Risk-neutral Counterparts Research Articles

Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used to incorporate conditional heteroscedasticity in the logarithmic returns of Ethereum, and Bayesian nonlinear expectations are adopted to introduce model uncertainty, or ambiguity, about the conditional mean and volatility of the logarithmic returns of Ethereum. Extended Girsanov’s principle is employed to change probability measures for introducing a family of alternative GARCH models and their risk-neutral counterparts. The Bayesian credible intervals for “uncertain” drift and volatility parameters obtained from conjugate priors and residuals obtained from the estimated GARCH model are used to construct Bayesian superlinear and sublinear expectations giving the Bayesian lower and upper estimates for the price of an Ether option, respectively. Empirical and simulation studies are provided using real data on Ethereum in AUD. Comparisons with a model incorporating conditional heteroscedasticity only and a model capturing ambiguity only are presented.

Liquidity-free implied volatilities: An approach using conic finance

In this paper, we consider the problem of calculating risk-neutral implied volatilities of European options without relying on option mid prices but solely on bid and ask prices. We provide an approach, based on the conic finance paradigm, that allows to uniquely strip risk-neutral implied volatilities from bid and ask quotes, and that does not require restrictive assumptions. Our methodology also allows to jointly calculate the implied liquidity of the market. The idea outlined in this paper can be applied to calculate other implied parameters from bid and ask security prices as soon as their theoretical risk-neutral counterparts are strictly increasing with respect to the former.

FROM BID-ASK CREDIT DEFAULT SWAP QUOTES TO RISK-NEUTRAL DEFAULT PROBABILITIES USING DISTORTED EXPECTATIONS

Risk-neutral default probabilities can be implied from credit default swap (CDS) market quotes. In practice, mid-CDS quotes are used as inputs, as their risk-neutral counterparts are not observable. We show how to imply risk-neutral default probabilities from bid and ask quotes directly by means of formulating the CDS calibration problem to bid and ask market quotes within the conic finance framework. Assuming the risk-neutral distribution of the default time to be driven by a Poisson process we prove, under mild liquidity-related assumptions, that the calibration problem admits a unique solution that also allows to jointly calculate the implied liquidity of the market.

CONIC CVA AND DVA FOR OPTION PORTFOLIOS

In this paper, we propose a framework for credit and debit valuation adjustments (CVA and DVA, respectively) for options and option portfolios which is based on conic finance, that is, where the positions are valued at their bid or ask prices depending on whether they are assets or liabilities. This can be achieved by transforming the pricing measure via appropriate distortion functions, depending on (at least) one parameter. We apply our methodology, which is based on the Wang transform, to portfolios of European commodity futures options, and we show that both CVA and DVA are significantly impacted by bid-ask spreads, when compared to their traditional risk-neutral counterparts. In particular, we show that DVA decreases when computed under conic finance settings, which is in line with the regulatory efforts to rein in DVA gains for financial institutions resulting from their own credit quality deterioration. Finally, we investigate the robustness of our approach with respect to the calibrated parameters, and we show that the calibrated distortion parameter is an excellent explanatory variable for the observed bid-ask spreads.

Inventory Management for High-Frequency Trading With Imperfect Competition

We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain around the continuous-time limit. Unlike in the risk-neutral case, the optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large. In contrast, the HFTs' risk-adjusted profits and the equilibrium price impact converge to their risk-neutral counterparts. Compared to a social-planner solution for cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity.

Optimal monetary policy for a pessimistic central bank

We consider the impact of pessimism on monetary policy within a model with backward-looking expectations and persistence in the dynamics of output and inflation. Pessimistic monetary authorities behave as if they believed that the worst economic conditions were very likely and move the policy instrument to hedge against their negative consequences. With respect to their risk-neutral counterparts, they apply a more aggressive Taylor rule, reducing the inflation rate volatility. The impact of pessimism on monetary policy is magnified by economic uncertainty. A calibration exercise for the U.S. economy confirms the relevance of pessimism as it shows that pessimistic monetary authorities react to a one-standard-deviation supply shock moving the policy instrument by about one percent more than their risk-neutral counterparts. Our conclusions also hold when the monetary authorities observe inflation and output with a time lag.

Platform flexibility strategies: R&D investment versus production customization tradeoff

Product platforms are assets that are shared by multiple products. We study the optimal investment in platform flexibility. Each platform type is characterized by its functionality that determines its R&D investment and unit production cost, as well as the customization cost to produce the end products from the platform. The firm can invest in a portfolio of specialized platforms that align with the functionalities of a specific product and flexible platforms that cover the functionalities of a product range at lower customization cost. We characterize the optimal platform portfolio strategy using an ex-ante investment versus ex-post production customization tradeoff curve and show comparative statics of these costs, demand forecast, and the decision maker’s regret and risk attitude. Flexible platforms provide operational hedging for risk-averse decision makers who thus should invest more than risk-neutral counterparts. In contrast to manufacturing flexibility, the regret of sub-optimal investments increases as demand is more negatively correlated.

Platform Flexibility Strategies: R&D Investment versus Production Customization Tradeoff

Product platforms are assets that are shared by multiple products. We study the optimal investment in platform flexibility. Each platform type is characterized by its functionality that determines its R&D investment and unit production cost, as well as the customization cost to produce the end products from the platform. The firm can invest in a portfolio of specialized platforms that align with the functionalities of a specific product and flexible platforms that cover the functionalities of a product range at lower customization cost. We characterize the optimal platform portfolio strategy using an ex-ante investment versus ex-post production customization tradeoff curve and show comparative statics of these costs, demand forecast, and the decision maker’s regret and risk attitude. Flexible platforms provide operational hedging for risk-averse decision makers who thus should invest more than risk-neutral counterparts. In contrast to manufacturing flexibility, the regret of sub-optimal investments increases as demand is more negatively correlated.

Conic CVA and DVA for Option Portfolios

In this paper, we propose a framework for credit and debit valuation adjustments (CVA and DVA, respectively) for options and option portfolios which is based on conic finance, that is, where the positions are valued at their bid or ask prices depending on whether they are assets or liabilities. This can be achieved by transforming the pricing measure via appropriate distortion functions, depending on (at least) one parameter. We apply our methodology, which is based on the Wang transform, to portfolios of European commodity futures options, and we show that both CVA and DVA are significantly impacted by bid-ask spreads, when compared to their traditional risk-neutral counterparts. In particular, we show that DVA decreases when computed under conic finance settings, which is in line with the regulatory efforts to rein in DVA gains for financial institutions resulting from their own credit quality deterioration. Finally, we investigate the robustness of our approach with respect to the calibrated parameters, and we show that the calibrated distortion parameter is an excellent explanatory variable for the observed bid-ask spreads.

Worth the Risk? The Behavioural Path to Well‐Being

AbstractThere is increasing interest in the ‘economics of happiness’, reflected in the volume of articles appearing in mainstream economics journals exploring the major determinants of self‐reported well‐being. We contribute by exploring the factors influencing how satisfied farmers are with their quality of life. We find that farm income, subjective perceptions relating to the adequacy of household income, debt, health and personal characteristics such as age and relationship status are significantly associated with farmers’ self‐reported life satisfaction. While significantly associated with farm income, farm structural variables such as farm size, farm type and the presence of a farm successor were not found to be significantly related with life satisfaction. Our results also suggest that farmers who are more risk averse enjoy significantly lower levels of both life satisfaction and farm income than their more risk seeking or risk neutral counterparts. We suggest that, in the same way that risk aversion inhibits farmers from making choices that could lead to an increase in their income, it may also constrain farmers (and the wider public at large) from engaging in certain types of behaviours that could lead to an increase in their self‐reported quality of life. Finally, we find that while farm income is significantly related to self‐reported life satisfaction, the direct correlation between these variables is weak, suggesting that farmer life satisfaction can be distinct from business success.

Optimal Monetary Policy for a Pessimistic Central Bank

We consider the impact of pessimism on monetary policy within a model with backward looking expectations and persistence in the dynamics of output and inflation. We show that pessimistic monetary authorities move their instruments to hedge against the worst economic shocks. With respect to their risk-neutral counterparts, they apply a more aggressive Taylor rule, so that the inflation rate is less volatile. Our conclusions hold when the monetary authorities observe inflation and output with a time lag. Our analysis extends that of van der Ploeg (2009), as we allow for time-discounting of future social welfare losses due to deviations of output and inflation from first-best values.

Pricing and Hedging Variable Annuity Guarantees with Multiasset Stochastic Investment Models

Variable annuities are often sold with guarantees to protect investors from downside investment risk. The majority of variable annuity guarantees are written on more than one asset, but in practice, single-asset (univariate) stochastic investment models are mostly used for pricing and hedging these guarantees. This practical shortcut may lead to problems such as basis risk. In this article, we contribute a multivariate framework for pricing and hedging variable annuity guarantees. We explain how to transform multivariate stochastic investment models into their risk-neutral counterparts, which can then be used for pricing purposes. We also demonstrate how dynamic hedging can be implemented in a multivariate framework and how the potential hedging error can be quantified by stochastic simulations.

Risk-Averse Insider Trading in Multi-Asset Sequential Auction Markets

We extend Kyle's (Kyle, 1985) analysis of sequential auction markets to the case in which a risk-averse insider possesses private information on the liquidation value of a number of risky assets. We confirm: i) in a multi-asset setting, Holden and Subrahmanyam's counter-intuitive result that risk-aversion induces informed agents to consume more rapidly their long-lived private information vis-a-vis their risk-neutral counter-parts, so that with risk-averse insiders securities markets are more efficient; ii) in a multi-period scenario, Caballe and Krishnan's result that the insider operates in such a way that the price impact of signed volume (order flow) is symmetric across all risky assets.

Credit and Liquidity Risks in Euro Area Sovereign Yield Curves

In this paper, we propose a model of the joint dynamics of euro-area sovereign yield curves. The arbitrage-free valuation framework involves five factors and two regimes, one of the latter being interpreted as a crisis regime. These common factors and regimes explain most of the fluctuations in euro-area yields and spreads. The regime-switching feature of the model turns out to be particularly relevant to capture the rise in volatility experienced by fixed-income markets over the last years. In our reduced-form set up, each country is characterized by a hazard rate, specified as some linear combinations of the factors and regimes. The hazard rates incorporate both liquidity and credit components, that we aim at disentangling. The estimation suggests that a substantial share of the changes in euro-area yield differentials is liquidity-driven. Our approach is consistent with the fact that sovereign default risk is not diversifiable, which gives rise to specific risk premia that are incorporated in spreads. Once liquidity-pricing effects and risk premia are filtered out of the spreads, we obtain estimates of the actual – or real-world – default probabilities. The latter turn out to be significantly lower than their risk-neutral counterparts.

Adaptive grid risk-sensitive filter for non-linear problems

A novel adaptive grid-based method has been proposed for risk-sensitive state estimation in non-linear non-Gaussian problems. The algorithm, which is based on point-mass approximation, is called the adaptive grid risk-sensitive filter (AGRSF). Although risk-sensitive estimators have been known to be robust compared to their risk-neutral counterparts, the implementation of risk-sensitive filters (RSFs) is almost impossible except for very trivial systems like linear Gaussian systems. The existing extended risk-sensitive filter (ERSF) fails to take care of non-Gaussian problems or severe non-linearities. Recently, other variants of RSFs have been proposed for extending the range of applications of risk-sensitive techniques. The AGRSF has been formulated to act as a benchmark and aid in the validation of other RSFs. The algorithm uses a modified form of information state-based recursive relation and provides guidelines for the adaptive choice of grid points to improve the numerical efficiency. The developed filter has been applied to a single-dimensional non-linear poorly observable system and a non-linear two-dimensional bearing only tracking problem. The convergence of the algorithm has been shown by simulation. The estimation efficiency and computational load of AGRSF has been compared with other RSFs.

Risk-Sensitive Dynamic Market Share Attraction Games

We present partial results showing that risk-sensitive oligopolists would spend less on advertising than would their risk-neutral counterparts. The model is an infinite-horizon stochastic game in which each firm's “goodwill” is a random function of both its own and its competitors' current and past advertising expenditures. Single-period firm profits have a market share attraction form. Each firm seeks to maximize its expected exponential utility of the sum of discounted profits. We analyze the impact that risk sensitivity and other parameters have on equilibrium advertising strategies by exploiting the special structure of the stochastic game model.Journal of Economic LiteratureClassification Number: C73.