgetary limits. Within this framework network planners face the nonrandom uncertainty of deliberate outages. Unlike in previous approaches, the risk associated with this uncertainty is explicitly addressed in the proposed model. Risk characterization is implemented through the minimax weighted regret paradigm. The resulting mixed-integer nonlinear programming formulation is transformed into an equivalent mixed-integer linear programming problem for which efficient commercial solvers are available. Numerical results illustrate the performance of the proposed methodology. The risk-based expansion plans are compared with those achieved by a previously reported risk-neutral model. An out-of-sample assessment is carried out to show the advantages of the risk-based model over the risk-neutral approach. In addition, the tradeoff between risk mitigation and cost minimization is analyzed.

Affine Bond Pricing with a Mixture Distribution for Interest Rate Time-Series Dynamics

Starting from the discrete-time ane term structure model by Dai, Le & Singleton (2006), this paper proposes a Radon-Nikodym derivative which implies that factors follow a mixture distribution under the physical measure. The model thus maintains attractive features of an ane relation between yields and factors, while allowing for nonlinear and non-normal time-series dynamics. Empirically thet of the discrete- time 3-factor ane model is found to be substantially improved by the inclusion of two components to describe the time-series dynamics. Relative to the risk-neutral model, the mixture model is able to let the variance of the one-period rate be higher and faster increasing in the variance factor, and to introduce negative skewness and positive excess kurtosis. When weights on the components depend on factors, the model produces a speed of mean reversion and variance of the one-period rate that both increase fast with higher levels of the yield curve. The added second component is found to capture infrequent relatively large simultaneous shifts in direction of a yield curve that is at a lower level, is steeper, and is more positively curved.

Common Forward Rate Volatility

Statistical analyses of forward interest rate behavior provide evidence that these rates share a common volatility. We develop a risk-neutral term structure model based on this assumption. The main feature of this model is that each discounted bond price is both an explicit local martingale and a diffusion. The Markov property of discounted bonds is convenient for pricing interest rate derivatives. We give price formulas for caps and swaptions and compare caplet prices to the market-standard Black formula. The two formulas have nearly identical numerical values.

Do Professional Poker Players 'Know When to Hold'Em'? Evidence Against Risk-Neutral Dynamic Optimization from Televised Poker Tournaments

Professional poker players’ behavior in high-stakes, televised tournaments is significantly more conservative than that prescribed by risk-neutral models of dynamic optimization for decisions to call or fold after final ‘river’ bets. Had players adhered to a risk-neutral dynamically-optimal decision rule in these decisions they would have folded less than 10 percent of the hands played and experienced an increase in the share of chips at the table of 1.9 percent. In reality players folded significantly more often – more than 40 percent of the time – and experienced an average gain of only 1.3 percent. While the cost of this conservative play is not statistically significant, the players’ reticence is surprising given that the median player in our sample spends $10,000 to enter the poker tournament, plays for a cash prize pool of nearly $1 million and has substantial experience playing poker. Several explanations may explain the conservative decisions, including probability weighting and players’ overconfidence in being able to determine the strength of an opponent’s cards. The implication of professionals in a high-stakes competition deviating from risk-neutral decision making is explored.

Comments on: On a mixture of the fix-and-relax coordination and Lagrangean substitution schemes for multistage stochastic mixed integer programming

It is well known that introducing integer variables into stochastic linear programs with recourse has serious consequences for structural analysis and algorithm design. In particular, convexity of the objective function is lost, preventing, to name just two examples, the direct application of duality reasoning or subgradient based cutting planes. When passing from risk neutral models to formulations allowing for risk aversion, convexity may get lost as well, depending on how risk is quantified. Another source of complication is in passing from two-stage to multistage models. If done in the linear case, this often captures convexity, but it always adds another dimension of complexity, namely dynamics regarding availability of information. The present paper proposes an algorithmic approach to a class of stochastic programs involving all three above mentioned complicating features: integer variables, risk aversion, and multistage decision making. With finite probability spaces, such models allow for equivalent representation as mixed-integer linear programs (MILPs). The bad news, however, is that the sheer dimensionality of the latter usually prevents successful direct application of even the most advanced MILP solution methods and solvers. Rather, the art is in bringing together solution techniques from different branches of integer, or from a broader perspective global, optimization to utilize favorably the hidden structures, mainly decomposition structures. This is the theme of the present paper. The diversity of constraints assembled in a multistage stochastic mixed-integer program, in principle, gives rise to various possible relaxations. In the present paper, the focus is on the integrality and the nonanticipativity constraints. Their relaxation

Alternative Defaultable Term Structure Models

The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the existence of an equivalent risk-neutral probability measure is not required. In particular, the real-world dynamics of the instantaneous defaultable forward rates under a jump-diffusion extension of a HJM type framework are derived. Thus, by establishing a modelling framework fully under the real-world probability measure, the challenge of reconciling real-world and risk-neutral probabilities of default is deliberately avoided, which provides significant extra modelling freedom. In addition, for certain volatility specifications, finite dimensional Markovian defaultable term structure models are derived. The paper also demonstrates an alternative defaultable term structure model. It provides tractable expressions for the prices of defaultable derivatives under the assumption of independence between the discounted growth optimal portfolio and the default-adjusted short rate. These expressions are then used in a more general model as control variates for Monte Carlo simulations of credit derivatives.

Alternative Defaultable Term Structure Models

The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the existence of an equivalent risk-neutral probability measure is not required. In particular, the real-world dynamics of the instantaneous defaultable forward rates under a jump-diffusion extension of a HJM type framework are derived. Thus, by establishing a modelling framework fully under the real-world probability measure, the challenge of reconciling real-world and risk-neutral probabilities of default is deliberately avoided, which provides significant extra modelling freedom. In addition, for certain volatility specifications, finite dimensional Markovian defaultable term structure models are derived. The paper also demonstrates an alternative defaultable term structure model. It provides tractable expressions for the prices of defaultable derivatives under the assumption of independence between the discounted growth optimal portfolio and the default-adjusted short rate. These expressions are then used in a more general model as control variates for Monte Carlo simulations of credit derivatives.

Technical Note—A Risk-Sensitive Model for Managing Perishable Products

This article presents a risk-sensitive model for managing perishable products assuming the supplier is averse to the variation of revenues. While traditional risk-neutral revenue management models offer optimal strategies in the long run, they are exposed to the variation of revenue flows. If a short-term revenue target is a primary concern for the supplier, the risk-neutral assumption fails to provide the best policy needed. The proposed model uses an exponential function with a risk-sensitive parameter instead of the conventional risk-neutral objective. The risk parameter measures how the supplier is sensitive to the deviation of revenues. We show that the new objective function captures the supplier's risk behavior. We develop a recursive procedure for the optimal solution in closed form. The optimal policy has attractive properties such as nested active price set, monotonicity with respect to the remaining time and inventory, and threshold-type control. When the supplier is more sensitive to the uncertain revenue flows, the risk-sensitive model leads to more conservative pricing policies. Finally, we show that the risk-neutral model is a special case of the proposed framework.