Showing papers on "Stochastic discount factor published in 2023"
TL;DR: In this paper , the authors investigated the valuation of exchange options when the market is affected by changing economic conditions as well as liquidity risks and derived a risk-neutral measure with the use of regime switching Esscher transform.
Abstract: We investigate the valuation of exchange options when the market is affected by changing economic conditions as well as liquidity risks. The volatility and expected returns of both stocks are assumed to be controlled by a continuous-time Markov chain to reflect the effects of varying economic conditions, and a liquidity discounting factor is employed to capture the impact of market liquidity on stock prices. Once the model has been established, we construct a risk-neutral measure with the use of regime-switching Esscher transform, and the characteristic function is then derived in an analytical form, so that a closed-form formula for exchange options can be presented. We further analyze the effects of the two considered factors on exchange option prices numerically.
6 citations
TL;DR: This paper proposed a model-free methodology to estimate international stochastic discount factors (SDFs) that jointly price cross-sections of international stocks, bonds, and currencies in markets with frictions.
1 citations
TL;DR: This paper showed that market-wide illiquidity significantly affects the distribution of the stochastic discount factor (SDF) and, therefore, the asset pricing model specification, and that marketwide liquidity risk significantly boosts up the volatility of the SDF, causing minor effects on higher moments of its distribution.
TL;DR: In this article , the authors identify state-dependent components in the stochastic discount factor using the Euler equation and develop tractable algorithms for filtering, smoothing, and sieve maximum likelihood estimation.
TL;DR: The authors study a large currency cross-section using asset pricing methods that account for omitted-variable and measurement-error biases, and find that only a small fraction of the over 100 nontradable candidate factors considered have a statistically significant risk premium, mostly relating to volatility, uncertainty, and liquidity conditions, rather than macro variables.
Abstract:
We study a large currency cross-section using asset pricing methods that account for omitted-variable and measurement-error biases. First, we show that the pricing kernel includes at least three latent factors that resemble (but are not identical to) a strong U.S. “dollar” factor and two weak high Sharpe ratio “carry” and “momentum” slope factors. Evidence for an additional “value” factor is weaker. Second, using this pricing kernel, we find that only a small fraction of the over 100 nontradable candidate factors considered have a statistically significant risk premium, mostly relating to volatility, uncertainty, and liquidity conditions, rather than macro variables.
TL;DR: In this paper , a consumption-based equilibrium framework for credit risk pricing based on the Epstein-Zin (EZ) preferences is presented, where the default time is modeled as the first hitting time of a default boundary and bond investors have imperfect/partial information about the firm value.
Abstract: We present a consumption‐based equilibrium framework for credit risk pricing based on the Epstein–Zin (EZ) preferences where the default time is modeled as the first hitting time of a default boundary and bond investors have imperfect/partial information about the firm value. The imperfect information is generated by the underlying observed state variables and a noisy observation process of the firm value. In addition, the consumption, the volatility, and the firm value process are modeled to follow affine diffusion processes. Using the EZ equilibrium solution as the pricing kernel, we provide an equivalent pricing measure to compute the prices of financial derivatives as discounted values of the future payoffs given the incomplete information. The price of a zero‐coupon bond is represented in terms of the solutions of a stochastic partial differential equation (SPDE) and a deterministic PDE; the self‐contained proofs are provided for both this representation and the well‐posedness of the involved SPDE. Furthermore, this SPDE is numerically solved, which yields some insights into the relationship between the structure of the yield spreads and the model parameters.
TL;DR: In this paper , a dynamic conditional correlation copula (DCC-copula) model with skewed-t kernel was proposed to model dynamic correlations and non-normality among forex factors.
TL;DR: In this article , the authors considered two aspects of the arbitrage pricing theory: the factors in the statistical asset pricing model are related to a theoretically consistent set of factors defined by their conditional covariation with the stochastic discount factor (SDF) used to price securities within inter-temporal asset pricing models.
01 May 2023
TL;DR: In this article , a methodology is suggested for approximated consideration of both seasonal and random fluctuations in the environment, which have some impact on the overall group activity and may be considered via modification of the risk-adjusted discount rates.
Abstract: In this article, we focus on considering different risk factors influencing the cash flows of a group of companies. A methodology is suggested for approximated consideration of both seasonal and random fluctuations in the environment, which have some impact on the overall group activity and may be considered via modification of the risk-adjusted discount rates. The main steps of the suggested methodology are described, and the elements of the risk-adjusted discount rate are presented. Although it is the general convention to use the market rate as the discount rate in most cases, under certain circumstances—i.e., stochastic shocks related to the level of interest rates, shifts, and turnabouts in the social environment, as well as the market transformations due to annual/seasonal epidemics, the use of a risk-adjusted discount rate becomes essential. The influence of the seasonal and random changes in the general environment on the companies’ activity through modification of the discount rate is illustrated both numerically and graphically in the article, providing analysis of the impact of exogenous parameters on companies’ output, profits, net present value, and discounted payback period for the initial investment.
TL;DR: In this paper , the generalized Dupire formula has been extended to the case of general stochastic drift and/or general local volatility, where the drift is given as a difference of two stochastically different short rates.
Abstract: We derive generalizations of the Dupire formula to the case of general stochastic drift and/or the case of general stochastic local volatility. First, we handle the case in which the drift is given as a difference of two stochastic short rates. Such a setting is natural in a foreign exchange context where the short rates correspond to the short rates of the two currencies, in an equity single-currency context with stochastic dividend yield, or in a commodity context with stochastic convenience yield. We present the formula in both a call surface formulation and a total implied variance formulation where the latter avoids calendar spread arbitrage by construction. We provide derivations for the case where both short rates are given as single factor processes, and we present limits for a single stochastic rate or all deterministic short rates. The limits agree with published results. Then we derive a formulation that allows a more general stochastic drift and diffusion, including one or more stochastic local volatility terms. In the general setting, our derivation allows for the computation and cali ration of the leverage function for stochastic local volatility models. Despite being implicit, the generalized Dupire formula can be used numerically in a fixed-point iterative scheme.
TL;DR: In this paper , a class of multivariate GARCH models that explicitly model correlation dependent pricing kernels is introduced, and a large subclass admits closed-form recursive solutions for the moment generating function under the risk-neutral measure.
TL;DR: In this article , the authors explain time-varying expected returns by time-variation in the covariance of the market return with the pricing kernel, which is essentially orthogonal to news about expected returns.
TL;DR: In this article , the stochastic discount factor (SDF) that prices individual stocks can be represented as a factor model with GLS cross-sectional regression slope factors, and the conditions that must hold for dimension reduction to a number of factors smaller than the number of characteristics to be possible without having to invert a large covariance matrix.
Abstract: When expected returns are linear in asset characteristics, the stochastic discount factor (SDF) that prices individual stocks can be represented as a factor model with GLS cross-sectional regression slope factors. Factors constructed heuristically by aggregating individual stocks into characteristics-based factor portfolios using sorting, characteristics-weighting, or OLS cross-sectional regression slopes do not span this SDF unless the covariance matrix of stock returns has a specific structure. These conditions are more likely satisfied when researchers use large numbers of characteristics simultaneously. Methods to hedge unpriced components of heuristic factor returns allow partial relaxation of these conditions. We also show the conditions that must hold for dimension reduction to a number of factors smaller than the number of characteristics to be possible without having to invert a large covariance matrix. Under these conditions, instrumented and projected principal components analysis methods can be implemented as simple PCA on certain portfolio sorts.
16 May 2023
TL;DR: In this paper , the authors consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i) law-invariant, ii) cash- or shift invariant, and iii) positively homogeneous, and possibly plugged into a general function.
Abstract: Focusing on gains instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i) law-invariant, ii) cash- or shift-invariant, and iii) positively homogeneous, and possibly plugged into a general function. We model the market via a generalized version of the multi-dimensional Black-Scholes model using $\alpha$-stable L\'evy processes and give supplementary results for the classical Black-Scholes model. The optimal solution to this problem is a Nash subgame equilibrium given by the solution of an extended Hamilton-Jacobi-Bellman equation. Moreover, we show that the optimal solution is deterministic and unique under appropriate assumptions.
TL;DR: This paper developed a new three-factor coin model where momentum is replaced by a mispricing factor based on size and risk-adjusted momentum, which significantly improves pricing performance, and applied almost stochastic dominance, which does not require any assumption about the return distribution or degree of risk aversion.
Abstract: Cryptocurrency returns are highly nonnormal, casting doubt on the standard performance metrics. We apply almost stochastic dominance, which does not require any assumption about the return distribution or degree of risk aversion. From 29 long–short cryptocurrency factor portfolios, we find eight that dominate our four benchmarks. Their returns cannot be fully explained by the three-factor coin model of Liu et al. So we develop a new three-factor model where momentum is replaced by a mispricing factor based on size and risk-adjusted momentum, which significantly improves pricing performance.
TL;DR: This paper developed a nonmonotonic pricing kernel with long-run and short-run variance risk premiums for option valuation, with a proposed pricing kernel retaining a U-shaped pattern that significantly improves the fitting ability for index options pricing and implied volatility.
Abstract: This article develops a nonmonotonic pricing kernel with long-run and short-run variance risk premiums for option valuation, with a proposed pricing kernel retaining a U-shaped pattern that significantly improves the fitting ability for index options pricing and implied volatility. The estimation results show that the long-run volatility component is critical in generating the negative risk premium. In the in-sample and out-of-sample tests, the model with the new pricing kernel has more accurate predictions, especially the year around the financial crisis, wherein there is a decrease of an average of 35% root mean square error relative to the benchmark. Considering the bull and bear market states, our model improves implied volatility root mean square error by 23% on average.