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 rate”
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 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 …
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…
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.
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.
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 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…
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.
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.
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.
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…
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.
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…
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 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…
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…
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…
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 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 analyzes insurance risks using stochastic models.
problem Interest rate and variance risks in unit-linked insurance policies.
method General stochastic volatility models and stochastic interest rates are used to price unit-linked life insurance contracts.
result A perfect hedging strategy is provided and compared with the Black-Scholes model.
This paper models short rates with jumps using PDEs.
problem Capturing jumps and spikes in interest rates.
method PDE approach for pricing interest rate derivatives.
result Established Feynman-Kač representation and derived solutions.
We show that different rates should be used for borrowing and discount rates, and that the risk-free rate should be used for discounting when assessing and comparing the cost of energy accross diffferent producers and technologies, on the example of photovoltaics. Recent quantitative models using the same rate for borr…
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…
Cash collateral is perfect in that it provides simultaneous counterparty credit risk protection and derivatives funding. Securities are imperfect collateral, because of collateral segregation or differences in CSA haircuts and repo haircuts. Moreover, the collateral rate term structure is not observable in the repo mar…
We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving Brownian motion, and they are supposed to be currently observable. It is shown t…
Alternative perspective on mean-field LIBOR market model, maintaining practicality and applicability.
problem Maintaining practicality and applicability of mean-field LIBOR market model.
method Embedding mean-field model in a classical setup, controlling term rate variances over large time horizons.
result Framework can be directly applied to model term rates from SOFR, ESTR, or other nearly risk-free overnight rates.
Investment strategy optimized for ambiguity and interest rate risk.
problem Dynamic asset allocation with interest rate risk and ambiguity.
method Closed-form solution for optimal investment strategy.
result Ambiguity affects speculative motives, not hedging of interest rate risk.
The paper introduces a new short rate model with memory components.
problem Modeling short rate dynamics with past values.
method Integrates memory (delay) components into Merton or Vasiček models.
result Analytical solutions for bond prices and forward rates.
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…
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…
Paper examines pricing and hedging for cross-currency swaps referencing backward-looking rates.
problem Pricing and hedging cross-currency swaps with backward-looking rates.
method Uses interest rate and currency futures for hedging, analyzes arbitrage-free multi-curve setting.
result Explicit pricing and hedging results for CCBS with backward-looking rates.
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 propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJ…
Physics of Financehep-th
We give a brief introduction to the Gauge Theory of Arbitrage. Treating a calculation of Net Present Values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. Thi…
This article presents valuation of Treasury Bonds (T-Bonds) on Macedonian Stock Exchange (MSE) and empirical test of duration, modified duration and convexity of the T-bonds at MSE in order to determine sensitivity of bonds prices on interest rate changes. The main goal of this study is to determine how standard valuat…
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…
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…
Flow taxes and stock taxes preserve portfolio neutrality under specific conditions.
problem Analyzing the impact of different types of taxes on portfolio choice.
method Extending the neutrality result to a full system of ownership taxes, showing how each tax modifies the drift of the wealth process.
result The combined system of taxes preserves portfolio neutrality under three conditions, and the drift-shift symmetry generalizes to a drift-shift-and-rescale symmetry.
We investigate the joint description of the interest-rate term stuctures of Italy and an AAA-rated European country by mean of a --here proposed-- correlated CIR-like bivariate model where one of the state variables is interpreted as a benchmark risk-free rate and the other as a credit spread. The model is constructed …
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 …
New model for options pricing accounting for time-varying interest rates, volatility, and equity premium.
problem Inaccuracies in Black-Scholes-Merton model for real market conditions.
method Integrates stochastic variance, interest rates, and equity premium into a PDE framework.
result Derives new PDEs and approximates option prices using finite difference methods.
The paper models SOFR and EFFR dynamics, reconciling diffusive and piecewise paths.
problem Updating interest rate models for SOFR, which is becoming a key benchmark.
method Calibrates a model to SOFR and EFFR futures prices, reconciling diffusive and piecewise paths.
result The model reflects key empirical features of SOFR dynamics and reconciles diffusive and piecewise paths.
We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters. A successful joint calibration t…
We present a model of predatory traders interacting with each other in the presence of a central reserve (which dissipates their wealth through say, taxation), as well as inflation. This model is examined on a network for the purposes of correlating complexity of interactions with systemic risk. We suggest the use of s…