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Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider the subgame perfect strategies. The later are characterized through an extended Hamilton Jacobi Bellman (HJB) equation. A fixed point iteration is employed to solve the extended HJ…
This paper studies a singular dividend control problem for a firm with heterogeneous shareholders whose discount rates follow a given distribution. The central planner aggregates expected discounted payoffs using an ambiguity aggregation function $phi$, which captures shareholder heterogeneity and ambiguity attitudes but also leads to time inconsistency. To address this issue, we seek a time-homogeneous equilibrium d…
We introduce an infinite-horizon, continuous-time portfolio selection problem faced by an agent with periodic S-shaped preference and present bias. The inclusion of a quasi-hyperbolic discount function leads to time-inconsistency and we characterize the optimal portfolio for a pre-committing, naive and sophisticated agent respectively. In the more theoretically challenging problem with a sophisticated agent, the time…
We illustrate a problem in the self-financing condition used in the papers "Funding beyond discounting: collateral agreements and derivatives pricing" (Risk Magazine, February 2010) and "Partial Differential Equation Representations of Derivatives with Counterparty Risk and Funding Costs" (The Journal of Credit Risk, 2011). These papers state an erroneous self-financing condition. In the first paper, this is equivale…
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 market, for derivatives netting sets are perpetual while repo tenors are typically in months. This arti…
There is a persistent lack of funding, especially for SMEs, that cyclically worsens. The factoring and invoice discounting market appears to address delays in paying commercial invoices: sellers bring still-to-be-paid invoices to financial organizations, intermediaries, typically banks that provide an advance payment. This article contains research on novel decentralized approaches to said lending services without in…
We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations…
This paper develops a unified framework that links firm-level predictive signals, cross-asset spillovers, and the stochastic discount factor (SDF). Signals and spillovers are jointly estimated by maximizing the Sharpe ratio, yielding an interpretable SDF that both ranks characteristic relevance and uncovers the direction of predictive influence across assets. Out-of-sample, the SDF consistently outperforms self-predi…
Loss Given Default (LGD) is a key risk parameter in determining a bank's regulatory capital. During LGD-estimation, realised recovery cash flows are to be discounted at an appropriate rate. Regulatory guidance mandates that this rate should allow for the time value of money, as well as include a risk premium that reflects the "undiversifiable risk" within these recoveries. Having extensively reviewed earlier methods …
We present a thorough empirical study on real interest rates by also including risk aversion through the introduction of the market price of risk. With the view of complex systems science and its multidisciplinary approach, we use the theory of bond pricing to study the long term discount rate. Century-long historical records of 3 month bonds, 10 year bonds, and inflation allow us to estimate real interest rates for …
The paper intends to perform a relevant study on the closed-end fund puzzle in the perspective of an emerging market. Quarterly data of 36 closed-end mutual funds traded in Dhaka Stock Exchange are collected over the sample period of 2016 to 2019. Dependent and independent variables are mapped down by exploring previous researches. Weight of top 10 investments, fund size, fund age, fund maturity, turnover and dividen…
The traditional way of building a yield curve is to choose an interpolation on discount factors, implied by the market tradable instruments. Since then, constructions based on specific interpolations of the forward rates have become the trend. We show here that some popular interpolation methods on the forward rates correspond exactly to classical interpolation methods on discount factors. This paper also aims at cla…
In this paper we extend the existing literature on xVA along three directions. First, we enhance current BSDE-based xVA frameworks to include initial margin in presence of defaults. Next, we solve the consistency problem that arises when the front-office desk of the bank uses trade-specific discount curves (CSA discounting) which differ from the discount rate adopted by the xVA desk. Finally, we clarify the impact of…
We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives valuation and risk analysis has moved from exotic derivatives managed on simple single asset classes to simple derivatives embedding the new or previously neglected type…
This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switch according to a finite state Markov chain. The change in the discount rate leads to time inconsistencies of the investor's…
We review different approaches for measuring the impact of liquidity on CDS prices. We start with reduced form models incorporating liquidity as an additional discount rate. We review Chen, Fabozzi and Sverdlove (2008) and Buhler and Trapp (2006, 2008), adopting different assumptions on how liquidity rates enter the CDS premium rate formula, about the dynamics of liquidity rate processes and about the credit-liquidit…
This paper investigates an infinite horizon, discounted, consumption-portfolio problem in a market with one bond, one liquid risky asset, and one illiquid risky asset with proportional transaction costs. We consider an agent with liquidity preference, modeled by a Cobb-Douglas utility function that includes the liquid wealth. We analyze the properties of the value function and divide the solvency region into three re…
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review t…
Reinforcement learning trains a policy to maximize expected return by interacting with an environment: states, actions, rewards, and (usually) a discount factor.
Put-call parity is the no-arbitrage link C − P = F − K (discounted) — a European call and put with the same K and T are one instrument plus cash.
Equity Risk Premium measures the excess return investors expect from equities over risk-free assets and is a core framework for evaluating relative equity valuation.
A market bubble is a price path driven more by narrative, leverage, and new buyers than by discounted cash flow — obvious after, argued during.
Distressed Debt Ratio — Share of debt trading at deep discounts — early warning for credit cycle turns.
Yield to maturity is the constant discount rate that sets the bond’s dirty price equal to its remaining cash flows if held to maturity and coupons are reinvested at that same rate.
A zero-coupon bond pays no coupon and one cash flow at maturity — duration equals maturity, and the whole return is pull-to-par plus yield change.
Discount Window borrowing measures bank use of Federal Reserve emergency liquidity and serves as a signal of funding pressure and banking-sector strain.
A risk-neutral (equivalent martingale) measure is a probability reweighting that makes discounted asset prices martingales — prices are then discounted expected payoffs under that measure, not under the real-world P.
US 10-Year Real Yield measures the inflation-adjusted yield on 10-year Treasuries and is a key benchmark for discount rates, financial conditions, and macro asset pricing.
Buy closed-end funds at a wide discount to NAV and fade rich premiums — a stubborn retail-structure anomaly.
Buy closed-end funds at a wide discount to NAV and fade rich premiums — a stubborn retail-structure anomaly.
Discount Window borrowing measures bank use of Federal Reserve emergency liquidity and serves as a signal of funding pressure and banking-sector strain.
Distressed Debt Ratio — Share of debt trading at deep discounts — early warning for credit cycle turns.
A market bubble is a price path driven more by narrative, leverage, and new buyers than by discounted cash flow — obvious after, argued during.
Put-call parity is the no-arbitrage link C − P = F − K (discounted) — a European call and put with the same K and T are one instrument plus cash.
Reinforcement learning trains a policy to maximize expected return by interacting with an environment: states, actions, rewards, and (usually) a discount factor.
A risk-neutral (equivalent martingale) measure is a probability reweighting that makes discounted asset prices martingales — prices are then discounted expected payoffs under that measure, not under the real-world P.
US 10-Year Real Yield measures the inflation-adjusted yield on 10-year Treasuries and is a key benchmark for discount rates, financial conditions, and macro asset pricing.
Yield to maturity is the constant discount rate that sets the bond’s dirty price equal to its remaining cash flows if held to maturity and coupons are reinvested at that same rate.