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A fund manager invests both the fund's assets and own private wealth in separate but potentially correlated risky assets, aiming to maximize expected utility from private wealth in the long run. If relative risk aversion and investment opportunities are constant, we find that the fund's portfolio depends only on the fund's investment opportunities, and the private portfolio only on private opportunities. This conclus…
This paper proposes an investment strategy through resource allocation into Kalshi Crypto Event Contracts in order to effectively hedge exposure to spot asset volatility. Using Bitcoin as a proof of concept, we treat corresponding Kalshi markets on the asset's future price as option contracts, and through construction of different portfolio allocations present a framework for which event contracts can be effectively …
The domain of hedge fund investments is undergoing significant transformation, influenced by the rapid expansion of data availability and the advancement of analytical technologies. This study explores the enhancement of hedge fund investment performance through the integration of machine learning techniques, the application of PolyModel feature selection, and the analysis of fund size. We address three critical ques…
We develop an optimal currency hedging strategy for fund managers who own foreign assets to choose the hedge tenors that maximize their FX carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged with FX forwards. The chosen liquidity risk metric is Cash Flow at Risk (CFaR). The strategy involves time-dispersing the total nominal hedge value into future time buc…
In volatile financial markets, balancing risk and return remains a significant challenge. Traditional approaches often focus solely on equity allocation, overlooking the strategic advantages of options trading for dynamic risk hedging. This work presents DeltaHedge, a multi-agent framework that integrates options trading with AI-driven portfolio management. By combining advanced reinforcement learning techniques with…
We investigate whether the volatility risk premium is negative by examining the statistical properties of delta-hedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility risk premium and the mean delta-hedged portfolio returns. Using a sample of S&P 500 index options, we provide empirical t…
For a trading desk, residual climate hedging valuation adjustment (HVA) is the climate cost left after its inherited hedge and any admissible overlay have been taken into account; it therefore cannot be inferred from a stand-alone stress loss. We obtain this residual by comparing paired climate-on and baseline worlds and reoptimizing the overlay for each hedge universe, which also turns hedge-instrument discovery int…
Benoit Mandelbrot's scientific legacy spans an extraordinary range of disciplines, from linguistics and fluid turbulence to cosmology and finance, suggesting the intellectual temperament of a "fox" in Isaiah Berlin's famous dichotomy of thinkers. This essay argues, however, that Mandelbrot was, at heart, a "hedgehog": a thinker unified by a single guiding principle. Across his diverse pursuits, the concept of scaling…
This paper addresses the trade-off between internalisation and externalisation in the management of stochastic trade flows. We consider agents who must absorb flows and manage risk by deciding whether to warehouse it or hedge in the market, thereby incurring transaction costs and market impact. Unlike market makers, these agents cannot skew their quotes to attract offsetting flows and deter risk-increasing ones, lead…
This paper aims to investigate the role of gold as a hedge and/or safe haven against oil price and currency market movements for medium (calm period) and large (extreme movement) fluctuations. In revisiting the role of gold, our study proposes new insights into the literature. First, our empirical design relaxes the assumption of homogeneous investors in favour of agents with different horizons. Second, we develop a …
Liquidity Providers on Automated Market Makers generate millions of USD in transaction fees daily. However, the net value of a Liquidity Position is vulnerable to price changes in the underlying assets in the pool. The dominant measure of loss in a Liquidity Position is Impermanent Loss. Impermanent Loss for Constant Function Market Makers has been widely studied. We propose a new metric to measure Liquidity Position…
We introduce a trade strategy representation theorem for performance measurement and portable alpha in high frequency trading, by embedding a robust trading algorithm that describe portfolio manager market timing behavior, in a canonical multifactor asset pricing model. First, we present a spectral test for market timing based on behavioral transformation of the hedge factors design matrix. Second, we find that the t…
Dealers make money by providing liquidity to clients but face flow uncertainty and thus price risk. They can efficiently skew their prices and wait for clients to mitigate risk (internalization), or trade with other dealers in the open market to hedge their position and reduce their inventory (externalization). Of course, the better control associated with externalization comes with transaction costs and market impac…
We consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold. Liquidation occurs in a disorderly manner and negatively impacts the market price of the asset. We consider the perspective of small investors whose trades do not induce market impact and who possess different levels of information about the liqui…
In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalised to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options with weights that are directly related to trading intuition. Additionally, we derive first and second order hedges for volatility swaps using only variance swaps. As dynamically tra…
Automated Market Makers based on concentrated liquidity, such as Uniswap v3, significantly improve capital efficiency but expose Liquidity Providers (LPs) to adverse selection costs, formalized as Loss-Versus-Rebalancing (LVR). While theoretical literature quantifies these costs, the interplay between realistic blockchain microstructure and endogenous pricing mechanisms remains under-explored. This paper develops a g…
A currency with stable purchasing power can always provide a psychological haven for people around the world. However, since the collapse of the Bretton Woods system, issuing more cheap currencies has become a common trend in the international community, and the legalization and over issuance of stablecoins will strengthen this trend. In this context, our study focused on a parallel monetary system based on a redeema…
We study cash-flow forecasting for derivatives used in liquidity management and clarify its relation to risk-neutral valuation and replication. While it is well known that expectations under different measures (e.g., $\mathbb{P}$ vs. $\mathbb{Q}$) can yield different undiscounted cash-flows, further inconsistencies arise when payment times are stochastic. We show that using discounting sensitivities (funding-curve he…
Systemic Risk Indicator — Aggregate capital shortfall under stress — connects banking to macro hedges.
Gold price reflects demand for a non-yielding reserve asset and is often used as a signal for real yields, macro uncertainty, and confidence in fiat systems.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
Crypto Market Maker Inventory — Dealer inventory and hedge needs shaping crypto microstructure.
Trade the VIX curve as a first-class market — trend on VIX, carry on contango, and a respect for inversion — not just an equity hedge overlay.
A collar is long stock, long a put, and short a call — a banded payoff, often structured to be zero-debit.
Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.
Gamma is the sensitivity of delta to the underlying — how fast the hedge ratio moves, and who is chasing whom.
LEAPS Options — Long-dated equity options used for leveraged directional or hedge overlays.
A protective put is long the asset and long a put — a floor under the position for a premium that bleeds.
A put option is the right to sell the underlying at a strike — convex downside, or a hedge that costs carry.
Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.
Volatility of Volatility — Uncertainty about future volatility, critical for tail hedges and vol-of-vol products.
Catching a falling knife is buying a crashing asset because it ‘looks cheap,’ without a catalyst or a hedge — you can catch it, but you usually bleed.
Cheap and rich are relative-value words: cheap means wide or low versus a model, a history, or a hedge; rich means tight or expensive on that same yardstick — not ‘I like the story.’
Wrong-way risk is when exposure rises at the same time the counterparty’s credit worsens — the hedge or the receivable fails exactly when you need it.
Russia’s August 1998 default and devaluation blew up leveraged relative-value books, culminating in the LTCM rescue — a reminder that ‘hedged’ can mean ‘short liquidity in every state.’
Key Rate Duration — Bucketed rate sensitivity across curve points for relative-value and hedge construction.
Macaulay duration is the present-value-weighted average time to receive a bond’s cash flows — duration in years, before the modified-duration hedge ratio.
Modified duration is the percent price change for a 1% (100bp) parallel yield move — the first-order hedge ratio from the yield function.
TIPS are US Treasuries whose principal adjusts with CPI — a real-rate instrument, not a magic inflation hedge for every horizon.
Beta is the regression slope of an asset’s return on a factor (usually the market) — a hedge ratio, not a destiny.
A hedge fund is a lightly constrained private pool that can short, lever, and charge performance fees — a legal wrapper, not a strategy.
Long the convertible and short the delta in the stock — harvest cheap implied vol / credit, with funding and squeeze risk.
Beta is the regression slope of an asset’s return on a factor (usually the market) — a hedge ratio, not a destiny.
Catching a falling knife is buying a crashing asset because it ‘looks cheap,’ without a catalyst or a hedge — you can catch it, but you usually bleed.
Cheap and rich are relative-value words: cheap means wide or low versus a model, a history, or a hedge; rich means tight or expensive on that same yardstick — not ‘I like the story.’
Crypto Market Maker Inventory — Dealer inventory and hedge needs shaping crypto microstructure.
Delta is the first derivative of option value to the underlying — the hedge ratio and a moneyness label.
Gamma is the sensitivity of delta to the underlying — how fast the hedge ratio moves, and who is chasing whom.
A hedge fund is a lightly constrained private pool that can short, lever, and charge performance fees — a legal wrapper, not a strategy.
Key Rate Duration — Bucketed rate sensitivity across curve points for relative-value and hedge construction.
LEAPS Options — Long-dated equity options used for leveraged directional or hedge overlays.
Macaulay duration is the present-value-weighted average time to receive a bond’s cash flows — duration in years, before the modified-duration hedge ratio.
Modified duration is the percent price change for a 1% (100bp) parallel yield move — the first-order hedge ratio from the yield function.
A put option is the right to sell the underlying at a strike — convex downside, or a hedge that costs carry.
Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.
Russia’s August 1998 default and devaluation blew up leveraged relative-value books, culminating in the LTCM rescue — a reminder that ‘hedged’ can mean ‘short liquidity in every state.’
Systemic Risk Indicator — Aggregate capital shortfall under stress — connects banking to macro hedges.
TIPS are US Treasuries whose principal adjusts with CPI — a real-rate instrument, not a magic inflation hedge for every horizon.
Trade the VIX curve as a first-class market — trend on VIX, carry on contango, and a respect for inversion — not just an equity hedge overlay.
Volatility of Volatility — Uncertainty about future volatility, critical for tail hedges and vol-of-vol products.
Wrong-way risk is when exposure rises at the same time the counterparty’s credit worsens — the hedge or the receivable fails exactly when you need it.