- Arbitraging on Decentralized Exchanges (with Xuedong He and Yutian Zhou).
Working Paper. [Abstract]
Decentralized exchanges (DEXs) are alternative venues to centralized exchanges to trade
cryptocurrencies (CEXs) and have become increasingly popular. An arbitrage opportunity arises when
the exchange rate of two cryptocurrencies in a DEX differs from that in a CEX. Arbitrageurs can then
trade on the DEX and CEX to make a profit. Trading on the DEX incurs a gas fee, which determines the
priority of the trade being executed. We study a gas-fee competition game between two arbitrageurs
who maximize their expected profit from trading. We derive the unique symmetric mixed Nash
equilibrium and find that (i) the arbitrageurs may choose not to trade when the arbitrage
opportunity is small; (ii) the probability of the arbitrageurs choosing a higher gas fee is lower;
(iii) the arbitrageurs pay a higher gas fee and trade more when the arbitrage opportunity becomes
larger and when liquidity becomes higher. The above findings are consistent with our empirical
study.
- Portfolio Selection with Time-Varying Taxation (with Xianhao Zhu).
Working Paper. [Abstract]
The capital gains tax rate has fluctuated significantly over time, leading to substantial changes in
investors' optimal strategies, as documented by the empirical studies. This paper proposes a novel
continuous-time portfolio selection framework with a time-varying capital gains tax rate. Featuring
differential tax rate announcement time and implementation time, our framework is able to capture
the investors' anticipation over a potential future tax rate change before its announcement, as well
as their reaction to an announced tax change yet to be implemented. The optimal investment strategy
embodies the interaction between the time-varying tax rate and the lock-in and diversification
effects proposed in the existing literature. Furthermore, our findings provide theoretical support
for the permanent and transitory effects of tax rate changes documented in the empirical studies.
The strength of the transitory effect depends on the size of the tax rate change, and the tax rate
uncertainty mostly affects the transitory effect and has a negligible impact on the permanent
effect. Moreover, the permanent effect vanishes under a zero interest rate while the transitory
effect persists.
- Periodic Evaluation with Non-Concave Utility (with Cong Qin and Harry Zheng).
submitted. [Abstract|SSRN]
A fund manager's performance is often evaluated annually and compared with a benchmark, such as a
market index. In addition, the manager may be subject to trading constraints, such as limited use of
leverage, no short-selling, and a forced liquidation clause. We formulate this as a periodic
evaluation problem with a non-concave utility, a stochastic reference point, and trading
constraints. The value function is characterized as the unique solution to a Hamilton-Jacobi-Bellman
equation with periodic terminal and boundary conditions, which must be imposed carefully due to
possible discontinuities at the terminal time and/or on the liquidation boundary. We find that, at
the evaluation time, future investment opportunities induce a discontinuity in the value function on
the liquidation boundary, leading to a substantial change in local risk-aversion. More importantly,
this local concavity/convexity weakens and shifts inward from the liquidation boundary to the
interior region as the evaluation horizon increases. As a result, the joint effect of periodic
evaluation and forced liquidation can generate highly nonlinear investment strategies, which is
helpful in understanding the complexity of trading strategies in the loss region.
- Pricing Model for Data Assets in Investment-Consumption Framework with Ambiguity (with Xiaoshan Chen
and Zhou Yang).
submitted. [Abstract|SSRN|arXiv]
Data assets are data commodities that have been processed, produced, priced, and traded based on
actual demand. Reasonable pricing mechanism for data assets is essential for developing the data
market and realizing their value. Most existing literature approaches data asset pricing from the
seller's perspective, focusing on data properties and collection costs, however, research from the
buyer's perspective remains scarce. This gap stems from the nature of data assets: their value lies
not in direct revenue generation but in providing informational advantages that enable enhanced
decision-making and excess returns. This paper addresses this gap by developing a pricing model
based on the informational value of data assets from the buyer's perspective. We determine data
asset prices through an implicit function derived from the value functions in two robust
investment-consumption problems under ambiguity markets via indifference pricing principle. By the
existing research results, we simplify the value function, using mathematical analysis and
differential equation theory, we derive general expressions for data assets price and explore their
properties under various conditions. Furthermore, we derive the explicit pricing formulas for
specific scenarios and provide numerical illustration to describe how to use our pricing model.
- Arbitrage in Perpetual Contracts (with Min Dai and Linfeng Li).
submitted. [Abstract|SSRN]
Perpetual contracts, designed to track the underlying price through a funding swap mechanism, have
gained significant popularity in cryptocurrency markets. However, observed price discrepancies
between perpetual contracts and the underlying asset cannot be explained solely by transaction fees.
By examining the impact of the clamping function inherent in the funding swap mechanism -- an
overlooked aspect in existing literature -- we derive model-free no-arbitrage bounds for perpetual
contracts. Our findings reveal that these bounds persist as intervals even without transaction fees,
due to the clamping function. Empirical analysis using two years of Binance data supports the
validity of our proposed bounds.
- Optimal Tax-Timing with Transaction Costs (with Min Dai, Yaoting Lei, and Hong Liu).
submitted. [Abstract|SSRN]
We develop a dynamic portfolio model incorporating capital gains tax (CGT), transaction costs, and
year-end taxation. We find that even tiny transaction costs can lead to significant deferral of
large losses and transaction costs affect loss deferrals much more than gain deferrals. Our model
can thus help explain the puzzle that even when investors face equal long-term/short-term CGT rates,
they may still defer realizing large capital losses for an extended period of time, displaying the
disposition effect. In addition, we find misestimating transaction costs is costly. We also provide
several unique, empirically testable predictions and shed light on recently proposed tax policy
changes.
- Optimal Design of Automated Market Makers on Decentralized Exchanges (with Xuedong He and Yutian Zhou).
submitted. [Abstract|SSRN|arXiv]
Automated market makers are a popular mechanism used on decentralized exchange, through which users
trade assets with each other directly and automatically through a liquidity pool and a fixed pricing
function. The liquidity provider contributes to the liquidity pool by supplying assets to the pool,
and in return, they earn trading fees from investors who trade in the pool. We propose a model of
optimal liquidity provision in which a risk-averse liquidity provider decides the amount of wealth
she would invest in the decentralized market to provide liquidity in a two-asset pool, trade in a
centralized market, and consume in multiple periods. We derive the liquidity provider's optimal
strategy and the optimal design of the automated market maker that maximizes the liquidity
provider's utility. We find that the optimal unit trading fee increases in the volatility of the
fundamental exchange rate of the two assets. We also find that the optimal pricing function is
chosen to make the asset allocation in the liquidity pool efficient for the liquidity provider.
- Calibration of Local Volatility Models under the Implied Volatility Criterion (with Xinfu Chen, Min Dai, and Zhou Yang).
submitted. [Abstract|SSRN]
We study non-parametric calibration of local volatility models, which is formulated as an inverse
problem of partial differential equations with Tikhonov regularization. In contrast to the existing
literature minimizing the distance between theoretical and market prices of options as a calibration
criterion, we instead minimize the distance between theoretical and market implied volatilities,
complying with market practices. We prove that our calibration criterion naturally leads to the
well-posedness of the calibration problem. In particular, comparing to Jiang and Tao (2001), we
obtain a global uniqueness result, where no additional weight functions are required. Numerical
results reveal that our method achieves a better trade-off between minimizing calibration errors and
reducing overfitting.
- Patience is a Virtue: Optimal Investment in the Presence of Market Resilience (with Nan Chen, Min Dai, and Qiheng Ding).
submitted. [Abstract|SSRN]
This paper investigates an optimal investment problem in an illiquid market, modeling explicitly the
effects of three key features of market microstructure --- market tightness, market depth, and
finite market resilience --- on the investor's decision. By employing a Bachelier process to model
the dynamic of the fundamental value of the asset and assuming CARA-type utility for the investor,
we manage to obtain the investor's optimal dynamic trading strategy in closed form by solving the
resulting high-dimensional singular control problem. Furthermore, we extend the model to incorporate
return-predicting signals and utilize an asymptotic expansion approach to derive approximate optimal
trading strategies. The theoretical and numerical results emphasize the vital role of patience.
Specifically, rather than dispersing small trades continuously over time as advocated by the
existing literature, our findings suggest that investors should strategically time their trading
activities to align with the aim portfolio in the presence of market resilience. To quantify this
timing decision, we introduce a patience index that enables investors to strike a balance among
various competing goals, including achieving currently optimal risk exposure, incorporating signals
about future predictions, and minimizing trading costs, by leveraging market resilience.
- Non-Concave Utility Maximization with Transaction Costs (with Shuaijie Qian).
submitted. [Abstract|SSRN|arXiv]
This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and
proportional transaction costs. The commonly used concavification principle for terminal value is no
longer valid here, and we establish a proper theoretical characterization of this problem. We first
give the asymptotic terminal behavior of the value function, which implies any transaction close to
maturity only provides a marginal contribution to the utility. After that, the theoretical
foundation is established in terms of a novel definition of the viscosity solution incorporating our
asymptotic terminal condition. Via numerical analyses, we find that the introduction of transaction
costs into non-concave utility maximization problems can prevent the portfolio from unbounded
leverage and make a large short position in stock optimal despite a positive risk premium and
symmetric transaction costs.
- Designing Stablecoins (with Yizhou Cao,
Min Dai, Steven Kou and Lewei Li).
Mathematical Finance, 35(1):263-294, 2025. [Abstract|SSRN|Article]
Stable coins, which are cryptocurrencies pegged to other stable financial assets such as U.S. dollar,
are desirable for payments within blockchain networks, whereby being often called the “Holy Grail of
cryptocurrency.” However, existing cryptocurrencies are too volatile for these purposes. By using
the option pricing theory, we design several dual-class structures that offer a fixed income crypto
asset, a stable coin pegged to a traditional currency, and leveraged investment instruments. To
understand the impact of the proposed coins on the speculative and non-speculative demands of
cryptocurrencies, we study equilibrium with and without the stable coins. Our investigation of the
values of stable coins in presence of jump risk and black-swan type events shows the robustness of
the design.
- An Equilibrium Model for the Cross Section of Liquidity Premia (with Johannes Muhle-Karbe and Xiaofei Shi).
Mathematics of Operations Research, 48(3):1423-1453, 2023. [Abstract|SSRN|arXiv|Article]
We study a risk-sharing economy where an arbitrary number of heterogenous agents trades an arbitrary
number of risky assets subject to quadratic transaction costs. For linear state dynamics, the
forward-backward stochastic differential equations characterizing equilibrium asset prices and
trading strategies in this context reduce to a system of matrix-valued Riccati equations. We prove
the existence of a unique global solution and provide explicit asymptotic expansions that allow us
to approximate the corresponding equilibrium for small transaction costs. These tractable
approximation formulas make it feasible to calibrate the model to time series of prices and trading
volume, and to study the cross-section of liquidity premia earned by assets with higher and lower
trading costs. This is illustrated by an empirical case study.
- Leveraged Exchange-Traded Funds with Market Closure and Frictions (with Min Dai, Steven Kou and H. Mete Soner).
Management Science, 69(4):2517-2535, 2023. [Abstract|SSRN|Article]
Although leveraged ETFs are popular products for retail investors, how to hedge them poses a great
challenge to financial institutions. We develop an optimal rebalancing (hedging) model for leveraged
ETFs in a comprehensive setting, including overnight market closure and market frictions. The model
allows for an analytical optimal rebalancing strategy.
The result extends the principle of "aiming in front of target" introduced by
Gârleanu
and Pedersen (2013) from a constant weight between current and future positions to a
time-varying weight, because the rebalancing performance is monitored only at discrete time points
but the rebalancing takes place continuously. Empirical findings and implications for the weekend
effect and the intraday trading volume are also presented.
- A Stochastic Representation for Nonlocal Parabolic PDEs with Applications (with Min Dai and Steven Kou).
Mathematics of Operations Research, 47(3):1707-1730, 2022 [Abstract|SSRN|Article]
We establish a stochastic representation for a class of nonlocal parabolic terminal-boundary value
problems, whose terminal and boundary conditions depend on the solution in the interior domain; in
particular, the solution is represented as the expectation of functionals of a diffusion process
with random jumps from boundaries. We discuss three applications of the representation, the first
one on the pricing of dual-purpose funds, the second one on the connection to regenerative
processes, and the third one on modeling the entropy on a one-dimensional non-rigid body.
- Inventory Management for High-Frequency Trading with Imperfect Competition (with Sebastian Herrmann, Johannes Muhle-Karbe and Dapeng Shang).
SIAM Journal on Financial Mathematics, 11(1):1-26, 2020. [Abstract|SSRN|arXiv|Article]
We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit
information about future price changes. For discrete trading rounds, the HFTs' optimal trading
strategies and their equilibrium price impact are described by a system of nonlinear equations;
explicit solutions obtain around the continuous-time limit. Unlike in the risk-neutral case, the
optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large.
In contrast, the HFTs' risk-adjusted profits and the equilibrium price impact converge to their
risk-neutral counterparts. Compared to a social-planner solution for cooperative HFTs, Nash
competition leads to excess trading, so that marginal transaction taxes in fact decrease market
liquidity.
- Optimal Tax-timing with Asymmetric Long-term/short-term Capital Gains Tax (with Min Dai, Hong Liu and Yifei Zhong).
The Review of Financial Studies, 28.9:2687-2721, 2015. [Abstract|SSRN|Article]
We develop an optimal tax-timing model that takes into account asymmetric long-term and short-term
tax rates for positive capital gains and limited tax deductibility of capital losses. In contrast to
the existing literature, this model can help explain why many investors not only defer short-term
capital losses to long term but also defer large long-term capital gains and losses. Because the
benefit of tax deductibility of capital losses increases with the short-term tax rates, effective
tax rates can decrease as short-term capital gains tax rates increase.
