Hedge Fund Index Rules and Construction
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Level Design Compare: FPS vs TPS Games
“FPS and TPS share common ground as shooting games, focusing on aiming and target selection as core gameplay. These form the basis for player engagement and strategy, setting the stage for further exploration of their differences.”
ON MERTON’S OPTIMAL PORTFOLIO PROBLEM UNDER SPORADIC BANKRUPTCY
“Consider a stock market following a geometric Brownian motion and a riskless asset continuously compounded at a constant rate. Assuming the stock can go bankrupt, i.e., lose all of its value, at some exogenous random time (independent of the stock price) modeled as the first arrival time of a homogeneous Poisson process, we study the Merton’s optimal portfolio problem consisting of maximizing the expected logarithmic utility of the total wealth at a preselected finite maturity time. First, we present a heuristic derivation based on a new type of Hamilton-Jacobi-Bellman equation. Then, we formally reduce the problem to a classical controlled Markovian diffusion with a new type of terminal and running costs. A new version of Merton’s ratio is rigorously derived using Bellman’s dynamic programming principle and validated with a suitable type of verification theorem. A real-world example comparing the latter ratio to the classical Merton’s ratio is given.”
Hedge Fund Index Rules and Construction
“A Hedge Fund Index is very useful for tracking the performance of hedge fund investments, especially the timing of fund redemption. This paper presents a methodology for constructing a hedge fund index that is more like a quantitative fund of fund, rather than a weighted sum of a number of early replicable market indices, which are re-balanced periodically. The constructed index allows hedge funds to directly hedge their exposures to index-linked products. That is important given that hedge funds are an asset class with reduced transparency, and the returns are traditionally difficult to replicate using liquid instruments.”
Crypto Inverse-Power Options and Fractional Stochastic Volatility
“Recent empirical evidence has highlighted the crucial role of jumps in both price and volatility within the cryptocurrency market. In this paper, we introduce an analytical model framework featuring fractional stochastic volatility, accommodating price–volatility co-jumps and volatility short-term dependency concurrently. We particularly focus on inverse options, including the emerging Quanto inverse options and their power-type generalizations, aimed at mitigating cryptocurrency exchange rate risk and adjusting inherent risk exposure. Characteristic function-based pricing–hedging formulas are derived for these inverse options. The general model framework is then applied to asymmetric Laplace jump-diffusions and Gaussian-mixed tempered stable-type processes, employing three types of fractional kernels, for an extensive empirical analysis involving model calibration on two independent Bitcoin options data sets, during and after the COVID19 pandemic. Key insights from our theoretical analysis and empirical findings include: (1) the superior performance of fractional stochastic-volatility models compared to various benchmark models, including those incorporating jumps and stochastic volatility, (2) the practical necessity of jumps in both price and volatility, along with their co-jumps and rough volatility, in the cryptocurrency market, (3) stability of calibrated parameter values in line with stylized facts, and (4) the suggestion that a piecewise kernel offers much higher computational efficiency relative to the commonly used Riemann–Liouville kernel in constructing fractional models, yet maintaining the same accuracy level, thanks to its potential for obtaining explicit model characteristic functions.”
Price and Payoff Autocorrelations in a Multi-period Consumption-Based Asset Pricing Model
“This paper highlights the hidden dependence of the basic pricing equation of a multi-period consumption-based asset pricing model on price and payoff autocorrelations. We obtain the approximations of the basic pricing equation that describe the mean price “to-day,” mean payoff “next-day,” price and payoff volatilities, and price and payoff autocorrelations. The deep conjunction of the consumption-based model with other versions of asset pricing, such as ICAPM, APM, etc. (Cochrane, 2001), emphasizes that our results are valid for other pricing models.”