We define risk-free portfolios using three gauge invariant differential operators that require such portfolios to be insensitive to price changes, to be self-financing, and to produce a zero real return so there are no risk-free profits. This definition identifies the risk-free rate as the return of an infinitely diver…
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48 results for “Risk-Free”
Traders underestimated risk-free rates, leading to poor investments.
problem Incorrect setting of risk-free rates by traders.
method Analysis of investment decisions and financial models.
result Underestimating risk-free rates led to flawed investment decisions.
Study affine models for alternative risk-free rates and derive caplet pricing formulas.
problem Valuation of caplets/floorlets in models for alternative risk-free rates.
method Affine process for RFRs, explicit valuation formulas for various derivatives.
result Explicit formulas for caplet/floorlet pricing in affine models for RFRs.
The Sharpe ratio is a way to compare the excess returns (over the risk free asset) of portfolios for each unit of volatility that is generated by a portfolio. In this paper we introduce a robust Sharpe ratio portfolio under the assumption that the risk free asset is unknown. We propose a robust portfolio that maximizes…
The paper simplifies hedging and portfolio allocation in markets without a risk-free asset.
problem Optimal hedging and portfolio allocation in markets without a risk-free asset.
method Establishes equivalence between hedging with and without numeraire change, uses oblique projections.
result Explicit expressions for optimal strategies and efficient frontier computation.
The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the risk-free interest rate. In reality, the risk free interest rate is unknown and need …
The investment risk minimization problem with budget and return constraints has been the subject of research using replica analysis but there are shortcomings in the extant literature. With respect to Tobin's separation theorem and the capital asset pricing model, it is necessary to investigate the implications of a ri…
This study shows how monetary uncertainty affects stock market reactions to macroeconomic news.
problem Understanding stock market reactions to macroeconomic news under varying levels of monetary uncertainty.
method Decomposes stock market response into cash flow and risk-free rate channels, analyzing time-varying effects.
result High monetary uncertainty weakens the positive stock market response to macroeconomic news.
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relati…
Research proposes a risk-free machine learning model for COVID screening from routine blood tests.
problem Rapid antigen tests have low sensitivity and are not suitable for widespread screening.
method Stacked Ensemble Machine Learning model using routine blood tests.
result 100% accuracy, precision, recall and F1-score in identifying COVID patients.
We consider the mean--variance portfolio optimization problem under the game theoretic framework and without risk-free assets. The problem is solved semi-explicitly by applying the extended Hamilton--Jacobi--Bellman equation. Although the coefficient of risk aversion in our model is a constant, the optimal amounts of m…
Extends option pricing framework without risk-free asset using Levy jumps.
problem Valuing derivatives in markets without a traded risk-free bond.
method Introduces common Levy jump dynamics, uses Ito-Levy calculus, FFT, and COS algorithms.
result Calibrations show jump models reduce pricing errors and fit volatility smiles better than Black-Scholes.
The premium of dynamic tradingq-fin.PM
It is well established that in a market with inclusion of a risk-free asset the single-period mean-variance efficient frontier is a straight line tangent to the risky region, a fact that is the very foundation of the classical CAPM. In this paper, it is shown that in a continuous-time market where the risky prices are …
The paper uses option theory to estimate corporate bond liquidity spreads.
problem Estimating liquidity spreads for corporate bonds.
method Option-theoretic approach considering risk-free rate volatility and credit risk.
result The model provides a robust tool for pricing illiquid bonds.
A new model uses a Levy-driven process to value credit index swaptions.
problem Valuation of credit index swaptions in financial markets.
method Proposes a Levy-driven Ornstein-Uhlenbeck process to model risk-free rate and default intensities.
result Derives formulas for characteristic function, moments, and stationary distribution.
We study conditions for existence, uniqueness and invariance of the comprehensive nonlinear valuation equations first introduced in Pallavicini et al (2011). These equations take the form of semilinear PDEs and Forward-Backward Stochastic Differential Equations (FBSDEs). After summarizing the cash flows definitions all…
The paper reviews origins of the approach to pricing derivatives post-crisis by following three papers that have received wide acceptance from practitioners as the theoretical foundations for it - [Piterbarg 2010], [Burgard and Kjaer 2010] and [Burgard and Kjaer 2013]. The review reveals several conceptual and technica…
This paper addresses credit valuation adjustment with a new closeout convention.
problem Accurate estimation of financial claim value considering counterparty credit risk.
method Theoretical and computational analysis of a nonlinear valuation system using neural networks.
result A neural network-based algorithm effectively solves the high-dimensional nonlinear valuation system.
Machine learning improves portfolio allocation between index and risk-free assets.
problem Finding optimal portfolio rules for time-varying returns and volatility.
method Two Random Forest models: one for sign probabilities of excess return, the other for optimized volatility.
result Substantial improvements in utility, risk-adjusted returns, and maximum drawdowns over buy-and-hold.
In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. Th…
Optimal buying and selling times for homes in fluctuating interest rates.
problem Maximizing profit from buying and selling homes in a market with variable interest rates.
method Nested optimal stopping problem solved using a nonnegative concave majorant approach.
result Investor's optimal buying and selling strategies derived for CIR interest rates.
We analyze the practical consequences of the bilateral counterparty risk adjustment. We point out that past literature assumes that, at the moment of the first default, a risk-free closeout amount will be used. We argue that the legal (ISDA) documentation suggests in many points that a substitution closeout should be u…
Analytical approximations for Asian option sensitivities in Black-Scholes model.
problem Calculating sensitivities of Asian options in the Black-Scholes model.
method Small maturity/volatility approximation and large deviations theory.
result Good agreement with alternative numerical simulation results for practical cases.
We explain a persistent cost-of-carry spread in EUA market and suggest ECB policy change.
problem Persistent cost-of-carry spread in EUA market.
method Cointegration analysis of EUA spread with credit spread and risk-free rate.
result Cointegration found between EUA spread, credit spread, and risk-free rate.
PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)q-fin.PR
Derives PDEs for pricing RFR derivatives under a new FMM model.
problem Valuation of interest rate derivatives under a new FMM model.
method Develops PDEs and finite differences methods for numerical solution.
result First use of PDE methods for RFR derivatives valuation.
We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility with respect to thei…
Real life hedging in the Black-Scholes model must be imperfect and if the stock's drift is higher than the risk free rate, leads to a profit on average. Hence the option price is examined as a fair game agreement between the parties, based on expected payoffs and a simple measure of risk. The resulting prices result in…
Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisitq-fin.PM
The conventional wisdom of mean-variance (MV) portfolio theory asserts that the nature of the relationship between risk and diversification is a decreasing asymptotic function, with the asymptote approximating the level of portfolio systematic risk or undiversifiable risk. This literature assumes that investors hold an…
What are the prices of random variables? In this paper, we define the least-squares prices of coin-flipping games, which are proved to be minimal, positive linear, and arbitrage-free. These prices depend both on a set of games that are available for investing simultaneously and on a risk-free interest rate. In addition…
The credit crisis and the ongoing European sovereign debt crisis have highlighted the native form of credit risk, namely the counterparty risk. The related Credit Valuation Adjustment, (CVA), Debt Valuation Adjustment (DVA), Liquidity Valuation Adjustment (LVA) and Replacement Cost (RC) issues, jointly referred to in t…
Portfolio Optimization in Rq-fin.PM
We consider the problem of finding the efficient frontier associated with the risk-return portfolio optimization model. We derive the analytical expression of the efficient frontier for a portfolio of N risky assets, and for the case when a risk-free asset is added to the model. Also, we provide an R implementation, an…
Dynamic pricing model considers ambiguity in endowment growth rate.
problem Dynamic asset pricing under ambiguous endowment growth rate.
method α-maxmin expected utility model for ambiguity, intra-personal equilibrium strategies, market equilibrium.
result Asset prices reflect ambiguity in endowment growth rate.
In this article, inspired by Shi, et al. we investigate the optimal portfolio selection with one risk-free asset and one risky asset in a multiple period setting under cumulative prospect theory (CPT). Compared with their study, our novelty is that we consider a stochastic benchmark, and portfolio constraints. We test …
Study finds optimal retirement timing in uncertain wage scenarios.
problem Optimal retirement timing in presence of uncertain wages.
method Formulated as a free boundary problem in an incomplete market.
result Developed a method to determine optimal retirement timing.
In this paper, we study the classical problem of maximization of the sum of the utility of the terminal wealth and the utility of the consumption, in a case where a sudden jump in the risk-free interest rate creates incompleteness. The value function of the dual problem is proved to be solution of a BSDE and the dualit…
Study uses RL to optimize risky vs. risk-free asset allocation.
problem Optimal asset allocation in volatile financial markets.
method Formulated as MDP, uses DDPG with TiDE for dynamic policy learning.
result DDPG-TiDE outperforms Q-learning and buy-and-hold strategies.
The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading is subject to proportional transaction costs, and where the existence of a risk-free numéraire is not assumed. Constructions leading t…
This paper derives a portfolio decomposition formula when the agent maximizes utility of her wealth at some finite planning horizon. The financial market is complete and consists of multiple risky assets (stocks) plus a risk free asset. The stocks are modelled as exponential Brownian motions with drift and volatility b…
This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in fina…
In this article, we study the problem of pricing defaultable bond with discrete default intensity and barrier under constant risk free short rate using higher order binary options and their integrals. In our credit risk model, the risk free short rate is a constant and the default event occurs in an expected manner whe…
In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it hits a deterministic barrier level. We derive analytical formulas for the expec…
Discrete time portfolio optimisation managing value at risk under heavy tail return distributionq-fin.PM
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to the Value at Risk assuming a heavy tail distribution of the stock prices return. We use Markov Decision Process and dynamic programming principle to get…
Solves portfolio optimization with costs using numerical methods.
problem Dynamic portfolio optimization with transaction costs and constraints.
method Numerical dynamic programming techniques.
result Problems can now be solved tractably.
Within the setup of continuous-time semimartingale financial markets, we show that a multiprior Gilboa-Schmeidler minimax expected utility maximizer forms a portfolio consisting only of the riskless asset if and only if among the investor's priors there exists a probability measure under which all admissible wealth pro…
Expands robust profit opportunities to include distributional uncertainty.
problem Distributional uncertainty in financial markets.
method Formulates infinite dimensional primal problems, simplifies to finite dimensional dual problems using Wasserstein distance.
result Distributional uncertainty can enhance robustness of profit opportunities.
This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To co…
We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings. We show that when mean returns and volatilities of the assets are small and ther…
Optimal Convergence Tradingmath.OC
This article examines arbitrage investment in a mispriced asset when the mispricing follows the Ornstein-Uhlenbeck process and a credit-constrained investor maximizes a generalization of the Kelly criterion. The optimal differentiable and threshold policies are derived. The optimal differentiable policy is linear with …